tag:blogger.com,1999:blog-69913863709423225292024-03-19T00:29:59.888-04:00Perry Sadorsky's blogAn analysis of current economic and financial eventsPerry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.comBlogger175125tag:blogger.com,1999:blog-6991386370942322529.post-41389640677940745332016-04-01T15:52:00.002-04:002016-04-01T15:52:25.285-04:00Predicting US Recessions Using the Yield Curve<!--[if gte mso 9]><xml>
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In last week’s Economic Forecasting and Analysis class, we
talked about how the yield curve could be used to predict economic recessions.
There is a deep literature on this topic going back to the late 1980s. The
basic idea is that the market for government bonds is very sensitive to monetary
policy. Normally, the yield curve is upward sloping, the difference between
yields of long bonds (say 10 years) and short bonds (3 month T bills) is
positive to compensate investors for the additional risk in holding bonds for
longer periods of<span style="mso-spacerun: yes;"> </span>time. In recessions,
central banks cut benchmark interest rates in order to stimulate the economy. A
reduction in interest rates lowers the yield on new issues of government bonds.
Consequently, if the bond market expects a recession and a cut in central bank
rates, bond investors will start selling short term bonds and buy long term
bonds to lock in the higher yields. This pushes the price of long bonds up and
reduces the price of short bonds. Since bond prices and yields are inversely
related, short yields rise and long yields fall. The yield curve inverts when
the yield spread becomes negative.</div>
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<br /></div>
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The Federal Reserve Bank of New York has been actively studying
this topic for a long time, and there is lots of useful information posted on
their <a href="https://www.newyorkfed.org/research/capital_markets/ycfaq.html">website</a>. The existing literature shows that the yield spread is a good
predictor of recessions one year into the future. <span style="mso-spacerun: yes;"> </span>The New York Fed posts data on the NBER dating of
US recessions and the yield spread and uses this data to estimate the
probability of a US recession using a probit model. The dependent variable is a
binary variable equal to one if the economy is currently in a recession and zero otherwise.
The independent variable is a 12 month lag of the yield spread. The New York
Fed posts the data, model results, and recession probability chart but this is
still a worthy exercise to work through. For estimation in R, I have loaded the data into a csv file with the spread variable lagged 12 months.</div>
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<br /></div>
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Here is the probit regression output. </div>
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<br /></div>
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="background-color: white; border: medium none; color: black; font-family: "Lucida Console"; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; margin: 0px; outline: medium none; text-indent: 0px; text-transform: none; white-space: pre-wrap ! important; word-break: break-all; word-spacing: 0px;" tabindex="0"><span style="font-size: small;">Deviance Residuals:
Min 1Q Median 3Q Max
-2.4163 -0.5152 -0.2630 -0.1147 2.8313
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.54086 0.08047 -6.721 1.8e-11 ***
Spread -0.65560 0.06702 -9.782 < 2e-16 ***
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 540.93 on 673 degrees of freedom
Residual deviance: 398.29 on 672 degrees of freedom
AIC: 402.29
Number of Fisher Scoring iterations: 6
</span></pre>
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<br /></div>
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The estimated
parameter values are close but not identical to the ones from the New York Fed (intercept = -0.5330, slope = -0.6330.
Different estimation procedures for probit may be the result of the minor differences
in results.</div>
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<br /></div>
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Here is the probability of US recession chart. </div>
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<img alt="" height="357" 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" width="400" /> </div>
<div class="MsoNormal">
Probabilities over 40% seem to be accurate predictors of future recessions.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The probit estimates can be used to predict the probability
of a US recession. The following table shows the probabilities for the next 12
months. The probability of a US recession 12 months from now is currently very
low at 6.6%.</div>
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<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 18pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> <span style="font-size: small;"> recession prob 2016/2017
March 0.03154117 3
April 0.03596135 4
May 0.02441563 5
June 0.01899524 6
July 0.02056696 7
Aug 0.02757996 8
Sept 0.02556458 9
Oct 0.02972609 10
Nov 0.02595748 11
Dec 0.03154117 12
Jan 0.04087655 1
Feb 0.06621488 2</span></pre>
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The R script is posted below.</div>
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#########################################################<br /># Economic forecasting and analysis<br /># April 2016<br /># Perry Sadorsky<br /># Predicting US Recessions Using the Yield Curve<br />##########################################################<br /><br /><br /># model and data from:<br /># https://www.newyorkfed.org/research/capital_markets/ycfaq.html<br /><br /><br />Book1 <- read.csv("C:/recessions/Book1.csv")<br />View(Book1)<br /><br /><br />mydata = ts(Book1, start=1960, freq =12)<br /><br />myprobit <- glm(NBER_Rec ~ Spread, family=binomial(link="probit"), data=mydata)<br />summary(myprobit)<br /><br />prob_in = predict(myprobit,<br /> type = "response")<br /><br />plot(prob_in)<br /><br />df1 = cbind(mydata[,"Spread"], prob_in)<br />plot(df1[,2], main="Probability of US recession", ylab="", xlab="")<br /><br /><br />newdata = data.frame(Spread = c(2.01,<br /> 1.92,<br /> 2.18,<br /> 2.34,<br /> 2.29,<br /> 2.10,<br /> 2.15,<br /> 2.05,<br /> 2.14,<br /> 2.01,<br /> 1.83,<br /> 1.47<br /> <br />))<br /><br /><br /><br />prob_out = predict(myprobit, newdata,<br /> type = "response")<br /><br />prob_out<br /><br />prob_out_t = cbind(prob_out,c(seq(from = 3,to = 12, by=1),1,2))<br />colnames(prob_out_t)=c("recession prob", "2016/2017")<br /><br />prob_out_t <br />rownames(prob_out_t) = c("March", "April","May", "June", "July","Aug", "Sept","Oct", "Nov", "Dec","Jan", "Feb" )<br />prob_out_t<br /><br /> </div>
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Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-36117333254153503732015-12-08T15:53:00.000-05:002015-12-08T16:59:43.931-05:00Oil Prices and the Canadian Dollar: December 2015This has been a difficult year for the Canadian dollar. Ever since oil prices started falling in mid 2014, the Canadian dollar has traded lower. Currently, in this low interest rate environment, oil prices seem to be the main driver of the Canadian dollar. From an international investment perspective, Canada is seen as consisting of safe banks and companies specializing in extracting natural resources. As a result, our currency and stock market both tend to follow commodity prices. Right now, commodity prices are depressed (especially oil) and this has taken the Canadian dollar down to lows not seen for over ten years.<br />
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Here are some plots of oil prices ($US per barrel, WTI) and how many US dollars one Canadian dollar buys. The monthly data are sourced from FRED. Notice the close correlation between the two data sets over the last half of the sample period.<br />
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<img alt="" height="325" src="data:image/png;base64,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" width="400" /><br />
<br />
As a starting point, I estimate a linear relationship between the two series.<br />
<img alt="" height="325" 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s+lkH07WUBhEFBiOLWgKuymgfi7Ey5ZOFl+6/G+GeV6PckSAkoEZxeUrjoCXTKaDM0UclDBw02vNyegRHCCwcRVa/jX2Iuq+IDCzQkoEZyrMHG9Ie3yn/WX33eifMIuBJQIzjGYuFJAufA4OkkJT+87OeJbPFftW54SUIZh+P58fyt9fO22AScYlK4xCPXb8qeqb1BAYeNK4ZUtbh9Qvj/f394/v0f/+z+ZfH3sllKcXVDVdRm/35YvcWJKEFD4cfOA8jeeDMMwDF8fv498fewTUZxdcCXXjiY/BBROd/OAUkkgfzLLTgnF2QXXcIdo8iM4Jbx0sws3cfOAUq+gPDLJeMZnCycYXMDdTuSwlHDWzS4kd/OA8hNBRhGlqJ+Y4gFuO1K6JZYT3T2gDMO/HPK//dPJ4HyDU20ZZW8bTcIIKMwRUCI43+AsW+YpnLkBfjp5HCJ1Oz8ElAjONzjF6k/nCieR3BJLlYDS4iZZ6Fp5x+XTk1E0CaaCwhwBZTdvTWe3Du6oHPAaJ6NT9RTuQWGOgBLB+QYNh+b4Mp1UN+QkPYuAwhwBJYLzDeYcff9BWcicbEWl83TuQaFKQBnm/ljgjn8u0CkHVQGfnhubKHOJU/UsMiKluweUn2wy+WWy/3x9zD71ImcdVMWU96sRZG66x9kKSdw8oFR+1f0LTy/mkgdVYflg/AG9Md1zXAO2UF3gnm4eUJ79MUB/LBAONg4NR58p5SbyBxQzUNzWzQOKCgqcb1LeOG4Tc09Vf84gf36C49w8oPy7B6VeJHEPChzviDF4Uo95usK0cygCCnd294AyDMPkrwX+2iWbDMNwm2tK2qs8me0+Bk8qIl0fkAIKdyagRLjDNSVznZzjbE+l+47B46rJoXNGYZxZ3JaAEuHal5XqEHXtXebHXmPnjmNwGUrWrTBVOTBVYyCMgBLhwleW8Xjgo96t7F752GUM3iUrO5IhAwElwlWvceVNiMtvS6R32W6PqM7pbEwnk0dUMiCSgBLhqle0ciS4xqw/S+QJKNWqyeokMbdfyioQTECJcNXL2Y6jAj16jNzb75PdMU9sVA0oedIY3IeAEuGS17JyULnkbtI2Pgy2J4yX1nBcGp4rDc4tAxxBQIlwvWvZ5AqucHJP24ftdWsION4mR7WAAvEElAgXu5a5WPPjlIBy4p0up7cBbkVAiXCxy5mAwo/ggHJ6oU6xECIJKBEudkUTUHjYXldYsgaxAG5IQInQ9bW1+qlRuZuH7XWF9hpWVGUEGrgAASVCv9fKuSDyNrLLVowolFYcFaIzXIaAEqHHC2WjcLLvGGBEobQusJp8hCsRUCJ0d5UcB5GycFJdeMuG9lobOb1UIdtSS3M4wZUIKBH6uko+Wlv9oZzcEVBoeKlCtvHddzjBlQgoEfq6SpYjyuPfSS4pSyxbtjX3CP1a/v7ueD/T020BXRBQIvR1oSzvO5lUTcqMstfm+uoohpmi2vjZcsnqGo5o0o7rBOIJKBG6u1ZWQ8Mko+w4DBhROjUpsA21dFv+IJICSwgoEXq8ClcndLZUUKSQiykTyVxGmYspDgagQUCJ0MWFuFqrr/63fHzJyqs/06+FAWVoht32+oUYuDMBJUL+i2y1Vl/NImWIWbjy9iNHMMId6qWA8vihPNIaKy9/Bu4jYUD5/nx/e/v4mjzw/vkd0qpDJL/CVkeaSUAZasPMS+tvPHJEklg4wgkxW1Rz7dyS5YE0t/xZiRZIJVtA+fp4q4aRucf7kPzy+jSgDH9jyr4B5YjPygtHOB/Tt3v769VlBBRgTq6A8vXRSCHNJ3NLfnltB5Thb0aZPPjSJto/r1jtks1teYQlGm/oJJGsCI6NxYBrSxVQvj/fWxHkydOJ5b+8lp9xy6Fl4cffp5tor2FLXzU+ygsoB2l045aqleIWkCqgfH38vfnk1efTyn+FfStMHh+OGdF3XGcZp9rrFFB2Ue3GakZcvsBLiwFXlS6gPKmgCCgHOLfwvstn5cYw6WP6ocqSmJ4EdpEqoDwpkfR7E0ryS/by5HHQiL79s/Lq8ORj+naPAtu42KZXgY1yBZRWkaTf+knPAaUcaXKOPeZrzjU3FehdAFZLFlCG+heKvz/fywc7kv8yXR1UXhppTg8uxsVTvBXKBU5pGNC7fAFlGP4PJCOdVk7+l+oa3RhIxo+/NNIkCQenh6RbWVgy8XYA6+QMKFeT5xo9N5ZUp3ImT83thTHphuaCbHmcOBiAdQSUCEmu0XNJoswi5VPVl7dXSxdeLTvNBdnqI44EYLV0AWXyVZ3xZE+/8zxJLtNz0zqTZxul++qOCCj9eilMzM0MVhdbMo24pHnm7OC2cgWU6Z8FHKcV3+LZrBFQqlmkHGmWFFGS7CxPvZQsFz61fbHVywMXkyqgfH38qZNMI4nfg7LdXFFkLqA8Hnn6WdaH3e4sDChL3tYlh8eSba1eHrieRAHl6+Ntoe5SSqprazmWNLJI+VR8gznI0xDQeMdfzaMCCvCqRAFlWiIpCiYqKMep5pKJx5KntpQ9TXLq+OeF5ZCFx4OAArwqVUAZz/EUt5zUfoFbL3q5tlbjSPmp+oymcZRqRa29/NNHnr5wyUtWxKAwrxaQgBVyBZRhPNFTfJen03Qy5Lu8znmUT54+wiUtGXS31DZWTAwlzAFOB4iRLqBcUi9XsWocmUz9nNY4jrQ8B9x88uXmuw+RUgWUn+pJp18lbkl+CZtEkMn8TtWp7WVnr76hdy4hCCgQJlVA+TH+Ns9FwkrmS1iZPKr/LX/IvFMstPp9vO0xIKBAmIQBZewiYSXtJWwyxjRKJm/z9ZVzms423rvV7lxAgkjJA8pYxxNAaa9ik4bNFVGGIo5UIwtd8JZtJ51DgI4CSsfyXMjKnDF+avxvI6C0lyQzbxPQi3wBZfL3eKpfO+5NklGhGkfmIki1mjJ5Vfl4+D7dy5YsKEQCfUkWUCa/nm38x3n8scC929DIH48FqtGkGm7mtsJeyny5/IXeF6A7uQLK10fx1wEncaXPhJJheJgLKMNMIWTu3yXLs7vG2/fqCwG6kCqgTP7YTvW33XeZUDIMEgtHuGryaBdXxmvLsKeXtCKgKJwAXUsXUCYFlOKvBQoo6y2fI1hYRKk+whFeCijeC+ACEgeUooDy/fne6Z2yAb08qWdsXKxcsiyQlNWUlU1nmSX58hpvhCMKGJIFlD8JZfJtnq7vkj26l5eXRvZaczn7Q4B2h1/jjTjuYAb6kiugjGZ1vj7e/uSTyQ2zfTm0l9vF/+0ZYrwGiSSny7wpL81kAdeWLKAMo1988kgn35/vb13/GpTTAooPo5d3mWjyQ0ABHvIFlCs6JaC41l/e9d5QBy3wIKBEOOUeFNf63jUm1C5WOBlT9gN+pAoo479dXDDF82wTk0FLQOna3Ft54Wjy4FYnYEgWUBp+7kNxk+z67brcd6QaLo8Ys0UBIK1eAsrga8arNz0egQxIXYipfr2UX5/ONzmogH11FFD8orZFG2oMFQoqp1gxfpdzOkfUTp4+MteehU8BbNFbQOmzhBLTy6/egGI4CbB6/B7nkqPLJ3OPPF3SQQUcR0CJENDLT4eK3ccShf2ntvT528je7aq3ZF1AKecQd20mcF+9BRRTPIs38fS+ky2tUtif0658LOmrt7+Wb25FU5c0bGEF5bhiD3BPHQWUfgsoZwaUuUFor3SyfW1XMunhVzuqmmwWRofVGWVhDCp/fqmpAK/qJqD4WzzLt9L4/L3LrIGAUjXX240Fqi9f2L3B70J55Cw53gBWSxVQ/KK2HTY0HicOGsMElKpGEas9eD/NMRkCSsIGANeWKqBcVmRAmfy3fGT3DRmWfqwYsOeqXEvWkyEfOAyA4wgoEc4KKMORQ4iqfumlCZ12TWXJejLkA4cBcJB0AeXr489szs+vuP/R6x0oZwcUQ0iAck6yvfDyFe6y2KFrADhCroDy/fn+J56M00rHX+IJ7eVXP1Ubn7bbq3BytPK9zlCDAahKFVAm39SZRpJJcaUjwb287sO38WmdatWquti5PVxmkYUtf2kTp+8mcBmJAkrzOzx/7JtSfrf78fV3Tmm3gk3CS3Y1miRsZ35LhvnTO7bapH3bqRgD7CtRQJmWSIqCyREVlPFvp/2XVH5TyW4bzHa9Lj9Az32k5qn2ML9jRWFLfWJdQFm+xYSZDOhdqoAynuMpbjn5+ti9djL97flFINnrl+tnu1gLKPuqFg/2nezYWJ+YCxCN1b60RQEF2F2ugDKMJ1yK7/IccP/J18e0YvJ3Vqd8ZJVsF+vq5E62RvZlXGzYvTN3Gf7nAke1TPLqFgUUYHfpAkqsm1ZQhiKavNrCLdMNnVq4y0f0yV7D/6FTNhtrPAATNw8o7XtQdvvzyTmv1y8NV+MlbzgULdnl4xLbvvWJJe/7ui3eMLYCx7l7QBnu9C2e1cWSyRoaC1zS010OGJX3CoXL13PDGAqkIqBEyHB9XzfeLIkjGfbuUO1dDtv9p/lyyQJPH3lphQDHEVAinH6JX50qBJSh+RWYPPu+cBLq6SMASQgoLXv9ev3Th4F9A8oNi//lPFeqHV/4/gooQEcElN28NZ3etqePLHnt4+ck+xUpz7s5NtekJUWUVDsCMCGgRMgwEmwZmRIOzKfI1gOTvFh9qvoq7yaQn4ASIclgYGRaLWG/lYlknFfOaBHAngSUYfLV4pG9vmXc94Bx81iTdt+r0zppWwvwqrsHlNYv0d/vr//0O2a8jb6u0u9erJZkl6v9v/y+E4Ae3TygPPldsRf+VfdLPNLJ5JE7yBPIGhnxnm8NcBM3DyjP/hjgRf9Y4ELVEbHTfVku1T4+zYi3LW4Bl3fzgHLHCsryIe2x2OTenOPbeJpse3fPjAgw3D6g/LsHpV4kueI9KK9OCoxDybUDSs5dE1CA27p7QBmGYfznAv/YJZsMw5AmoJTNaDesLJxccnRMvlNlpszcWoC9CCgRkowoLwWUudpJkn3ZRfJo8nDV/gdoEFAiJBlUlgeUasnkYgNkXzty7fk1gJKAEiHPuFLOF8wtM84lF5vfucyOAFyYgBIh1XD49LP45L6TJS/pxTX2AuAOBJQIHQ2KbzPObtcOrrEXADchoERIPjSWWWQ8p5O88UtcYy8AbkVAiZB5dJy7K+Ua6eQCuwBwTwJKhIRjZDV/VB+JbdduRBOArgkoEbKNlJO7X8ePN/7bkU6bvd016l4Ag4ASI9WAUc7pVGd2Oh3nOm32sEe2mJutA+iRgBIh1WjRmNbp+t7YHtv8sD1blK/qtzcABgElRqqhojqSdT26D8l6+FW7ZAsBBbgYASVCtqHiSnMBvUerQUABqBFQIiQcKq5RNVne/sz7u1e2uFLuBBBQIhgt9vVq1Mg/cu/Vwsw5DOAlAkoEA8aOXu3MXuY+ZAuAMQElglFnF+vG714CCgBjAkoEI+JGW0oLAgpAjwSUCEbELbb3Xv57UACYEFAi5BwU89/0sGPz8u/sj17aCXA0ASVCwvFmUlTINihma08MlR6ABwElQrbBphwIx/9OlgzOCveMJoN7ZQD+ElAiZBtpHu1p/ND4OaBhCxcep5mEdaC2sv3lAuGNAshCQImQbaRZElCCx8tXs0U5RVV96nRzsWmuiDW3DMDdCCgREo40czM7b4XJS45oyatrnixfriFJhy8vR1XfiINbB5CagBLhlF5ufHZ/GkGqUw9H7MW6dXYRUBoVkfZTfU1UARxEQIkQ38tLPruXg+JkdKzmlR1buHqdFw4oAPwQUCIE9/KSGYTH44/R/fHv+JEjPtBvXGG18DMXwgLMdVH7kRMbDNAFASVCzoBSZpHJwo1P/Du2bfXLy3rPEZWel9rz6rPxDQbohYASIWFAmaSQauHkseQuUWD7YLykShFpYdVECgFYQUCJEN/LT2cTyjhS/rccXMv/LmzMLj3QY0BZuB4hBmBCQIlwSi/PDXvVcshQuwdlKFperrC9a/uOu9sDQSMKrEgJuwSUFYEP4A4ElAjBvbxwrK3mkjiAy4cAABL7SURBVHaN5KWAcsRebxnO2/u1brUb40W2mhBAHgJKhMhefmnIfBpK1gWUQycsVpQ6hmYU2JgS1rVnl00DXJiAEiGsl18d8CZFlKdraNdXygXyOC6gbCGgAMwRUCLkHPDK5DG38OTZuYUzD645A8pQvAth2wVITkCJkD+gNBZeMoVRVlYSllLaU1dzTwXI2V0A5xJQIuT8RL5kNufp2sqRNXNJoBEFpASAVASUCMG9/DbydMnGz+N/q8ssqcH0MuQLKACpCCgR4gPK8k03KiVLfmhsemEDMshc9QG4JwElwllTPO2tz9UM2rmkXWboMaD02GaAyxNQIiQMKC/dMfr4d8mOzBVj0k6gCCgACQkoEbIFlPJWkkmAqC7wUhsma3v8N+HYL6AAJCSgRMh2D8okiFQDRDW47NKY7b2xez3maY8BEExAiRDfy+0hfJJLJkFkklG2N6P9yIp1Vn/eaPfQA8AWAkqEhMPeXDR5tWryNAntG1DK1ybsWwC2E1AiJBxEyyDyajQZFtwPOynJDJu7IjKgqKkAnEhAiZBwkGuXTybLzK2hus7JApOVb2/200d2sWOoAmAFASVCwhGuOqczCSuThatrWPJIuf6nbVsYjALSyaEbAmCOgBIhvpeXjPGN9FC+dnkcqT6yPFUsWXKvesySNrRbAsBBBJQIwb28vPhRraCUw381vlSXqW5o+XifJBkkaQbAnQkoESJ7eWFho8wcQ5FXJk+VL5xbePibaboLKMOCkAfAoQSUCDkDylCEj2E+iIxf+DR8TCJLjwFl8C0egFMJKBHyBJQyOlTDx5IF5sbvRh6aW6DR2tauAnBdAkqE4F6ujvFzxYBygbJMMl5gXDipZpS5yLK8IKF0AYCAEiG+l98KyxeeW8NkmcnC47WV699z3wC4AQElwlm9PJch5pZsZ5G5/5Yrb+eVy1DpATiOgBJhl15+dTicLNx4+Vz+GLd8Lrs8nt3Y2u7cJIQBnEVAibC9l18aDucCxFy2mBRCqkGkGl/22rsVzg1A1UB2SksArkpAibCxl18aDidpY+6HcYGkEWXGy8/ZsmvV9j9dbYZ49PQRALYQUCIcFFCqMWL886QEUn15+cPTIHJQNKk2sr1Me8njZGgDwLUJKBGOCCiNxDCXNsrl5wJNI6CM486+R8/CUT9JOFiSpQBYTUCJsL2Xy3gx+XkcSqrLNF5SLlYNLuVLdtm1xqoyB5Th7PtgAK5NQImwSy9Xg8KksDHURs1qLaS6wGTNc3bftblVza38oIQEQB4CSoTde7la6hg/1cgfT0PG8nSy+64tTx5PGwZA1wSUCPuWGSaljmGmHPJWVETmGlN9ZPKSMhLtu19zm3668KGNAeAsAkqEvXp5rtRRLtAuMMyN642qyVxeOdGSpAVApwSUCNt7uRoyJulhboHq1hvh5vFz8vqEgAJwYQJKhC29XE0Yy6PDwmrH3CaSFEuqBBSACxNQIqzr5UbxY+H6X8ox1a2nTSc/ktd4AFhNQImwopcbL1kYUF4qMJT1klfbfFaayZ+iAFhBQInwUi8/HW6PCCjDtmqESgYA+7p5QPn6eHt7e//8PngzC3t5eSVgSSB4aSZoYrzw0xKFe0EA2J2A8vb+8fF+cEpZ0stHTKkszzHltM7cI+2ttJcEgIUElH/R5Pvz/e3t7e3j64jNPI0RB70NT290HZdJyh8OmksCgKcElL+1k6+Pf+P5rkmlPbey44bmNrqk+FGWUl6aJHq6DAAsJ6DMTO48ksoeUaU60h/a9euKH5Nyy0ulkSVTTgCwkIAScI9sJQcEb7Gx0XbxQ2kEgFMIKKEBJazGsGPxQ2kEgHg3DyhBThnjXy1+CCIA5CGgRDirl59+i2e8ZPVnADiFgNLy/fl+0E2yMRbGDt8TBiAbAWU3b02ntKfavKdLVh8BgEgCSoTTA8rbi7/dREAB4FwCSoRzA0rjh3Lh6rMAEExAGR6/5r6w22+TPfcelEnhZG6ux7d4AMjj7gHlJ5s0fpnsLr8l5cxe/hs72nM9AJDEzQPK9+d7K4I8eXqxs6Z4HtFkLpfIKADkdPOA8vXRnsh59vxC8b1cvUO2nMFJElDMLgEwcfOAcs0Kytw9sDm/raOiA0Dp5gHl3z0o9SJJt/egNIJItjSw8DvP6isAd3P3gDIMw78kUtrvrwjmCShDsvH+aUDJlqgAiCGgRMhwD0pOT7PU0+UBuCQBJcLp3+LJrFrdyXzTDAABBJQImYfVDDlmkkvGD5bLnNFAAKIJKBHSDqupZoLmbo99PDVXVgHgegSUCAG9vKLAkG0CZa491eJKaMsACCegRDi6l9cN3pEBpfiKVGVDjYAS1k4AkhBQIhzay6vH78di7dyw3WRDjUZWk5aAAnBDAkqEnAFlKBLDEe0sc8bTOkr5lPkdgLsRUCIkDyhPCxtbVAPKeOvL17PiJpvjykIAHEpAiZDzHpTqwuuaWqacx38nuaQMQ8snpBppo3xW0QWgawJKhIBeXlct2CWgTKJAmQyqJZOXajbttNHYYuNVAGQmoETIPDpurDSUN4tUbx95KyzfaCNtVGNZNahlfgsAKAkoEZKPjlvu1VgYUOYeebV8Mn6k/HeuDQs3BEAeAkqEsF5+KWpsySXjlZTrbCywrp3Vl0+enfzQrrIAkJyAEiGml1fPm7QXfjrAN6oXe+14uc65R8rGlAkGgPwElAgBvfzSpMbyhRemjTIK7F60aKeN6hZN9AD0S0CJ0GlAmZtbSTJj8jQ8CSgA/RJQIuzYy3P5ICygLFn/LpYkofYyAgpAvwSUCMfdirH82RULV6dRGgvsaK8kFJmoANiRgBJhl15eWDVZPv+ysETxUgN2se+G8sxJAbCcgBIhLKAcoXHfSWRAETIAbkVAidB1QJnbYsz8zjDzW08AuDYBJULMPSgxYooZ40QSduMLAHkIKBF27OX7THYEzCvdpzMBuiOgRDAErrY6oDwNHxnKUQDMEVAiGP+2WJEknr4kww09ADQIKBGO6OV2heBikxcv7c6S8CGgACQnoETYvZfbFYKfR7rOKJPGCygAdyOgRNi3l9uD6yOdHLT147yNTB4c/3fJep4+MvTZRQD3IaBECA4okwW6qKNMiiXjx8vdWb629vJdF5kArk1AiSCgtDUqQOsCyiB8AHROQIlwyj0o45+TjNPj0DD5ebzMsEdAAaBrAkqEI3p5brCvPrv71leYC1Xtkk+5Xwc3E4AUBJQIh/Zye+BPMqK3izpz6WoSU5LsCwABBJQIx/Vye34njyUBRQoB4EFAiXBoQOliEuRpQCl/3pJXqq8VgAA6IqBE2N7LjRF3som0pYiniWT8yJbINRd3Vq8QgHgCSoSNvdwecRslh2wj8biFb4XxYuULl2+iutHVKwTgFAJKhC29PDe4Tkb0uapJ8pG4mlEEFAAElAhHB5TH432NxONqyrBTzLpAtwAwCCgxjggoQ1FEaS+cULUIVH1qy2q3rxCAeAJKhI293Bhc2zdwJB+JGwGl+shLay5fu2WFAAQTUCJs7+WXBtdeRuLxFE9jfmfoZ48A2IuAEsHIOuetMNSqRNWfAbgwASWCYXVOWThpzFjNPQLA9QgoEYypE405HQEFgEFAiWFMHSvzR/WRuftOdCbAHQgoES48pr56++pkKqe8T3Yo8op7UABuSECJcNVhdUV0mIsgc3fIlgsAcAcCSoQeR9anmWDd5MtLN52UbeixJwFYQUCJ0N2wuiQTrL475O2vuc2VUz8vbQWArgkoEfoaUxcmj4MCyvC3ptL4AYALE1Ai9DWmLk8ee92DUl1sUjsRUABuRUCJ0NeY+lJpZMmtKnM5o/HaMsFUay0AXJWAEqG7YXXu/o9165mss7FM47UbWwJAXwSUCD2OrI17RJavofrI8okhuQTgtgSUCN0NsdVs8WpcaBRLJA8A2gSUCN2NxOUUz+r7YduPAECVgBKhu4F5Ut4oqx0rMkp3nQDAiQSUCN2NzXsFlMFsDgCrCCgRuhueJ1M8WwIKAKwgoETobjhv3z7S3e4A0B0BJUKPI3r1V5iYrAEghoASodNBXSIB4CwCSgRjPAC8RECJIKAAwEsElAgCCgC8RECJIKAAwEsElAgCCgC8RECJIKAAwEsElAgCCgC8RECJIKAAwEsElAgCCgC8RECJIKAAwEsElAgCCgC8RECJIKAAwEsElAhvAMCLThu1z9owLznxEElOz1TplirdUqVb5uiZc+n9PjhP5uiZKt1SpVuqdMscPXMuvd8H58kcPVOlW6p0S5VumaNnzqX3++A8maNnqnRLlW6p0i1z9My59H4fnCdz9EyVbqnSLVW6ZY6eOZfe74PzZI6eqdItVbqlSrfM0TPn0vt9cJ7M0TNVuqVKt1Tpljl65lx6vw/Okzl6pkq3VOmWKt0yR8+cS+/3wXkyR89U6ZYq3VKlW+bomXPpfQAgHQEFAEhHQAEA0hFQAIB0BBQAIB0BBQBIR0ABANIRUACAdAQUACAdAQUASEdAAQDSEVAAgHQEFAAgHQElm+/P97eH98/vP09+fcw9cytfH0UH3LlnxofMx9efp27cLY1euWO3fH++F93Q6of7dFGlZ1yEsxBQUvk5Mf4d9//Okse5Mx6WK0P0bfxcIMZ7f+ee+foY7e7XhwNmGIZ/585430dD0B275eec+TsMN/rhRl1U9oyLcCICSibfn++Vc+Xnge/P92JQLj4R3cD/n19+++LOPTPddwfMMAzliTTa9/t1y+8n/umlZaYfbtNF1Z5xEc5EQMntEdJbp82N/FwhPscfXe7cM9ML5uSpu3ZLI6DcrVu+Pv6F+clY2uiHm3TRXM/Ul3QRPoeAktpvcbocim6Y3v/vhK9pQLlrz/zb09qs+J27pTHFc9tuqQSUmX64Wxc92zsX4RMJKIk9Mv5Qm++83Qzo7+Xhz67fuGf+v5fvcYkcfaK7cbf8U72Z8bbdMhlKG/1wty5qhwwX4VMJKFlNbt66/bkx/vQioPz4Uyf48bja3rhbhsl9seNuum23CChzGgHFRfhsAkpK49j+4+bVxb+7b4rnR2UK/PHQjbvl2Q0Wt+wWUzxz5vbORTgBASWdP99y+/vobe/P+vN7CUb+H4nv2jPl9fFxDb17t8x80r1tt7hJdk4tZLgIJyGg5PJzYtQOed9w+/V3ALpzzxT7+vf7KjftlnLc0C3T/fQ14/8Vu+cinIeAkknlnoIRvyPof9O9v3HP/L1kzs+E3axbZu9BGe7aLeVY6he1/ajVllyEkxBQEpmZyPg7/vgty7Urw6175vfrKtOdv3O3jHpFt7QmMqr9cKMu+tszLsKpCCgAQDoCCgCQjoACAKQjoAAA6QgoAEA6AgoAkI6AAgCkI6AAAOkIKABAOgIKAJCOgAIApCOgAADpCCgAQDoCCgCQjoACAKQjoAAA6QgoAEA6AgoAkI6AAgCkI6AAAOkIKABAOgIKAJCOgAIApCOgAADpCCgAQDoCCgCQjoACXMDXx/vn99mNAHYkoMANfH++v/36+Bo/9/Xx+8j45xU2vny578/33w19ffzu2jSlfH++v39+f3++zzWs8dTv7nx9FCsGjiagwMX9hJPfMXj6/7GwhLHJOJ58ffzszNdHNYh8fbx9fLVSyKKAIqLACQQUuLTvz/fK0Pr1URYb/n88fUAZNfI3Xvyb4pns2E8+2SGg/K3ZAAEEFLiyucQxyi3Ppnh+Fv36nST6GwDePz8//p84mr78z8zS6Inx439yUmsqqrZLRUApmv7++f3/Yp+1XWg89Xd36kkPOIyAAhc2VykZP7MkoIziwv9zKr//+d1AMaL/Pve7vT+Pj/8zKWb82dDfhk8Wev/8rgaU//PJ/7swu9H6U5VNSSgQR0CBC5ufshnXHhYElPHIPKm+zJQcWrNIfx4f34r6fBalePm46DJ59b8Jnpld+Hmu8dSkQa3JIGB/Agpc2G4BZXrnaaX68ve/c8N5mVv+tuRZBpjbo9+v8oyLNrONeTTjxb1TQoEwAgpc2F5TPH/XsTSgzBVQKv7cVNK4B2W2jDG6Sfa3bDKeuClT0SOgzDwloMCpBBS4st1ukl0TUJZVUBotn/n+USOg/Ekej1eroECHBBS4tHpQGI+1L9+DMnrxfEDZ4ZvM1SX/rnYcJn5Dxf+1lJn7dYdx6Hp2h417UOAsAgpc3LNf1LbwWzzjPDO3fONbPLO3pf5WSip33FYSTvNbPL+NG+eT1i4s3zsFFIgloMANbPlV98VvCplLJOXLl/welGIFDzNpoLmRUe4YvbyxC4v3zu9BgWACCtCUbmpjZurn2PTQxe/YhUsRUICmdAHljF8772/xQDgBBWjKF1DCI4p4AicQUACAdAQUACAdAQUASEdAAQDSEVAAgHQEFAAgHQEFAEhHQAEA0hFQAIB0BBQAIB0BBQBIR0ABANIRUACAdAQUACAdAQUASEdAAQDSEVAAgHQEFAAgHQEFAEhHQAEA0hFQAIB0/gNiG2cxkmw2LwAAAABJRU5ErkJggg==" width="400" /><br />
The plot shows a positive correlation between oil prices and the exchange rate, but there seems to be some nonlinear behaviour towards the beginning and ending period of the data set.<br />
<br />
Next, I estimate a quadratic fit. This doesn't look too different from the linear fit.<br />
<img alt="" height="325" 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" width="400" /><br />
<br />
Perhaps a cubic fit is more appropriate. The cubic fit looks much better! Notice how the cubic curve fits the curvature at the beginning and ending period of the data.<br />
<img alt="" height="325" 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" width="400" /><br />
<br />
<br />
Here are the model fits. The cubic curve fits the best.<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 382px;"><colgroup><col style="mso-width-alt: 6769; mso-width-source: userset; width: 143pt;" width="190"></col>
<col span="3" style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="30" style="height: 22.2pt;">
<td class="xl67" height="30" style="height: 22.2pt; width: 143pt;" width="190"></td>
<td class="xl68" style="width: 48pt;" width="64">linear</td>
<td class="xl68" style="width: 48pt;" width="64">quadratic</td>
<td class="xl68" style="width: 48pt;" width="64">cubic</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl66" height="30" style="height: 22.2pt;">Adjusted R squared</td>
<td class="xl65">0.6511</td>
<td class="xl65">0.6507</td>
<td class="xl65">0.6923</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl69" height="30" style="height: 22.2pt;">Sigma</td>
<td class="xl70">0.0660</td>
<td class="xl70">0.0660</td>
<td class="xl70">0.0620</td>
</tr>
</tbody></table>
<br />
<br />
<br />
Here are some forecasts for each of the three regression models.<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 256px;"><colgroup><col span="4" style="width: 48pt;" width="64"></col>
</colgroup><tbody>
<tr height="30" style="height: 22.2pt;">
<td class="xl64" height="30" style="height: 22.2pt; width: 48pt;" width="64">oil price</td>
<td class="xl64" style="width: 48pt;" width="64">linear</td>
<td class="xl64" style="width: 48pt;" width="64">quadratic</td>
<td class="xl64" style="width: 48pt;" width="64">cubic</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">30.00</td>
<td class="xl63">0.77</td>
<td class="xl63">0.77</td>
<td class="xl63">0.75</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">35.00</td>
<td class="xl63">0.79</td>
<td class="xl63">0.78</td>
<td class="xl63">0.75</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">40.00</td>
<td class="xl63">0.80</td>
<td class="xl63">0.80</td>
<td class="xl63">0.77</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">45.00</td>
<td class="xl63">0.82</td>
<td class="xl63">0.81</td>
<td class="xl63">0.78</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">50.00</td>
<td class="xl63">0.83</td>
<td class="xl63">0.83</td>
<td class="xl63">0.80</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">55.00</td>
<td class="xl63">0.85</td>
<td class="xl63">0.84</td>
<td class="xl63">0.82</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl63" height="30" style="height: 22.2pt;">60.00</td>
<td class="xl63">0.86</td>
<td class="xl63">0.86</td>
<td class="xl63">0.85</td>
</tr>
<tr height="30" style="height: 22.2pt;">
<td class="xl65" height="30" style="height: 22.2pt;">65.00</td>
<td class="xl65">0.87</td>
<td class="xl65">0.87</td>
<td class="xl65">0.87</td>
</tr>
</tbody></table>
<br />
Today, oil is currently trading around $37 per barrel. An oil price of $35 per barrel produces an exchange rate forecast of 75 cents (using the cubic model). The actual exchange rate at time of writing is 74 cents. Overall, a fairly close fit.<br />
<br />
<br />
The R script and data set are posted below.<br />
#########################################################<br />
# Economic forecasting and analysis<br />
# Perry Sadorsky<br />
# December 2015<br />
# Oil prices and the Canadian dollar<br />
##########################################################<br />
<br />
<br />
rm(list=ls())<br />
# load libraries<br />
library(fpp)<br />
<br />
<br />
as2_data <- read.csv("C:/econ 6210/6210f15/assignment 2/as2_data.csv")<br />
View(as2_data)<br />
<br />
<br />
df = as2_data<br />
df = ts(df, start=1986, frequency=12)<br />
<br />
<br />
plot(df[,-1], main="Oil prices and exchange rates", ylab = "", xlab = "")<br />
<br />
<br />
oil = df[,"oil"]<br />
fx = df[,"fx"]<br />
<br />
<br />
# 5 year rolling correlations<br />
rollout1 = rollapply(df[,-1], 60 ,function(x) cor(x[,1],x[,2]), by.column=FALSE,align="right")<br />
rollout1 = na.omit(rollout1)<br />
plot(rollout1,main="Rolling 5 year correlations between FX and Oil prices")<br />
<br />
<br />
## linear fit<br />
lm1 = lm(fx ~ oil)<br />
summary(lm1)<br />
str(summary(lm1))<br />
<br />
rr = matrix(0,nrow=2, ncol=3)<br />
rr[1,1] = summary(lm1)$adj.r.squared<br />
rr[2,1] = summary(lm1)$sigma<br />
<br />
par(mfrow=c(2,2))<br />
plot(lm1)<br />
par(mfrow=c(1,1))<br />
<br />
plot(fx ~ oil, main="Linear fit",<br />
ylab="$US/$C", xlab="Oil prices ($/bbl)")<br />
abline(lm1)<br />
<br />
oil_f = c(30, 35, 40, 45, 50, 55, 60, 65)<br />
<br />
fcast1 <- forecast(lm1, newdata=data.frame(oil=oil_f))<br />
fcast1<br />
plot(fcast1, ylab="$US/$C", xlab="Oil prices ($/bbl)")<br />
<br />
<br />
## quadratic fit<br />
lm2 = lm(fx ~ oil + I(oil^2))<br />
summary(lm2)<br />
rr[1,2] = summary(lm2)$adj.r.squared<br />
rr[2,2] = summary(lm2)$sigma<br />
<br />
par(mfrow=c(2,2))<br />
plot(lm2)<br />
par(mfrow=c(1,1))<br />
<br />
<br />
plot(fx ~ oil, main="Quadratic fit",ylab="$US/$C", xlab="Oil prices ($/bbl)")<br />
curve( coef(lm2)[1] + coef(lm2)[2]*x + coef(lm2)[3]*x^2 , add=T )<br />
<br />
<br />
fcast2 <- forecast(lm2, newdata=data.frame(oil=oil_f))<br />
fcast2<br />
<br />
<br />
<br />
## cubic fit<br />
lm3 = lm(fx ~ oil +I(oil^2) +I(oil^3) )<br />
summary(lm3)<br />
rr[1,3] = summary(lm3)$adj.r.squared<br />
rr[2,3] = summary(lm3)$sigma<br />
<br />
par(mfrow=c(2,2))<br />
plot(lm3)<br />
par(mfrow=c(1,1))<br />
<br />
<br />
plot(fx ~ oil, main="Cubic fit",ylab="$US/$C", xlab="Oil prices ($/bbl)")<br />
curve( coef(lm3)[1] + coef(lm3)[2]*x + coef(lm3)[3]*x^2 + coef(lm3)[4]*x^3, add=T , col = "blue" )<br />
<br />
<br />
fcast3 <- forecast(lm3, newdata=data.frame(oil=oil_f))<br />
fcast3<br />
fcast3$mean<br />
<br />
<br />
tablef = cbind(oil_f, fcast1$mean, fcast2$mean, fcast3$mean)<br />
colnames(tablef) = c("oil price", "linear", "quadratic", "cubic")<br />
tablef<br />
<br />
colnames(rr) = c("linear", "quadratic","cubic")<br />
rownames(rr) = c("Adjusted R squared", "Sigma")<br />
rr<br />
<br />
<table cellpadding="0" cellspacing="0" class="GEM3DMTCOFB ace_text-layer ace_line GEM3DMTCKT" style="-webkit-text-stroke-width: 0px; background-color: white; border: none; color: black; cursor: text; font-family: 'Lucida Console' !important; font-size: 18pt !important; font-style: inherit !important; font-variant: inherit !important; font-weight: inherit !important; letter-spacing: normal; line-height: inherit !important; orphans: auto; outline: none; padding-bottom: 8px; padding-left: 6px; text-align: start; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; width: 810px; word-spacing: 0px; word-wrap: break-word;"><tbody>
<tr><td align="left" style="font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; vertical-align: top;"><pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-user-select: text; border: none; font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; margin: 0px; outline: none; white-space: pre-wrap !important; word-break: break-all;" tabindex="0"> date oil fx
1 1/1/1986 22.93 0.7107321
2 2/1/1986 15.46 0.7120986
3 3/1/1986 12.61 0.7138268
4 4/1/1986 12.84 0.7205130
5 5/1/1986 15.38 0.7269027
6 6/1/1986 13.43 0.7194762
7 7/1/1986 11.59 0.7242178
8 8/1/1986 15.10 0.7202017
9 9/1/1986 14.87 0.7208246
10 10/1/1986 14.90 0.7202017
11 11/1/1986 15.22 0.7213446
12 12/1/1986 16.11 0.7245852
13 1/1/1987 18.65 0.7349699
14 2/1/1987 17.75 0.7496252
15 3/1/1987 18.30 0.7579203
16 4/1/1987 18.68 0.7580352
17 5/1/1987 19.44 0.7456566
18 6/1/1987 20.07 0.7469934
19 7/1/1987 21.34 0.7540341
20 8/1/1987 20.31 0.7543754
21 9/1/1987 19.53 0.7602250
22 10/1/1987 19.86 0.7635336
23 11/1/1987 18.85 0.7594744
24 12/1/1987 17.28 0.7648184
25 1/1/1988 17.13 0.7779074
26 2/1/1988 16.80 0.7885192
27 3/1/1988 16.20 0.8005123
28 4/1/1988 17.86 0.8095200
29 5/1/1988 17.42 0.8082114
30 6/1/1988 16.53 0.8212878
31 7/1/1988 15.50 0.8281574
32 8/1/1988 15.52 0.8171938
33 9/1/1988 14.54 0.8151952
34 10/1/1988 13.77 0.8295313
35 11/1/1988 14.14 0.8206138
36 12/1/1988 16.38 0.8359806
37 1/1/1989 18.02 0.8394191
38 2/1/1989 17.94 0.8409722
39 3/1/1989 19.48 0.8365401
40 4/1/1989 21.07 0.8411844
41 5/1/1989 20.12 0.8385744
42 6/1/1989 20.05 0.8343067
43 7/1/1989 19.78 0.8409722
44 8/1/1989 18.58 0.8504848
45 9/1/1989 19.59 0.8454515
46 10/1/1989 20.10 0.8511363
47 11/1/1989 19.86 0.8549201
48 12/1/1989 21.10 0.8611039
49 1/1/1990 22.86 0.8532423
50 2/1/1990 22.11 0.8357710
51 3/1/1990 20.39 0.8474576
52 4/1/1990 18.43 0.8590327
53 5/1/1990 18.20 0.8512812
54 6/1/1990 16.70 0.8525149
55 7/1/1990 18.45 0.8643042
56 8/1/1990 27.31 0.8735150
57 9/1/1990 33.51 0.8633342
58 10/1/1990 36.04 0.8620690
59 11/1/1990 32.33 0.8594757
60 12/1/1990 27.28 0.8618461
61 1/1/1991 25.23 0.8650519
62 2/1/1991 20.48 0.8658758
63 3/1/1991 19.90 0.8641549
64 4/1/1991 20.83 0.8669267
65 5/1/1991 21.23 0.8696408
66 6/1/1991 20.19 0.8742023
67 7/1/1991 21.40 0.8700948
68 8/1/1991 21.69 0.8732099
69 9/1/1991 21.89 0.8795075
70 10/1/1991 23.23 0.8866034
71 11/1/1991 22.46 0.8847992
72 12/1/1991 19.50 0.8720677
73 1/1/1992 18.79 0.8642295
74 2/1/1992 19.01 0.8456660
75 3/1/1992 18.92 0.8383635
76 4/1/1992 20.23 0.8421762
77 5/1/1992 20.98 0.8339588
78 6/1/1992 22.39 0.8361204
79 7/1/1992 21.78 0.8386448
80 8/1/1992 21.34 0.8398421
81 9/1/1992 21.88 0.8179959
82 10/1/1992 21.69 0.8030194
83 11/1/1992 20.34 0.7890169
84 12/1/1992 19.41 0.7858546
85 1/1/1993 19.03 0.7825338
86 2/1/1993 20.09 0.7935248
87 3/1/1993 20.32 0.8018603
88 4/1/1993 20.25 0.7923302
89 5/1/1993 19.95 0.7875256
90 6/1/1993 19.09 0.7819220
91 7/1/1993 17.89 0.7800312
92 8/1/1993 18.01 0.7645260
93 9/1/1993 17.50 0.7567159
94 10/1/1993 18.15 0.7539772
95 11/1/1993 16.61 0.7590709
96 12/1/1993 14.52 0.7514277
97 1/1/1994 15.03 0.7591285
98 2/1/1994 14.78 0.7449344
99 3/1/1994 14.68 0.7329229
100 4/1/1994 16.42 0.7230658
101 5/1/1994 17.89 0.7242178
102 6/1/1994 19.06 0.7227522
103 7/1/1994 19.66 0.7232750
104 8/1/1994 18.38 0.7255315
105 9/1/1994 17.45 0.7385524
106 10/1/1994 17.72 0.7405762
107 11/1/1994 18.07 0.7327618
108 12/1/1994 17.16 0.7197869
109 1/1/1995 18.04 0.7076139
110 2/1/1995 18.57 0.7140307
111 3/1/1995 18.54 0.7103786
112 4/1/1995 19.90 0.7266386
113 5/1/1995 19.74 0.7348078
114 6/1/1995 18.45 0.7259528
115 7/1/1995 17.33 0.7346459
116 8/1/1995 18.02 0.7378985
117 9/1/1995 18.23 0.7402472
118 10/1/1995 17.43 0.7430525
119 11/1/1995 17.99 0.7388799
120 12/1/1995 19.03 0.7303002
121 1/1/1996 18.86 0.7315824
122 2/1/1996 19.09 0.7271670
123 3/1/1996 21.33 0.7322789
124 4/1/1996 23.50 0.7357269
125 5/1/1996 21.17 0.7303002
126 6/1/1996 20.42 0.7321716
127 7/1/1996 21.30 0.7300869
128 8/1/1996 21.90 0.7287567
129 9/1/1996 23.97 0.7302468
130 10/1/1996 24.88 0.7403020
131 11/1/1996 23.71 0.7473283
132 12/1/1996 25.23 0.7341066
133 1/1/1997 25.13 0.7410701
134 2/1/1997 22.18 0.7376807
135 3/1/1997 20.97 0.7285974
136 4/1/1997 19.70 0.7172572
137 5/1/1997 20.82 0.7244277
138 6/1/1997 19.26 0.7223868
139 7/1/1997 19.66 0.7259528
140 8/1/1997 19.95 0.7191658
141 9/1/1997 19.80 0.7208766
142 10/1/1997 21.33 0.7210325
143 11/1/1997 20.19 0.7078143
144 12/1/1997 18.33 0.7007217
145 1/1/1998 16.72 0.6940107
146 2/1/1998 16.06 0.6976420
147 3/1/1998 15.12 0.7059156
148 4/1/1998 15.35 0.6993985
149 5/1/1998 14.91 0.6919458
150 6/1/1998 13.72 0.6823610
151 7/1/1998 14.17 0.6725402
152 8/1/1998 13.47 0.6516356
153 9/1/1998 15.03 0.6571166
154 10/1/1998 14.46 0.6471654
155 11/1/1998 13.00 0.6491820
156 12/1/1998 11.35 0.6479622
157 1/1/1999 12.52 0.6581545
158 2/1/1999 12.01 0.6676905
159 3/1/1999 14.68 0.6589352
160 4/1/1999 17.31 0.6719979
161 5/1/1999 17.72 0.6844159
162 6/1/1999 17.92 0.6805036
163 7/1/1999 20.10 0.6715917
164 8/1/1999 21.28 0.6697027
165 9/1/1999 23.80 0.6770022
166 10/1/1999 22.69 0.6767731
167 11/1/1999 25.00 0.6814774
168 12/1/1999 26.10 0.6792555
169 1/1/2000 27.26 0.6903217
170 2/1/2000 29.37 0.6890849
171 3/1/2000 29.84 0.6845564
172 4/1/2000 25.72 0.6807815
173 5/1/2000 28.79 0.6685833
174 6/1/2000 31.82 0.6770481
175 7/1/2000 29.70 0.6766816
176 8/1/2000 31.26 0.6743998
177 9/1/2000 33.88 0.6727664
178 10/1/2000 33.11 0.6611570
179 11/1/2000 34.42 0.6482562
180 12/1/2000 28.44 0.6570734
181 1/1/2001 29.59 0.6652475
182 2/1/2001 29.61 0.6572029
183 3/1/2001 27.25 0.6415603
184 4/1/2001 27.49 0.6419309
185 5/1/2001 28.63 0.6488872
186 6/1/2001 27.60 0.6559528
187 7/1/2001 26.43 0.6532532
188 8/1/2001 27.37 0.6493928
189 9/1/2001 26.20 0.6377958
190 10/1/2001 22.17 0.6362537
191 11/1/2001 19.64 0.6280618
192 12/1/2001 19.39 0.6333924
193 1/1/2002 19.72 0.6251172
194 2/1/2002 20.72 0.6264094
195 3/1/2002 24.53 0.6298419
196 4/1/2002 26.18 0.6323111
197 5/1/2002 27.04 0.6450781
198 6/1/2002 25.52 0.6528267
199 7/1/2002 26.97 0.6469979
200 8/1/2002 28.39 0.6371862
201 9/1/2002 29.66 0.6344775
202 10/1/2002 28.84 0.6337136
203 11/1/2002 26.35 0.6363347
204 12/1/2002 29.46 0.6413545
205 1/1/2003 32.95 0.6487609
206 2/1/2003 35.83 0.6613319
207 3/1/2003 33.51 0.6774609
208 4/1/2003 28.17 0.6857770
209 5/1/2003 28.11 0.7225434
210 6/1/2003 30.66 0.7393715
211 7/1/2003 30.76 0.7235366
212 8/1/2003 31.57 0.7161785
213 9/1/2003 28.31 0.7334605
214 10/1/2003 30.34 0.7563724
215 11/1/2003 31.11 0.7616146
216 12/1/2003 32.13 0.7617307
217 1/1/2004 34.31 0.7717240
218 2/1/2004 34.69 0.7519362
219 3/1/2004 36.74 0.7526720
220 4/1/2004 36.75 0.7451565
221 5/1/2004 40.28 0.7252158
222 6/1/2004 38.03 0.7364855
223 7/1/2004 40.78 0.7561437
224 8/1/2004 44.90 0.7617887
225 9/1/2004 45.94 0.7763372
226 10/1/2004 53.28 0.8019889
227 11/1/2004 48.47 0.8355615
228 12/1/2004 43.15 0.8204118
229 1/1/2005 46.84 0.8164598
230 2/1/2005 48.15 0.8063866
231 3/1/2005 54.19 0.8223684
232 4/1/2005 52.98 0.8091270
233 5/1/2005 49.83 0.7964954
234 6/1/2005 56.35 0.8063216
235 7/1/2005 59.00 0.8177284
236 8/1/2005 64.99 0.8303579
237 9/1/2005 65.59 0.8491127
238 10/1/2005 62.26 0.8493290
239 11/1/2005 58.32 0.8463817
240 12/1/2005 59.41 0.8609557
241 1/1/2006 65.49 0.8641549
242 2/1/2006 61.63 0.8703978
243 3/1/2006 62.69 0.8640802
244 4/1/2006 69.44 0.8740495
245 5/1/2006 70.84 0.9009009
246 6/1/2006 70.95 0.8979079
247 7/1/2006 74.41 0.8854259
248 8/1/2006 73.04 0.8942944
249 9/1/2006 63.80 0.8959771
250 10/1/2006 58.89 0.8861320
251 11/1/2006 59.08 0.8803592
252 12/1/2006 61.96 0.8671523
253 1/1/2007 54.51 0.8501233
254 2/1/2007 59.28 0.8539710
255 3/1/2007 60.44 0.8560178
256 4/1/2007 63.98 0.8810573
257 5/1/2007 63.46 0.9131586
258 6/1/2007 67.49 0.9388790
259 7/1/2007 74.12 0.9521996
260 8/1/2007 72.36 0.9452689
261 9/1/2007 79.92 0.9739944
262 10/1/2007 85.80 1.0252204
263 11/1/2007 94.77 1.0339123
264 12/1/2007 91.69 0.9979044
265 1/1/2008 92.97 0.9901970
266 2/1/2008 95.39 1.0014020
267 3/1/2008 105.45 0.9971084
268 4/1/2008 112.58 0.9864852
269 5/1/2008 125.40 1.0007005
270 6/1/2008 133.88 0.9836711
271 7/1/2008 133.37 0.9871668
272 8/1/2008 116.67 0.9492169
273 9/1/2008 104.11 0.9450009
274 10/1/2008 76.61 0.8440956
275 11/1/2008 57.31 0.8216252
276 12/1/2008 41.12 0.8105698
277 1/1/2009 41.71 0.8164598
278 2/1/2009 39.09 0.8030838
279 3/1/2009 47.94 0.7908264
280 4/1/2009 49.65 0.8168600
281 5/1/2009 59.03 0.8674532
282 6/1/2009 69.64 0.8877841
283 7/1/2009 64.15 0.8905513
284 8/1/2009 71.05 0.9197940
285 9/1/2009 69.41 0.9245562
286 10/1/2009 75.72 0.9481369
287 11/1/2009 77.99 0.9440196
288 12/1/2009 74.47 0.9490367
289 1/1/2010 78.33 0.9580379
290 2/1/2010 76.39 0.9458948
291 3/1/2010 81.20 0.9776127
292 4/1/2010 84.29 0.9948269
293 5/1/2010 73.74 0.9612612
294 6/1/2010 75.34 0.9637625
295 7/1/2010 76.32 0.9595087
296 8/1/2010 76.60 0.9611688
297 9/1/2010 75.24 0.9680542
298 10/1/2010 81.89 0.9824148
299 11/1/2010 84.25 0.9872643
300 12/1/2010 89.15 0.9919651
301 1/1/2011 89.17 1.0061374
302 2/1/2011 88.58 1.0125557
303 3/1/2011 102.86 1.0239607
304 4/1/2011 109.53 1.0438413
305 5/1/2011 100.90 1.0330579
306 6/1/2011 96.26 1.0239607
307 7/1/2011 97.30 1.0467916
308 8/1/2011 86.33 1.0186411
309 9/1/2011 85.52 0.9975062
310 10/1/2011 86.32 0.9805844
311 11/1/2011 97.16 0.9758002
312 12/1/2011 98.56 0.9770396
313 1/1/2012 100.27 0.9871668
314 2/1/2012 102.20 1.0033109
315 3/1/2012 106.16 1.0062387
316 4/1/2012 103.32 1.0072522
317 5/1/2012 94.66 0.9903932
318 6/1/2012 82.30 0.9727626
319 7/1/2012 87.90 0.9859988
320 8/1/2012 94.13 1.0076582
321 9/1/2012 94.51 1.0221813
322 10/1/2012 89.49 1.0129660
323 11/1/2012 86.53 1.0030090
324 12/1/2012 87.86 1.0103051
325 1/1/2013 94.76 1.0079629
326 2/1/2013 95.31 0.9902951
327 3/1/2013 92.94 0.9761812
328 4/1/2013 92.02 0.9816433
329 5/1/2013 94.51 0.9807768
330 6/1/2013 95.77 0.9695559
331 7/1/2013 104.67 0.9613536
332 8/1/2013 106.57 0.9608917
333 9/1/2013 106.29 0.9669310
334 10/1/2013 100.54 0.9649715
335 11/1/2013 93.86 0.9536525
336 12/1/2013 97.63 0.9399380
337 1/1/2014 94.62 0.9140768
338 2/1/2014 100.82 0.9046499
339 3/1/2014 100.80 0.9003331
340 4/1/2014 102.07 0.9097525
341 5/1/2014 102.18 0.9179365
342 6/1/2014 105.79 0.9233610
343 7/1/2014 103.59 0.9311854
344 8/1/2014 96.54 0.9152480
345 9/1/2014 93.21 0.9081827
346 10/1/2014 84.40 0.8919015
347 11/1/2014 75.79 0.8830022
348 12/1/2014 59.29 0.8671523
349 1/1/2015 47.22 0.8249464
350 2/1/2015 50.58 0.8000640
351 3/1/2015 47.82 0.7925186
352 4/1/2015 54.45 0.8105698
353 5/1/2015 59.27 0.8212878
354 6/1/2015 59.82 0.8087343
355 7/1/2015 50.90 0.7774236
356 8/1/2015 42.87 0.7606298
357 9/1/2015 45.48 0.7538067
358 10/1/2015 46.22 0.7649939
</pre>
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-9609914857288601552015-11-24T12:50:00.000-05:002015-11-24T12:53:46.053-05:00Forecasting P/S for MagnaAuto parts maker Magna (MGA) started the month of November trading around $53 and then, wham!, it lost $5 in one day on the announcement of the Trans Pacific Partnership (<a href="https://ustr.gov/trade-agreements/free-trade-agreements/trans-pacific-partnership/tpp-full-text">TPP</a>). The TPP is <br />
a proposed partnership agreement that would establish terms of trade between 12 Pacific Rim countries: Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore, the U.S., and Vietnam. One of the concerns for auto parts maker Magna is that under NAFTA, only auto parts containing 60% North American content could move duty free between Canada, Mexico, and the US. The TPP reduces the local content threshold to something in the range of 35% to 40%.<br />
<br />
<br />
<img alt="MGA Magna International Inc. daily Stock Chart" border="0" src="http://finviz.com/chart.ashx?t=MGA&ty=c&ta=1&p=d&s=l" height="194" id="chart0" width="400" /><br />
<br />
Here is a plot of Magna's quarterly sales. The Great Recession had a huge impact on slowing Magna's sales, but afterward, sales climbed steadily until late 2014.<br />
<img alt="" height="306" src="data:image/png;base64,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" width="400" /><br />
One interesting question is how does Magna currently compare on a standard valuation measure like price to sales (P/S). The P/S ratio, like P/E, P/B, and P/CF, is a measure of valuation. Lower values are preferred (generally less than 1 for P/S), but it is important to take into account industry effects. Also, like other valuation measures, a low P/S could indicate a value stock or it could indicate something else is wrong with the company.<br />
<br />
My approach is to compare price to trailing 12 month sales with price to forward 12 month sales. If the forward P/S is less than the trailing P/S the company may be undervalued. For this comparison I will need forecasts of future sales.<br />
<br />
I use a variety of different uni-variate models to forecast Magna's quarterly sales. Forecasting approaches include simple averages, Holt, Holt-Winters, ETS, ARIMA, and ANN. Data from the first quarter of 2001 to the fourth quarter of 2012 are used for training. Models are tested on out-of-sample forecasts over the period 2013:1 to 2015:3.<br />
<br />
Here is table of forecast accuracy measures ranked on MASE.<br />
<br />
<br />
<table border="0" cellpadding="0" cellspacing="0" style="width: 556px;"><colgroup><col style="mso-width-alt: 5489; mso-width-source: userset; width: 116pt;" width="154"></col>
<col span="3" style="mso-width-alt: 2446; mso-width-source: userset; width: 52pt;" width="69"></col>
<col span="3" style="mso-width-alt: 2304; mso-width-source: userset; width: 49pt;" width="65"></col>
</colgroup><tbody>
<tr height="19" style="height: 14.4pt;">
<td class="xl65" height="19" style="height: 14.4pt; width: 116pt;" width="154"></td>
<td class="xl65" style="width: 52pt;" width="69">ME</td>
<td class="xl65" style="width: 52pt;" width="69">RMSE</td>
<td class="xl65" style="width: 52pt;" width="69">MAE</td>
<td class="xl65" style="width: 49pt;" width="65">MPE</td>
<td class="xl65" style="width: 49pt;" width="65">MAPE</td>
<td class="xl65" style="width: 49pt;" width="65">MASE</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt Winters training</td>
<td class="xl67">10.3605</td>
<td class="xl67">416.6794</td>
<td class="xl67">272.9042</td>
<td class="xl67">-0.1470</td>
<td class="xl67">5.7363</td>
<td class="xl67">0.3097</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ETS training</td>
<td class="xl67">101.3534</td>
<td class="xl67">432.8289</td>
<td class="xl67">308.9523</td>
<td class="xl67">1.6208</td>
<td class="xl67">6.4568</td>
<td class="xl67">0.3506</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">STL training</td>
<td class="xl67">112.1135</td>
<td class="xl67">451.0617</td>
<td class="xl67">310.0710</td>
<td class="xl67">1.9976</td>
<td class="xl67">6.5669</td>
<td class="xl67">0.3519</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ARIMA training</td>
<td class="xl67">-0.1629</td>
<td class="xl67">447.0967</td>
<td class="xl67">321.3737</td>
<td class="xl67">-0.3155</td>
<td class="xl67">6.3713</td>
<td class="xl67">0.3647</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ANN2 training</td>
<td class="xl67">0.9323</td>
<td class="xl67">498.2682</td>
<td class="xl67">385.9291</td>
<td class="xl67">-0.9804</td>
<td class="xl67">7.5023</td>
<td class="xl67">0.4379</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ANN training</td>
<td class="xl67">-0.3573</td>
<td class="xl67">501.1293</td>
<td class="xl67">387.6661</td>
<td class="xl67">-1.0337</td>
<td class="xl67">7.5453</td>
<td class="xl67">0.4399</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt linear training</td>
<td class="xl67">3.4478</td>
<td class="xl67">516.7124</td>
<td class="xl67">389.2279</td>
<td class="xl67">-0.4852</td>
<td class="xl67">7.8051</td>
<td class="xl67">0.4417</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt ES training</td>
<td class="xl67">32.4932</td>
<td class="xl67">522.0256</td>
<td class="xl67">394.1387</td>
<td class="xl67">0.2721</td>
<td class="xl67">7.8724</td>
<td class="xl67">0.4472</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt dampled training</td>
<td class="xl67">49.4785</td>
<td class="xl67">519.0834</td>
<td class="xl67">396.3995</td>
<td class="xl67">0.3593</td>
<td class="xl67">7.8883</td>
<td class="xl67">0.4498</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ES training</td>
<td class="xl67">107.7185</td>
<td class="xl67">527.2579</td>
<td class="xl67">408.3396</td>
<td class="xl67">1.5849</td>
<td class="xl67">7.9818</td>
<td class="xl67">0.4634</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Naive training</td>
<td class="xl67">110.0000</td>
<td class="xl67">532.8356</td>
<td class="xl67">417.0213</td>
<td class="xl67">1.6185</td>
<td class="xl67">8.1515</td>
<td class="xl67">0.4732</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt linear test</td>
<td class="xl67">-151.2323</td>
<td class="xl67">765.2259</td>
<td class="xl67">576.4225</td>
<td class="xl67">-2.2910</td>
<td class="xl67">6.9925</td>
<td class="xl69">0.6541</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt damped test</td>
<td class="xl67">297.9467</td>
<td class="xl67">656.7112</td>
<td class="xl67">583.8959</td>
<td class="xl67">3.0695</td>
<td class="xl67">6.7486</td>
<td class="xl67">0.6626</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt Winters test</td>
<td class="xl69">24.8474</td>
<td class="xl67">691.3100</td>
<td class="xl67">601.4257</td>
<td class="xl67">-0.1406</td>
<td class="xl67">7.1852</td>
<td class="xl67">0.6825</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Holt ES test</td>
<td class="xl67">-274.5440</td>
<td class="xl67">859.5667</td>
<td class="xl67">625.6039</td>
<td class="xl67">-3.7699</td>
<td class="xl67">7.6591</td>
<td class="xl67">0.7099</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Naive test</td>
<td class="xl67">510.9091</td>
<td class="xl67">739.0499</td>
<td class="xl67">626.0000</td>
<td class="xl67">5.6066</td>
<td class="xl67">7.1001</td>
<td class="xl67">0.7104</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ES test</td>
<td class="xl67">510.9714</td>
<td class="xl67">739.0929</td>
<td class="xl67">626.0396</td>
<td class="xl67">5.6074</td>
<td class="xl67">7.1005</td>
<td class="xl67">0.7104</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ARIMA test</td>
<td class="xl67">-298.4399</td>
<td class="xl67">823.3481</td>
<td class="xl67">638.6404</td>
<td class="xl67">-4.0160</td>
<td class="xl67">7.7919</td>
<td class="xl67">0.7247</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">STL test</td>
<td class="xl67">578.2432</td>
<td class="xl67">789.4180</td>
<td class="xl67">648.2347</td>
<td class="xl67">6.4402</td>
<td class="xl67">7.3382</td>
<td class="xl67">0.7356</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ETS test</td>
<td class="xl67">649.8151</td>
<td class="xl67">815.6195</td>
<td class="xl67">685.7139</td>
<td class="xl67">7.2909</td>
<td class="xl67">7.7528</td>
<td class="xl67">0.7781</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">S. Naive test</td>
<td class="xl67">864.0909</td>
<td class="xl67">966.5054</td>
<td class="xl67">864.0909</td>
<td class="xl67">9.8515</td>
<td class="xl67">9.8515</td>
<td class="xl67">0.9805</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">S. Naive training</td>
<td class="xl67">450.2500</td>
<td class="xl67">1132.3782</td>
<td class="xl67">881.2500</td>
<td class="xl67">6.6540</td>
<td class="xl67">17.4009</td>
<td class="xl67">1.0000</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ANN test</td>
<td class="xl67">1073.7787</td>
<td class="xl67">1149.9015</td>
<td class="xl67">1073.7787</td>
<td class="xl67">12.3361</td>
<td class="xl67">12.3361</td>
<td class="xl67">1.2185</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">ANN2 test</td>
<td class="xl67">1105.4155</td>
<td class="xl67">1178.8549</td>
<td class="xl67">1105.4155</td>
<td class="xl67">12.7111</td>
<td class="xl67">12.7111</td>
<td class="xl67">1.2544</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td height="19" style="height: 14.4pt;">Mean training</td>
<td class="xl67">0.0000</td>
<td class="xl67">1550.3499</td>
<td class="xl67">1302.3281</td>
<td class="xl67">-11.0193</td>
<td class="xl67">29.8710</td>
<td class="xl67">1.4778</td>
</tr>
<tr height="19" style="height: 14.4pt;">
<td class="xl66" height="19" style="height: 14.4pt;">Mean test</td>
<td class="xl68">3184.2841</td>
<td class="xl68">3228.7508</td>
<td class="xl68">3184.2841</td>
<td class="xl68">37.0207</td>
<td class="xl68">37.0207</td>
<td class="xl68">3.6134</td>
</tr>
</tbody></table>
<br />
Based on the MASE for the test measures, Holt linear trend ranks lowest. Notice, however, that Holt-Winters has the lowest absolute ME among the test measures. I will estimate the Holt-Winters approach on data from 2001:1 to 2015:3, and then forecast 6 quarters ahead. <br />
<br />
Here is a plot of the forecasts.<br />
<img alt="" height="306" src="data:image/png;base64,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" width="400" /><br />
Here are the forecasted values in table form.<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 18pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> <span style="font-size: small;"> Qtr1 Qtr2 Qtr3 Qtr4
2015 8385.564
2016 8185.603 8534.537 8029.078 8783.678
2017 8569.665 </span></pre>
<br />
<br />
Here is a comparison between the trailing P/S and the forward P/S.<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="background-color: white; border: medium none; color: black; font-family: "Lucida Console"; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; margin: 0px; outline: medium none; text-indent: 0px; text-transform: none; white-space: pre-wrap ! important; word-break: break-all; word-spacing: 0px;" tabindex="0"><span style="font-size: small;"> P/S ttm P/S forward
[1,] 0.5509724 0.5480994</span></pre>
<br />
<br />
The forward P/S ratio is slightly less than the trailing P/S ratio indicating slight undervaluation.<br />
<br />
It is important to compare company P/S ratios to industry averages. For this I use the auto parts P/S value of 0.69 from <a href="http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/psdata.html">Damodaran</a>, indicating that based on P/S, Magna is undervalued relative to the industry average.<br />
<br />
As with any valuation exercise, it is important to compare these results for P/S with those of other valuation ratios like P/E, P/B, and P/CF.<br />
<br />
<br />
The R code and data are posted below.<br />
<br />
#########################################################<br />
# Economic forecasting and analysis<br />
# Fall 2015<br />
# Perry Sadorsky<br />
# Forecasting sales of Magna<br />
# with smoothing methods, ARIMA, and ANN<br />
##########################################################<br />
<br />
<br />
# load libraries<br />
library(fpp)<br />
<br />
<br />
# import data<br />
as1_data <- read.csv("C:/econ 6210/6210f15/week 10/as1_data.csv")<br />
View(as1_data)<br />
<br />
df = as1_data<br />
<br />
<br />
# define as time series<br />
df = ts(df, start=2000, frequency=4)<br />
df<br />
<br />
# extract sales<br />
y = df[,"MGA"]<br />
# y = df[,"SPLS"]<br />
y<br />
<br />
<br />
# some graphs<br />
par(font.axis = 2)<br />
par(font.lab = 2)<br />
plot(y, main = "MGA quarterly sales ($ millions)", xlab="", ylab="" , col ="blue", lwd=2)<br />
tsdisplay(y)<br />
par(mfrow = c(1,1)) <br />
<br />
<br />
# generate some returns<br />
y.ret = diff(log(y)) * 100<br />
tsdisplay(y.ret)<br />
par(mfrow = c(1,1)) <br />
<br />
<br />
# training period<br />
train <- window(y,start=c(2001, 1),end=c(2012, 4))<br />
train<br />
<br />
# test period<br />
test <- window(y, start=2013)<br />
<br />
# number of steps to forecast<br />
h = length(test) <br />
<br />
# out of sample forecast<br />
y5 <- window(y,start=c(2001, 1) )<br />
h2 = 6<br />
<br />
##########################################################<br />
# forecast using simple methods<br />
##########################################################<br />
<br />
<br />
yfit1 <- meanf(train, h=h)<br />
yfit2 <- naive(train, h=h)<br />
yfit3 <- snaive(train, h=h)<br />
<br />
plot(yfit1)<br />
plot(yfit2)<br />
plot(yfit3)<br />
<br />
# make a nice plot showing the forecasts<br />
plot(yfit1, plot.conf=FALSE,<br />
main="Forecasts for quarterly TGT sales")<br />
lines(yfit2$mean,col=2)<br />
lines(yfit3$mean,col=3)<br />
legend("topleft",lty=1,col=c(4,2,3),<br />
legend=c("Mean method","Naive method","Seasonal naive method"))<br />
<br />
<br />
# plot with forecasts and actual values<br />
plot(yfit1, plot.conf=FALSE,<br />
main="Forecasts for quarterly TGT sales")<br />
lines(yfit2$mean,col=2)<br />
lines(yfit3$mean,col=3)<br />
lines(y)<br />
legend("topleft",lty=1,col=c(4,2,3),<br />
legend=c("Mean method","Naive method","Seasonal naive method"),bty="n")<br />
<br />
<br />
<br />
##########################################################<br />
# exponential smoothing approaches<br />
##########################################################<br />
<br />
# simple exponential moving averages<br />
yfit4 <- ses(train, h = h)<br />
summary(yfit4)<br />
plot(yfit4)<br />
<br />
<br />
# holt's linear trend method<br />
yfit5 <- holt(train, h=h) <br />
summary(yfit5)<br />
plot(yfit5)<br />
<br />
<br />
# holt's exponential trend method<br />
yfit6 <- holt(train, exponential=TRUE, h=h) <br />
summary(yfit6)<br />
plot(yfit6)<br />
<br />
<br />
# holt's damped trend method<br />
yfit7 <- holt(train, damped=TRUE, h=h) <br />
summary(yfit7)<br />
plot(yfit7)<br />
<br />
<br />
# holt winter's method<br />
yfit8 <- hw(train, seasonal="multiplicative", h=h) <br />
summary(yfit8)<br />
plot(yfit8)<br />
<br />
<br />
# ETS method<br />
y.ets <- ets(train, model="ZZZ") <br />
summary(y.ets)<br />
yfit9 <- forecast(y.ets, h=h)<br />
summary(yfit9)<br />
plot(yfit9)<br />
<br />
<br />
# STL method<br />
y.stl <- stl(train, t.window=15, s.window="periodic", robust=TRUE)<br />
summary(y.stl)<br />
yfit10 <- forecast(y.stl, method="naive",h=h)<br />
summary(yfit10)<br />
plot(yfit10)<br />
<br />
<br />
##########################################################<br />
# arima method<br />
##########################################################<br />
<br />
y.arima <- auto.arima(train)<br />
yfit11 <- forecast(y.arima, h=h)<br />
plot(yfit11)<br />
<br />
<br />
##########################################################<br />
# ANN<br />
##########################################################<br />
<br />
fit.ann <- nnetar(train)<br />
yfit12 = forecast(fit.ann,h=h)<br />
plot(yfit12)<br />
<br />
<br />
fit.ann2 <- nnetar(train, repeats= 100)<br />
yfit13 = forecast(fit.ann2,h=h)<br />
plot(yfit13)<br />
<br />
<br />
<br />
##########################################################<br />
# accuracy measures<br />
##########################################################<br />
<br />
<br />
a1 = accuracy(yfit1, test)<br />
a2 = accuracy(yfit2, test)<br />
a3 = accuracy(yfit3, test)<br />
a4 = accuracy(yfit4, test)<br />
a5 = accuracy(yfit5, test)<br />
a6 = accuracy(yfit6, test)<br />
a7 = accuracy(yfit7, test)<br />
a8 = accuracy(yfit8, test)<br />
a9 = accuracy(yfit9, test)<br />
a10 = accuracy(yfit10, test)<br />
a11 = accuracy(yfit11, test)<br />
a12 = accuracy(yfit12, test)<br />
a13 = accuracy(yfit13, test)<br />
<br />
<br />
#Combining forecast summary statistics into a table with row names<br />
a.table<-rbind(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13)<br />
<br />
row.names(a.table)<-c('Mean training','Mean test', 'Naive training', 'Naive test', 'S. Naive training', 'S. Naive test' ,<br />
'ES training','ES test', 'Holt linear training', 'Holt linear test', 'Holt ES training', 'Holt ES test' ,<br />
'Holt dampled training','Holt damped test', 'Holt Winters training', 'Holt Winters test', 'ETS training', 'ETS test' , <br />
'STL training','STL test', 'ARIMA training','ARIMA test', 'ANN training', 'ANN test','ANN2 training', 'ANN2 test' )<br />
<br />
# order the table according to MASE<br />
a.table<-as.data.frame(a.table)<br />
a.table<-a.table[order(a.table$MASE),]<br />
a.table<br />
<br />
# write table to csv file<br />
# write.csv(a.table, "C:/econ 6210/6210f15/week 10/atable.csv")<br />
<br />
<br />
## forecast 6 periods into the future<br />
<br />
plot(hw(y5, seasonal="multiplicative", h=h2))<br />
par(mfrow = c(1,1))<br />
<br />
y_forc =hw(y5, seasonal="multiplicative", h=h2)$mean <br />
# y_forc = holt(y5, h=h2)$mean<br />
<br />
<br />
# forecasted sales for 2016<br />
# sales_f = y_forc[3] + y_forc[4] + y_forc[5] + y_forc[6]<br />
<br />
sales_f = 0<br />
for (i in 1:4){<br />
sales_f = sales_f + y_forc[i]<br />
}<br />
sales_f <br />
<br />
<br />
<br />
<br />
<br />
# calculate price to forward sales<br />
# data on November 21, 2015<br />
price = 44.94 # current stock prices<br />
shares = 404.12 # millions of shares outstanding<br />
<br />
<br />
ptos_f = price/(sales_f/shares)<br />
ptos_f<br />
<br />
<br />
<br />
<br />
# calculate price to trailing sales<br />
last = tail(y,4)<br />
sales_t = 0<br />
for (i in 1:4){<br />
sales_t = sales_t + last[i]<br />
}<br />
sales_t <br />
<br />
<br />
ptos_t = price/( sales_t /shares)<br />
ptos_t<br />
<br />
ps = cbind(ptos_t, ptos_f)<br />
colnames(ps) = cbind("P/S ttm ", "P/S forward")<br />
ps<br />
<br />
# compare with industry average<br />
# http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/psdata.html<br />
# auto parts 0.69 <br />
<br />
<br />
Data<br />
<br />
<table cellpadding="0" cellspacing="0" class="GEM3DMTCOFB ace_text-layer ace_line GEM3DMTCKT" style="-webkit-text-stroke-width: 0px; background-color: white; border: none; color: black; cursor: text; font-family: 'Lucida Console' !important; font-size: 18pt !important; font-style: inherit !important; font-variant: inherit !important; font-weight: inherit !important; letter-spacing: normal; line-height: inherit !important; orphans: auto; outline: none; padding-bottom: 8px; padding-left: 6px; text-align: start; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; width: 765px; word-spacing: 0px; word-wrap: break-word;"><tbody>
<tr><td align="left" style="font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; vertical-align: top;"><pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-user-select: text; border: none; font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; margin: 0px; outline: none; white-space: pre-wrap !important; word-break: break-all;" tabindex="0"> datacqtr MGA
1 2000Q1 2808
2 2000Q2 2610
3 2000Q3 2354
4 2000Q4 2741
5 2001Q1 2863
6 2001Q2 2817
7 2001Q3 2517
8 2001Q4 2829
9 2002Q1 3121
10 2002Q2 2896
11 2002Q3 2962
12 2002Q4 3443
13 2003Q1 3496
14 2003Q2 3660
15 2003Q3 3566
16 2003Q4 4623
17 2004Q1 5103
18 2004Q2 5113
19 2004Q3 4784
20 2004Q4 5653
21 2005Q1 5718
22 2005Q2 5858
23 2005Q3 5381
24 2005Q4 5854
25 2006Q1 6019
26 2006Q2 6369
27 2006Q3 5424
28 2006Q4 6368
29 2007Q1 6423
30 2007Q2 6731
31 2007Q3 6077
32 2007Q4 6836
33 2008Q1 6622
34 2008Q2 6713
35 2008Q3 5533
36 2008Q4 4836
37 2009Q1 3574
38 2009Q2 3705
39 2009Q3 4669
40 2009Q4 5419
41 2010Q1 5512
42 2010Q2 6050
43 2010Q3 5942
44 2010Q4 6598
45 2011Q1 7189
46 2011Q2 7338
47 2011Q3 6970
48 2011Q4 7251
49 2012Q1 7666
50 2012Q2 7727
51 2012Q3 7411
52 2012Q4 8033
53 2013Q1 8361
54 2013Q2 8962
55 2013Q3 8338
56 2013Q4 9174
57 2014Q1 8455
58 2014Q2 8911
59 2014Q3 8820
60 2014Q4 9396
61 2015Q1 7772
62 2015Q2 8133
63 2015Q3 7661
</pre>
</td></tr>
<tr><td align="left" style="font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; vertical-align: top;"><br /></td></tr>
<tr><td align="left" style="font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; vertical-align: top;"><table cellpadding="0" cellspacing="0" style="width: 765px;"><tbody>
<tr><td align="left" height="" rowspan="1" style="font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; vertical-align: top;" width="1"><br /></td></tr>
</tbody></table>
</td></tr>
</tbody></table>
<br />
<br />
<br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-60665522849813268172015-11-19T17:22:00.000-05:002015-11-24T12:53:22.652-05:00The Shale Oil Effect?The global economy is currently in a period of slow economic growth. At the same time, global oil production has continued to increase while global oil demand remains stagnate. The result of these two market forces is an oil supply glut leading to rapidly falling oil prices.<br />
<br />
Here is a plot of WTI oil prices. Between 2011 and 2014, oil prices held fairly steady around $100 per barrel. Then in the latter half of 2014, oil prices plunged.<br />
<br />
<img alt="" height="228" src="data:image/png;base64,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width="400" /><br />
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Lets take a look at the relationship between global oil supply and oil prices (measured using WTI).<br />
<img alt="" height="227" src="data:image/png;base64,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" width="400" /> <br />
<br />
<br />
Up until 75,0000 barrels per day, the relationship between oil prices and World oil production looks like a typical supply curve: upward sloping. After 75,0000 barrels per day, however, the upward sloping relationship breaks down. <br />
<br />
Now look at how World oil production has evolved across time. Notice that 75,000 barrels per day occurred in 2011 and after 2011, oil supply increased considerably. <br />
<img alt="" height="228" 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" width="400" /><br />
What is so special about 75,000 barrels per day and the year 2011? For one thing, US
shale oil production started to increase dramatically in 2011.<br />
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<img alt="" height="216" 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" width="400" /><br />
<br />
It is hard to make a case that US shale oil production is the only source of excess supply in the global oil market, but the timing does look interesting. US shale oil production has helped the US to dramatically lower oil imports. If foreign oil producers do not cut their oil production, then lower US oil imports means more oil on global markets for which there is no immediate demand. When oil demand is unchanging, small changes in oil supply can have large effects on oil prices. <br />
<br />
<br />
<br />
R code and data are posted below.<br />
<br />
#########################################################<br />
# Economic forecasting and analysis<br />
# Perry Sadorsky<br />
# Oil supply<br />
# November 2015<br />
##########################################################<br />
<br />
<br />
rm(list=ls())<br />
# load libraries<br />
library(fpp)<br />
<br />
# import data <br />
global_oil_text <- read.csv("C:/oil/Nov 2015/global_oil_text.csv")<br />
View(global_oil_text)<br />
<br />
<br />
df = global_oil_text<br />
<br />
# tell R that data set is a time series<br />
df = ts(df, start=c(1986,1), frequency=12)<br />
df<br />
<br />
<br />
# scatter plot<br />
<br />
par(font.axis = 2)<br />
par(font.lab = 2)<br />
plot(df[,"price"] ~ df[,"supply"], xlab="World oil production (thousands bbl per day)", ylab="Oil prices (WTI $/bbl)")<br />
abline(v=75000)<br />
<br />
<br />
plot( df[,"supply"], main="World oil production (thousands bbl per day)", ylab="", xlab="")<br />
abline(h=75000,col="blue")<br />
abline(v=2011,col="blue")<br />
<br />
<br />
plot( df[,"price"], main="Oil prices (WTI $/bbl)", ylab="", xlab="")<br />
abline(h=100,col="blue")<br />
abline(v=2011,col="blue")<br />
<br />
<br />
<br />
<br />
<br />
<pre class="GEM3DMTCFGB" id="rstudio_console_output" style="-webkit-text-stroke-width: 0px; -webkit-user-select: text; background-color: white; border: none; color: black; font-family: 'Lucida Console'; font-size: 18pt !important; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; margin: 0px; orphans: auto; outline: none; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap !important; widows: auto; word-break: break-all; word-spacing: 0px;" tabindex="0"> supply price
Jan 1986 55650.36 22.93
Feb 1986 55660.37 15.46
Mar 1986 55162.50 12.61
Apr 1986 55266.68 12.84
May 1986 56447.75 15.38
Jun 1986 57220.10 13.43
Jul 1986 58359.09 11.59
Aug 1986 59013.24 15.10
Sep 1986 54978.18 14.87
Oct 1986 55334.80 14.90
Nov 1986 56264.43 15.22
Dec 1986 56434.73 16.11
Jan 1987 55634.93 18.65
Feb 1987 54938.33 17.75
Mar 1987 54196.69 18.30
Apr 1987 54870.27 18.68
May 1987 55674.96 19.44
Jun 1987 55375.71 20.07
Jul 1987 57939.92 21.34
Aug 1987 58737.60 20.31
Sep 1987 58130.08 19.53
Oct 1987 58325.25 19.86
Nov 1987 57862.85 18.85
Dec 1987 57936.91 17.28
Jan 1988 57137.66 17.13
Feb 1988 57217.71 16.80
Mar 1988 57578.92 16.20
Apr 1988 57890.10 17.86
May 1988 57606.93 17.42
Jun 1988 57271.74 16.53
Jul 1988 57695.99 15.50
Aug 1988 58852.67 15.52
Sep 1988 59206.88 14.54
Oct 1988 60890.87 13.77
Nov 1988 61350.14 14.14
Dec 1988 61597.29 16.38
Jan 1989 58706.81 18.02
Feb 1989 58227.58 17.94
Mar 1989 58629.78 19.48
Apr 1989 59059.99 21.07
May 1989 58980.95 20.12
Jun 1989 59017.96 20.05
Jul 1989 59536.22 19.78
Aug 1989 60428.66 18.58
Sep 1989 60511.70 19.59
Oct 1989 61081.98 20.10
Nov 1989 61842.35 19.86
Dec 1989 61485.18 21.10
Jan 1990 60921.39 22.86
Feb 1990 61178.88 22.11
Mar 1990 62082.42 20.39
Apr 1990 61805.93 18.43
May 1990 61238.41 18.20
Jun 1990 60409.37 16.70
Jul 1990 60513.80 18.45
Aug 1990 56965.63 27.31
Sep 1990 59513.98 33.51
Oct 1990 59854.23 36.04
Nov 1990 60672.39 32.33
Dec 1990 60883.96 27.28
Jan 1991 60637.25 25.23
Feb 1991 60326.57 20.48
Mar 1991 60581.69 19.90
Apr 1991 59183.33 20.83
May 1991 59006.36 21.23
Jun 1991 59198.90 20.19
Jul 1991 60191.61 21.40
Aug 1991 59495.34 21.69
Sep 1991 60534.06 21.89
Oct 1991 60489.45 23.23
Nov 1991 60735.22 22.46
Dec 1991 61143.30 19.50
Jan 1992 61259.80 18.79
Feb 1992 60422.66 19.01
Mar 1992 59773.36 18.92
Apr 1992 60133.34 20.23
May 1992 59005.23 20.98
Jun 1992 59247.74 22.39
Jul 1992 59712.62 21.78
Aug 1992 59699.38 21.34
Sep 1992 59960.92 21.88
Oct 1992 60758.67 21.69
Nov 1992 60469.68 20.34
Dec 1992 60790.38 19.41
Jan 1993 60623.27 19.03
Feb 1993 60978.60 20.09
Mar 1993 60263.60 20.32
Apr 1993 59560.25 20.25
May 1993 59746.64 19.95
Jun 1993 59462.45 19.09
Jul 1993 60068.67 17.89
Aug 1993 59890.97 18.01
Sep 1993 59902.29 17.50
Oct 1993 60366.06 18.15
Nov 1993 60429.91 16.61
Dec 1993 60817.46 14.52
Jan 1994 61137.55 15.03
Feb 1994 60959.68 14.78
Mar 1994 60866.98 14.68
Apr 1994 60409.54 16.42
May 1994 60851.50 17.89
Jun 1994 61161.43 19.06
Jul 1994 60767.31 19.66
Aug 1994 60661.91 18.38
Sep 1994 61270.47 17.45
Oct 1994 61768.27 17.72
Nov 1994 61943.60 18.07
Dec 1994 62265.65 17.16
Jan 1995 61841.11 18.04
Feb 1995 62343.97 18.57
Mar 1995 61605.44 18.54
Apr 1995 62402.88 19.90
May 1995 62413.88 19.74
Jun 1995 61555.18 18.45
Jul 1995 62507.51 17.33
Aug 1995 62641.35 18.02
Sep 1995 63036.63 18.23
Oct 1995 62673.54 17.43
Nov 1995 62892.32 17.99
Dec 1995 63286.53 19.03
Jan 1996 63236.80 18.86
Feb 1996 63633.93 19.09
Mar 1996 63486.32 21.33
Apr 1996 63338.64 23.50
May 1996 63338.60 21.17
Jun 1996 63660.57 20.42
Jul 1996 63737.67 21.30
Aug 1996 63386.74 21.90
Sep 1996 63858.81 23.97
Oct 1996 64222.40 24.88
Nov 1996 64670.32 23.71
Dec 1996 65244.27 25.23
Jan 1997 65182.45 25.13
Feb 1997 65541.03 22.18
Mar 1997 65528.60 20.97
Apr 1997 66047.78 19.70
May 1997 65398.23 20.82
Jun 1997 64625.69 19.26
Jul 1997 65070.24 19.66
Aug 1997 65950.21 19.95
Sep 1997 66312.32 19.80
Oct 1997 66826.90 21.33
Nov 1997 66680.22 20.19
Dec 1997 66496.43 18.33
Jan 1998 67706.50 16.72
Feb 1998 68081.35 16.06
Mar 1998 67965.25 15.12
Apr 1998 67828.25 15.35
May 1998 67293.60 14.91
Jun 1998 67014.12 13.72
Jul 1998 66877.51 14.17
Aug 1998 65903.82 13.47
Sep 1998 65984.28 15.03
Oct 1998 66098.41 14.46
Nov 1998 66946.70 13.00
Dec 1998 66771.57 11.35
Jan 1999 66986.56 12.52
Feb 1999 67311.78 12.01
Mar 1999 66988.91 14.68
Apr 1999 65545.34 17.31
May 1999 65351.49 17.72
Jun 1999 64307.10 17.92
Jul 1999 65818.11 20.10
Aug 1999 65704.19 21.28
Sep 1999 65747.39 23.80
Oct 1999 66253.79 22.69
Nov 1999 66236.07 25.00
Dec 1999 65422.50 26.10
Jan 2000 66449.89 27.26
Feb 2000 67065.69 29.37
Mar 2000 67098.94 29.84
Apr 2000 67757.84 25.72
May 2000 68276.19 28.79
Jun 2000 68074.38 31.82
Jul 2000 68695.12 29.70
Aug 2000 69526.13 31.26
Sep 2000 69542.82 33.88
Oct 2000 69980.34 33.11
Nov 2000 70536.25 34.42
Dec 2000 69280.21 28.44
Jan 2001 69197.45 29.59
Feb 2001 68718.72 29.61
Mar 2001 69380.85 27.25
Apr 2001 68451.23 27.49
May 2001 67760.76 28.63
Jun 2001 66206.98 27.60
Jul 2001 68146.13 26.43
Aug 2001 68319.83 27.37
Sep 2001 67852.78 26.20
Oct 2001 67750.04 22.17
Nov 2001 68100.41 19.64
Dec 2001 67692.72 19.39
Jan 2002 66957.16 19.72
Feb 2002 67028.49 20.72
Mar 2002 66824.85 24.53
Apr 2002 66288.45 26.18
May 2002 66859.48 27.04
Jun 2002 66705.97 25.52
Jul 2002 67186.75 26.97
Aug 2002 66914.73 28.39
Sep 2002 67465.25 29.66
Oct 2002 68876.21 28.84
Nov 2002 69006.41 26.35
Dec 2002 67352.85 29.46
Jan 2003 67750.17 32.95
Feb 2003 69368.13 35.83
Mar 2003 69883.66 33.51
Apr 2003 68809.99 28.17
May 2003 68772.78 28.11
Jun 2003 67977.18 30.66
Jul 2003 68603.80 30.76
Aug 2003 69058.90 31.57
Sep 2003 69660.75 28.31
Oct 2003 70623.51 30.34
Nov 2003 70860.66 31.11
Dec 2003 72127.32 32.13
Jan 2004 71908.24 34.31
Feb 2004 71883.68 34.69
Mar 2004 71812.53 36.74
Apr 2004 71780.99 36.75
May 2004 71415.96 40.28
Jun 2004 72973.42 38.03
Jul 2004 73514.84 40.78
Aug 2004 72484.39 44.90
Sep 2004 73112.26 45.94
Oct 2004 73726.30 53.28
Nov 2004 73419.80 48.47
Dec 2004 73093.08 43.15
Jan 2005 73339.66 46.84
Feb 2005 73647.20 48.15
Mar 2005 73950.20 54.19
Apr 2005 74253.15 52.98
May 2005 74361.09 49.83
Jun 2005 73971.47 56.35
Jul 2005 73868.22 59.00
Aug 2005 73843.76 64.99
Sep 2005 73400.82 65.59
Oct 2005 73477.49 62.26
Nov 2005 74002.10 58.32
Dec 2005 74262.01 59.41
Jan 2006 73615.30 65.49
Feb 2006 73618.16 61.63
Mar 2006 73471.33 62.69
Apr 2006 73481.70 69.44
May 2006 73055.31 70.84
Jun 2006 73046.19 70.95
Jul 2006 74057.77 74.41
Aug 2006 73707.14 73.04
Sep 2006 73397.34 63.80
Oct 2006 73742.62 58.89
Nov 2006 73315.94 59.08
Dec 2006 73177.34 61.96
Jan 2007 72880.72 54.51
Feb 2007 73149.19 59.28
Mar 2007 73105.49 60.44
Apr 2007 73334.45 63.98
May 2007 72856.48 63.46
Jun 2007 72399.25 67.49
Jul 2007 73010.59 74.12
Aug 2007 72404.48 72.36
Sep 2007 73153.84 79.92
Oct 2007 73910.88 85.80
Nov 2007 73618.15 94.77
Dec 2007 74124.33 91.69
Jan 2008 74181.22 92.97
Feb 2008 74362.90 95.39
Mar 2008 74548.65 105.45
Apr 2008 73992.41 112.58
May 2008 74319.47 125.40
Jun 2008 74328.01 133.88
Jul 2008 75085.07 133.37
Aug 2008 73955.00 116.67
Sep 2008 72980.02 104.11
Oct 2008 74068.02 76.61
Nov 2008 73884.87 57.31
Dec 2008 73070.30 41.12
Jan 2009 72019.68 41.71
Feb 2009 72494.34 39.09
Mar 2009 72329.59 47.94
Apr 2009 72624.92 49.65
May 2009 72227.01 59.03
Jun 2009 72396.61 69.64
Jul 2009 73358.35 64.15
Aug 2009 72795.45 71.05
Sep 2009 73263.57 69.41
Oct 2009 73747.24 75.72
Nov 2009 73824.71 77.99
Dec 2009 73625.77 74.47
Jan 2010 73632.93 78.33
Feb 2010 74063.96 76.39
Mar 2010 74408.76 81.20
Apr 2010 74333.61 84.29
May 2010 74401.81 73.74
Jun 2010 74467.73 75.34
Jul 2010 74846.09 76.32
Aug 2010 74749.35 76.60
Sep 2010 75035.95 75.24
Oct 2010 74940.15 81.89
Nov 2010 75411.37 84.25
Dec 2010 75345.10 89.15
Jan 2011 75931.03 89.17
Feb 2011 75134.36 88.58
Mar 2011 74107.92 102.86
Apr 2011 73999.31 109.53
May 2011 73290.18 100.90
Jun 2011 74086.23 96.26
Jul 2011 74457.62 97.30
Aug 2011 74918.48 86.33
Sep 2011 74270.84 85.52
Oct 2011 74781.26 86.32
Nov 2011 75749.90 97.16
Dec 2011 76164.56 98.56
Jan 2012 76309.87 100.27
Feb 2012 76605.41 102.20
Mar 2012 76249.59 106.16
Apr 2012 76579.83 103.32
May 2012 75844.27 94.66
Jun 2012 75741.28 82.30
Jul 2012 75935.54 87.90
Aug 2012 75939.75 94.13
Sep 2012 75433.90 94.51
Oct 2012 75967.65 89.49
Nov 2012 76485.91 86.53
Dec 2012 76548.01 87.86
Jan 2013 75841.70 94.76
Feb 2013 75619.31 95.31
Mar 2013 75829.48 92.94
Apr 2013 76265.67 92.02
May 2013 76224.17 94.51
Jun 2013 76206.31 95.77
Jul 2013 76685.55 104.67
Aug 2013 76427.00 106.57
Sep 2013 75902.27 106.29
Oct 2013 76280.91 100.54
Nov 2013 76563.42 93.86
Dec 2013 76906.65 97.63
Jan 2014 77250.37 94.62
Feb 2014 77787.54 100.82
Mar 2014 77182.17 100.80
Apr 2014 77208.42 102.07
May 2014 76966.98 102.18
Jun 2014 77309.30 105.79
Jul 2014 77549.51 103.59
Aug 2014 77731.23 96.54
Sep 2014 78557.70 93.21
Oct 2014 79219.63 84.40
Nov 2014 79111.22 75.79
Dec 2014 79920.56 59.29
Jan 2015 79331.65 47.22
Feb 2015 79289.10 50.58
Mar 2015 80063.86 47.82
Apr 2015 79886.39 54.45
May 2015 79277.44 59.27
Jun 2015 79998.37 59.82
Jul 2015 80415.85 50.90</pre>
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-52969550312726859322015-09-10T12:45:00.000-04:002015-09-10T12:45:50.543-04:00Expected Shortfall for a Canadian ETF Portfolio: September 2015August was a volatile month for world equity markets. Broad equity markets in North America and Europe started August in a narrow trading range before taking steep drops in the middle of the month and then rebounding slightly. Historically, August can be a bad month for equities because many traders in North America and Europe take vacations. As a result, there is less volume which tends to magnify bad events.<br />
<br />
In this post I look at the damage this volatility did to a Canadian ETF portfolio. The approach is to calculate expected shortfall (ES) for a balanced portfolio of Canadian ETFs. This is an update on an earlier <a href="http://perrysadorsky.blogspot.ca/2015/07/expected-shortfall-for-canadian-etf.html">post</a> that I did. ES calculates the average expected loss over a particular time period for a given confidence interval.<br />
<br />
I use a portfolio of five broad asset classes: Canadian equities,
Canadian REITs, US equities, Europe and Far East (EAFE) equities, and
Canadian bonds. I use daily data sourced from Yahoo Finance. The ticker
symbols and asset classes are as follows.<br />
<br />
"XIU.TO", # Canadian equities, <br /> "XRE.TO", # Canadian REITS, <br /> "XSP.TO", # US equities (SP500), <br /> "XIN.TO", # EAFE equities, <br /> "XBB.TO" # Canada bonds,<br />
<br />
<br />
The portfolio weights are: <br />
XIU 30%<br />
XRE 10%<br />
XSP 20%<br />
XIN 10%<br />
XBB 30%<br />
<br />
Here is how each of the ETFs have performed over the past 100 trading days.<br />
<br />
<img alt="" height="345" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAArUAAAJXCAIAAAACTjufAAAgAElEQVR4nO3dXbaqOBCGYcbFgByPo/Gm19qTOJcOhr5QYyxCqEB+KuF9Lro9WhsChvhJUKcFAADg19S6AQAAwBzyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTywWU8btM0TfP9+f738z67fz9u34cet2mabo/lp+z7b39hkqt6/dHbd5UA2tsdCn586n4O6vChzbAwGPLBhbyO3vfR6keC9Hzw86g40n+WvPP3AOrbGQq+h6v3WMKRzLAwCPLBpbhjVBzAGfPB7zCwvwQA9UWHAu9g/R7Pp/IBw0KXyAcX8zpO53lrEDibD9bjACMBYFBkKMieDxgW+kQ+uJrPHODPcZktH0SuVmC+EbBkeyiIzC/ELj/4XTLDQv/IBxfzPcj9o5V8AFxMZCgIhoAT5w8YFjpFPriUz3Eqj1fmF4BLiQ4Ft4erkJ8+YH7hSsgHV+IdpT8XMK/zgfzsE9cnAgOJDwXvf7wTwvto5vrE6yEfXMfvOPDzz/UnnH6HiNA/vveEPsjkqhgGAGP2hgL5jQXe+YTAkcywMCzywVXI70T5+VYUme5/JiFjcw2hgWDxpzaZYQRs2R8K5OcXpun2CH0/0lZwYFgYBPkAAABI5AMAACCRDwAAgEQ+AAAAEvkAAABI5AMAACCRDwAAgEQ+AAAAEvkAAABI5AMAACCRDwAAgEQ+AAAAEvkAAABI5AMAACAVygeP2+fnPr8/6cnveQIA0InC+eCbE5bleZ+JCAAA9KBsPviNBH5YAAAAdpXLB9M035/P+83PB5w/AK7pcZskhgPAtJLXJ74vPZjvz9dthgPgmp73eXXykAlHwDa7n19YvdsAILU+TJWCc4tpE46t9zTQgayHbdV8kDwcRB79+/vTLERTVrPGYJM6bba+bLfS4F5ylfHi7MNBMRvnD+oOCAaf6Is3u/7qNJUG95KrrDwg2B1fyAd2avptkqbS4F5ylaPkA/+Dzk7a7AL54GQNTVJWGtxLrpJ88EY+sFPTb5M0lQb3kqscJx+cRj44WUOTlJUG95KrHCUfuLcL3zOIsfmF4FTKv3//Xo/++/eP29zmtrjdeT7IOeGo1/lOAzb1kg+8qcXH7ZMRcg4H60df9wSv0Shx4QbQ3KV6dZaNdaPE+UUB1vSSD0QUeP0z8/WJfoEodoHAlQWX9iob+HzawM3Wl+1WGtxLrpL5BSfL/IJbyPqGfjn61ZmqoUnKSoN7yVWOMb+w/mjz4zbP2S9X3jrI3Z3+3vSL/TMKAx8PAzdbX7ZbaXAvucpR8sHjlng5YuqE42tHxSdl/JrXrlvf1ixnWZa/v7/uarit3Fepfal0jb6+l3zwvv7gJw58JxpUlJuqnzvYChP9DLLAj3667uM23e6rISHJ7sZunSncGiL8+5mCxAD6yQen5d/U6ERD3nUBFfTTb93c4vtrlg/EBM3G+se4OE2oWWA/+xMI6CcfJH5+Ye38dKMo28oH4lKGw6vr9ER9p83Wl+1WGtxLrnKg+YXVycTEnJA0IASLDT7RBg+ZgZukrDS4l1zlMNcflP38wrHOtzVqlMsH6zlUa53P4GFMPnCVo+aDA7Jcn5ilpvLqBm52/dVpKg3uJVc5Rj6o8fkFzULa5oPzb2IiDRv4MCYfuMpR8kEG5IOTNTRJWWlwL7nKMfJBpc8v7NI/Q+uLFs+/6ScfNG+SptLgXnKV5AOnWj7Q7FVrh8PYRzH5wFWOkQ+Kf36haD4IXqOQuq6t9v95X8mwdf2U36TIclKbdLim8urIB66SfOCQD07W0CRlpcG95CpHyQenVR774vlg685IWfzCaWWZfr24oH76xud6RKnB9yvbWRGQF/mg+Oq21qtpT9ILf+Sf/qkFRits6apvPG6JP9gokA+AuGHzQfDNxfmvnfpL+eqxyfsaNc1yXCNftzXLCd7261P/9sq3lX0gy3JK9LfzbevslexcQqg2v7C7ruyrq1NDk5SVBvfSwvyCUPn6gyX6HWpJ1yhElrPVJPEnmksZBj6Muf7AVXL9gUM+OFlDk5SVBveSqyQfvNUf+5QzCJrK/M/TlV4JoHSpXlFzYy+1YzEM8kFj8XMDpVddevk29zm2XOr5Ih8AceSDt4Ynr+JzEEWbFJmDOLmu3csqDZ5zY37hUi9jNecXjq1OXD7V6SEzcJOUlQb3kqtkfuHNbD5o2KQK+WDZ2POd7klNpZEnN1h52XxQ4oLlXDXLsvwZ++1mTQ23lfuqZl9S9jdlPfng7Zr5YPF2i+aNjnJdYgk188HhdenLdivtPLnrysvmg7XK5w/cGt1/D1xBbOo6x8qrM9gkZaXBveQqOX/wRj4IEvkgOHilrmv9t5FPZ8QXlVoTbDn5wFWSD5wm+UD0z3U6jzRsfWbufJPO1FRencEmKSsN7iVXST54Ix9see0ZMfrkfdNfJx9sfRiEfOAqyQeOkRfa9bUF5INemqSsNLiXXCX54O1SY1+q4CvrsT229VcV9v/uRZEl1jWSITdqi6mNTeq6plpu3PqcDfTIB1gWXT7wL+wKFgTv0TyURZZwo1/XkN1pyI3aYmpjU/PBqD0wr+BUDvTIB28GT15ZaJK4HMHVbI1QU/RTWJELss43O5IPcu1Jt9XxM70Gn1xXyfyCY/BEfWqTql3WU3pRJZoUHJ3EOHZ+dZpKg3vJVV50fmEKOf+xkL+LfcRo+vwexFbNqwOtb9dsw1ZNanu2+oDrPMrla/pS5f6mXG9P+SDwC45pP8ZgLR/snhLYSvC+tvkg2H47+cDdTz5YLp4P1noa+/qRdF40XuYvKng78oeRsUDTqt0m6QvcGZcz622ln2Y/7/Pqt5yf9zklIVjb2CztabtRFdZ+fpxZmKBRIx/glNSXQ/0LuTuAdw/1Y2vUSF24/88e+1s/bX7cVvFg485N/WxsmobbVeFFN0s+SFrUlfWTDwycTlSWXW0KUAwKmln85fc04NZTszspqzlVqDyduOhOlq4r12dQds9wrtd1puyS1x9snD/Ilw/6PYp3z70VavZWms++abtP3G43Pna1x+HK5kN0pHKM+YXipxN7eTE22CSxY5PygeZJiZ9yqDyZuq5cj1nkgxqe97n1GwabR7HfIYOn5fSvoElN6i4fxBdFPlj6yQfFTyf28mJsv0mamtRBKjjMJTVJ09GDZwV2K9fFmuWQD5obNR8sqyt43KMuUpfLB8vG4ZBlbyvzgWZRwaamLkdZaW349SvHyAcmTicqy7oeWerUKM/5bx3GSdMZS/l8cGA55IMCar9hMHsUrzPBsorU2cfDrXkNzet66uZHzimSD3Zr/Mox8oGJ04nKsq5Hljo1qYsKjnepy8ly1lGz0vXZhTXyQXMD5wNh/YK95B4Pg2f41qcrzsTleD7wV3em2UlNUlYaHH5d5Sj54LRLjX2DieSDw8s5X3ZypQY7pMEmlXOdja3QAyOryHLwRgKBWMX5JcPpOh/wcaar2H3/cWBRhwsystYnrbUn5nmfX2cQv59sio0GwbM4yi+VGvX26+nOssxJ8SVmJZZfer0Xv911PkjD/IKdmgOLcu8Vzjdp6w2Hchpid6UlpjxO1rjKUeYXPh9e8j/EVP0DTQMcxfFjQb+opBP165VqumW5PXlmD2gqDQ6/rpL5hTfygZ2aA4s6M5AFR6itspr5YHd15IMNn3OHz/v8PWvA9Ylt8sGxPbm+JCJeRj4gH2TD6cTxbmc8Hcrt4O1+8sHyuL3OFXgnDX6ywr6ONra0k7vi2J83uRjo5CqCLysDd6Rh88HawM8ijll3ifqdxFS3NNWYPatPNKV9nqmvjS2rST7Q/GG15+hMWBm4I/WSDwLfrjxNU/yKJNky5hfM1NhpkjjJqTweMs4vLNGeyfxCOcwv+JIuCBBlh/fk7tyBcg5CubpIzXoTNBc/uUo7femy8wuPW+obhF/kAzs1pprkzhCSD8gHztUOhwP5YMrxVc3u0FtCZ+9Tm6QsS90D1fJBnT7pVw6TD84mBPKBnRqDTZrU31m0u0DyQRfIB4Lyzbr/4p0xH5xcTlJZ0h5wG3s+H8SP9N1LGcgHBZEP7NT02yRNJfmgPBMTjuMdDv4L//r+Y+/pd2uynIfI0qStfLBEv4Vp962/X7AbMmqOBrv1/eQDdzVSu48zKcuuObIk1fTbJE0l+aCK9hOOox4O4lxa6f6pPHVXZ0+6jV3ng/jSzucD0YCkZifV+JVj5APvt5get09G4PsTMQgjndNIM7RKTjhenNs5dfaSnedi3ZLdfCD+MHimwb9HPCpOzNjZFUs/+UBEgdc/yQcYhJHOaaQZdVxqYw/YnQ4fVeS1XPOH/nzE1qv+1nxN6hpL6yUfrL869XGbZ37f2WCTOm22vmy38kCTds86nlydqxxofuEs5hdO1gzcJDfloTki4jMRB2ZPqo0Gu/W95IP39Qc/ceA70aBCPrBT02+TNJWl84F420E+OIZ8cLJm4Ca5SyZT80GwnnzwXWDexWV0qbEPfdF3zvg0Z7VmDOBSG4tUx7pHlk5lp2eSD4D2lJ0zOFuZsWNf6hi51MaiDvLBzgLzLu6wKSTy+zSv0yy7v2Hz9/dnqobbGW8r+0CW5VTub8r12hmYsisxIBh8ohl86t/e3VcH+smrc55fzsn6YfPBGtcf2Knpt0maymNN0sxcHp7ddJVcf+Bw/cHJGpqkrMx1QRLXHxREPrBT02+TNJXkgy6QD07W0CRlJfngu8C8i8uIfGCnpt8maSoL5YMzVzW7SvKBQz44WUOTlJXkg+8C8y4uI/KBnZp+m6SpJB90gXxwsoYmKStzDQjkg4IuNfahO7v9c6vgwGcjDxeM5FIbi+5Y6J/kA8CEMy/emr6t+SRkT8dI4Bcc036MoaeNxfVY6J/kgzeDJ686bVKnzdaX7VYeblL8jGJkfsF/KFj2unOg+QXvB9v8+1ISAvMLJ2tokrKS+YXvAvMuLiPygZ2afpukqWyYD4InCdw9A+WD4G+z1f7B94EPh06bXX91mspcAwL5oKB+xj5cVLyL7s4v+ClBucykBliycf6AH3TFQA4PCEk15f48sMC8i8uI4QDGnckHwUyQ2ud7Okae95nrDzC03QGh9BVF5IM3gyevOm1Sp83Wl+1WlphfiPTev9APzQXHjoHmFzJgfuFkDU1SVhaaX9g6xndr/MqLzi+srm2eJn5/gdvR28o+kGU5qf3tdaDGa/z7t+rj6+08H3D9wdWbXX91msozq/N7afBqJJEA1jXkAxXOH9ip6bdJmspcw4FfFj9/sLs6V8n5A4d8cLKGJikri+YD90/3GSVRQz5QIR/Yqem3SZpK8kEXyAcna2iSsrJCPnB3kg8OIh/Yqem3SZrKk00Kjgjkg1/fqYTvdYrRyxNLTDjmqlmW5c/YxKWmhtvKfXWyn0yf33r2azQTiJFJSWXbeskHycPBWj9jHy5t651Bq1Wb9BkQ/EsOsn4/EmDEuqPGu+76tEEwHGv6f2/5gOEAo0sdDoqu2qr3QPA7BuS8PhEw4nw+UC72WE2Ssvmg3HAw9llxazX9NklTeb5Jrq++yrJ03WW0+YVpmu/P5/3mDwh8v/K1m11/dZrKXBOO+tlGzYH89/cnrleIrDqXcvmg/XCgLBv4eBi42fqy3UryQSXvucb5/nzdzvn9SAb7nrUamqSszDUgZL8aaZh8sCxL2eEAMEVMH9Zf6fAutbHoWrnRQDNVkXN1eReXEcMBOuK6a81+e6lj5FIbi641ebdQYl01DzmuP7DYpE6brS/brczSJHdGcfcQve78wjnML5ysoUnKylwDQvbZxt36rvNBGvKBnZp+m6SpzNWk14hAPgh53MKf2OL7lS/d7Pqr01RmzAd5R4PdevLBm8HO12mTOm22vmy3knxQxeOW+hUov8gHJ2tokrKSfPBdYN7FeeTvucbHhuCbi5NfcbUsyx9fYTbubWUfyLKcyv1Nud6u8sHZhEA+OFlDk5SVBvfSMlg++H6W8Xmfb4/X/1POJnL+wFBNv03SVBrcS65yoPMHZ5EPTtbQJGWlwb3kKsfIB8HvTeTr0oCcLnWMXGpjgQN6yQf+Fyd6JxD4fmUgn0sdI5faWOCAXvLB4l+x/P6m5epfl6YsG/h82sDN1pftVhrcS66S+QWH+YWTNTRJWWlwL7nKMeYXMgh/HgqAp/VhWk/rPQ10IPNBl3dx1bx2xH///ef/93VDlIka99/1ojQ168rmTarc7BdTTYqsLlLZqklJzc5+wI/KYN8r1CRrzVZumoU9Gals1aTUZlceEHodfQx2PvKBwT0ZqWzVJPJBCQb7HvnA2p6MVLZq0jXzQYavS4sz2PnIBwb3ZKSyVZPIByUY7HvkA2t7MlLZqknXzAfL+a9LizPY+cgHBvdkpLJVk8gHJRjse+QDa3syUtmqSZfNB2UTgsHORz4wuCcjla2aRD4owWDfIx9Y25ORylZNunA+KMlg5yMfGNyTkcpWTSIflGCw75EPrO3JSGWrJpEPAABAZ8gHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkCrlg8dtmu/P9L973ufp7fb4Luv3jvTix82741MSWqSyjYe2TdM2bx0tNs2tfGsDww+F22Dl+fKWc+x5W5Yl3PjPA6vFNt5Sg4YdEIYfDZYxBwRGg6Aq+eB5n2/3+5y8Vc/7/NkV7ubnefQeSyx+7Wf3z8MHtLfiIwvQtO27hjabtruYwEO/bfj2cDnStd+oQ31yu/HuX3KgabylBg08IAw/GsSX1OmAwGiwoUY+eHWEp7/7n/d5vt1mLwx97wk/Se/d891Lsf21Xfxqhdc1V8NKMn/ZYnXP+3y7hd/daNrWfNM0G/jzJEQ2IbZd9Tdqo0+uutY7tMcGD6/63Ykjx3GDp8+ekQeE4UeD3W3scEBgNNhSIR98NtLvOs/7PLkdMd0e/j3RhXh7bLt/7Rb/PjDP85nTNvGj5b3QVWM1bWu+aZoN3DuduLxjdKQJ9Tdqo0/Ko9SddHzcNtf2bdvrz6I5v8XTZ87QA8Lwo8HuNvY3IDAabCqeD/wdJHeefzO2I725of3hQFP8+6/n07XkyJ5XHS2rzTsyIlTftIQNFO0MrM3K87XfJwNbt9/4+C5ptKUGDT4gDD8aaLdRNNXugMBoEFE6Hzy+F1W8yI61NxyItxHx04na4vDzG8162wJHy+M7n7TV2sS2tdm0hA30qdvQZqN2+2Rg6wIt+G3883vR0XeRrbfUoNEHhOFHA+02+iwPCIwGMYXzQeDE0mdfr08nrjf6uZ50eYQu5UgtDge21Fz2/lP/aHHnqXZHBE3b2m1a+gYG/m77ZsuNivbJ362LnFEMNF4szsCWGjTugDD8aJC4jYG/277ZbrsYDaKK5oPQhry283kPXY4kO5aIdt88F5qFSSn+6RTuD5ND2Wrh7zvcVSnxNzeKtjXbtOQNTG5Do43a7pPrrfvedbvd5IG79f4gOPa3efrMGXpAGH40SNvG5Ga02C5Ggx2Nvh9poBOmuAD6a2HsYHTjQp2VfABs+WZ9emtZDAiw7oqjAd+vDAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPLB6B63aZqm+f58//t5n3/+/al4uT0Cd774f7JZ9LOM16q2/xxAM7GR4XH7PvSqE0e1++fPwhgKBkM+GN/P8e0f+Mvye7SvBoVvnRxLfj3v8+rB3wWEBxUA7WyPDOt84B6KH8oMBUMhH1yBO0DXR+/jFj5YYzliZWOxP/cwLADWbI0MgXzwOXhT8wFDQcfIB9fwOkjn9XEpTh6KPziaD9ZjAqMCYFB4ZFjlg9v9Pr8KEvMBQ0HPyAcX8ZkA3EgCq9mD4PyCdlCITFEy9whYEhwZ1vngsTxu3zMNDAXXQD64hu/1QeED+3t5kT8b+SNyODMoAH0KjwyhfLA87/N0e5APLoR8cAWfg3TnvN7WBcy65XNSEejM1sgQzAevgHBnfuE6yAcX4B2iinmC16Pn8gEXJQH2bY4M4XywulZxjaFgKOSD4YlIEBgHPv/a+qyjsD68Nz/U5KoYEgBjIiPDVj4QVyswFAyOfDC49RcXiC9I+vnmku/dp/OBXDSzjYAh0ZFhMx98DuqUfLAwFPSKfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAIh8AAACJfAAAACTyAQAAkMgHAABAKpQPHrfPj4J/f/ibX/0GAKAThfPBNycsy/M+ExEAAOhB2XzwGwn8sAAAAOwqlw+mab4/n/ebnw84fwAAQA9KXp/4vvRgvj9ft9PSwQRgT7Gj15zWexroQOaDLu/iMopv6t/fn2YhmrKaNQab1Gmz9WW7lQb3kquMF2cfDiw7PyAYfKIv3uz6q9NUGtxLrrLygFBzfEm7/oB8YKem3yZpKg3uJVdJPnDIBydraJKy0uBecpUD54M0lxr7rqzCWbJRXWpHjbexoquPt4GojHyAoWw9yzz7GpfaSyNtrEsGbqOIxTiv03yw/9UHwTeR//79ez36798/cft1mmV9v7j99/dnp8ZtVHw5l7r96tD6+/3byj6QZTmV+5tyvZd6RRlgfmF9euzv788PCsFtbN7sYZqkrDS4l5ax5hcet/DFleNff+C/IVg2RoTKTXK2Rh/Ne5fKTdp6KHV1mkqDg52r5PoD58yA8OrhDZ/orUNMHH3kg9Kr01Qa3Euucox88P5w4+ekwZGvTuxx7PMzQbxmCUWH0tbrig9Mpe2utMc+UNOl9o9yY9fHl/+H9vv5pZ5TJfaJUj/5YFmWb0gYMB8ET48o/9C/UTkfiNEz2LCa7clSs1x1+vZSm6zvLcqAXkfq6i71nO6q/yaqa53lg2VZPl+TlDkftD15dfg0oCuLv2Mo1+x1KHE153d46izM1ho1e3sJtTxyFne3SXHMLzS32z9394Zm3ir7E31gdeJdh8H+WaFJ/rGsf3LPrDFpUcwvNNY2H4i1580HkXOeYkSI7IQDM6DBZQZrzq8uUrP7Ju9wPnD/jD998dWtvZ4RzbFHPignVz6IL8pCPljX5Hp1rNzsA00KnjAgH7jKUfKB+13n7yWJxb8fKfWFYfkM/VuL8gPsbtsO54Pg6nZPrCmvfoq3ed1sZdmZmgOHemTrtpYmzpFEyiLNdjtWM2gGW36sxlWSD5yMr1jV8kGuDpMaqU+ubmmaD8o1aXdpeU/YkA+2PO/zJws8bp+MUDYf+O+P/WE98sLgD/3xpR14oY20PGnU0L97Xlcea3ZwGGp7zBwbNUTe2qrZelQkjPi6tlp+rMZVkg+c0vlA/9qgX13GDuMiwuHl6FcXf2eiX05qk+JblzEfBPPW1rvBw6sjH2wRUeD1z4L5YOuAD3Ys0S00r0a954PUdx6F8sHhbL6VD3b3pD/or4sjIVLco3nrGWz5sRpXedl8MIUU+hILt/D6X3SRWjNtfIGKZjmpt7fW1fXt12iw3sbXofS6faYvlajR1/eSD9YfWHjc5nnOlw9SK4M5ceue+LvJ+oNyfI3xTdv982MrPebwMiPv/vV/Hn+Wd3dj0hrrMNWY0vJu7NbhHDm1sHsYrmVscLyFJZZfuXelDuNJS448IxnHzOZ6yQfv6w9+4sB3okElaejXl2l6Q+TVqNxhHxFfr/5lL3Wlx/6w0AKzHMaRbqAf1u2MHXZaUkGJfKDsVH63af5yUi0fLN5eqrDSvAP+cm647vTI6icfnBbf1APne7dGhPXp5WDNXnvzXyK05jds9yqb5fQM6Hp15xd1eDmaJ253gcF8kNqkyEqZXyhHf6RravSjwbpsyndB0oGa4OpyDT7TagYwuKPyjoepY5RmD5w5SPNeOHK+xq8c4/qDDHaHA002PDAiHD78KuSD5fe1f9k7E57rRT1elrSotvlgCb1TIR90wU4+CC7qfJP0NZo+fGwciwwaGUeD1LLUfHCyq5APvgvMu7jDphAjl7QYvD2FLqspsa4Dy59qXdZUetutrXd9m3xwcoFbp980691KGNXE3xscaFj8Twptafbz/7na2ePBNWw+WCvx9Gh6VS/dwqWo0mtJWvvWnbkas3umpw4jncRIM+ookQ80D2V/Gc4onm9S21Y/HxxeJvkgiHzwlv3kVfzdgJ35hfo1kzed4d/jbrt/Bid9dk+EpjbJrSL11NyxR4M1FfrJwvzCr/MDgv409W4+sHOE7h6eykX5R3G8YLdJyhr9UayZcNydb9U3TLMo5hcaq5wPlui7AfKBv5eCNdP2t01kb9KivrpCs0DyQRdqjtcd5YPl91iIn707eYWQpkazriyLqpkPJo9yIRlr/ErywVuTfJBlORmbZKQmPgCJRcXH1sp7UlNJPuhC5fdz8bP01o5QTXyPLCpjhkhazslFrZeTMR8sG7Oo/nuhkytS1viV5IO3+vmgQo3BJiXlA82TQj440xhRSZbWtb4AAB5QSURBVD5wmuSDrXOK1o7QP+87g7dqppSvEt9aQlKT4gs5vyjRJOXhkJQPIjW7qyMfFEQ+sFOzJB4Pkfde5APywTH154MrnFDMmw80R+g6vme8RmF3OSUGBHdqJHs+2K2p0yf9SvLB26XGPvuSno7dtzK9M7JpRppRx6U29hjlLvIPT02q2F1F8Dz8mRamSt2KjOutv9II8gE6MHw+WGxsnYU2HLL+fZZ93W6sOWcOz/j0xO4yyz2J5IOFfOB0ejLfYJNKNDsS58eYX1gKX7bmKkeZX3jcpqCCP/herqby6ko0+/DUiTuZL+5Z3642v6CvUVYyv/BdYN7FZUQ+sFOTuijywcnVucpR8sH7B9s+Jw3ynz+wfDgYqcm1qCn68xPxaxQGywdLrU+9uUrywVtPYx9+XeG5s7CNFtqQ5BMSmF/o2NYJg6179I/2yNQWkQ8AEyz0TwttSPe8z9P3VIJanxs7oHg+2Lozcn/XTG3UsPkgODkZ+X2a12mW3d+w+fv7M1XD7Yy3lX0gy3Iq9zflek2NTXmVGBAMPtE9Dj7T3o/Dpd5f+fbuvqrZl1IHscoDgt3xhesP7NT02yRNJdcf1PA6a/BzSeLjxvWJ3TY7co3RsvGNakUPGa4/iDfmGLvjC/nATk2/TdJUkg/Ke97nTxZ43D4ZgXwwbLOnz3c1kg/Or8uvJB+8kQ/s1PTbJE0l+aA8EQVe/yQfjN9s8sH5dfmVo+SDwAee065IIh/Yqem3SZpK8kF56w8sPG7zPJMPRm/28Plg2e6Z5IMt3ulE/76UhNDP2IcrstA/LbRB63mfxdchfScaVHraWHjcEzfqM2hnu3rJB8EzhzlPJwJtWeifFtpQzaU2diTkg2p6yQcb5w/qnk5Ulg1/iu98Tb9N0lQyv9AF5hdO1rRq0hT9uQfmF3Zr/Mox5he8jzNx/YHtJnXabH3ZbuXhJq27KPmgHPLByZpWTSIfnFyXXzlKPjjtUmMfetS8izZvQE2X2tiRxPPBAOxsWtf5gOsPMJTmXbR5A2q61MaOZPh8sJjZuq7zQRrmF+zU9NskTSXzC11gfuFkTcMmVfiSgIbzC0utq5F268kHb8aPByOrG7jZ+rLdyqL5YP01tOSDY8gHJ2saNol8cGZdfuUo+eD9/Ujz/eEuVIxNLqy+TGma+H0mbkdvK/tAluWc7G/T5ydtIjUH1ks+cC7yQnumpmGTyAdn1uVXjpEPPt+F5H8pStbvRzJ+PBhZ3cDN1pftVpY7fxD88jjOHxxDPjhZQ5OUleSD7wLzLu7DXYr4vM/utEHtr1tXlg18PAzcbH3ZbmWdfOD+ST44hnxwsoYmKSvJB98F5l3cR/C7kB43vl8ZA9ntouuCvL36UsfIpTYW3bHQP3vJB6+E4MWBxy3v9yMBzcW76NajGTv2pY6RS20sumOhf/aTD05jfsFOTb9N0lQWml84861qrvKy8wslLljOVbMsy5+xC581NdxW7qtCfcldpPw6bPXL0a+3n3zgvl/5O83A9QcWm9Rps/Vlu5U288E0TVfOB2tcf3CyhiYpK4+tLvVq5QNXI+3W95IPvOsPvr/iyvcnYjSRXnpyfmH9xQmHFzWGS20sunPsaiTjFySV/vyC/0/yAUZTKB9Muq+kvdQxcqmNRXeOHa3XzAfr7zp43OaZ33c22KROm60v26080yTRS3PNL7hzj8wvOMwvnKyhScrKEvMLWa5G2q3vJR/8fjPSy3eiQYV8YKem3yZpKtvmg8hnIMkHPvLByRqapKzMdUES+aAg8oGdmn6bpKk82SS/o7oy5RfKBicgyQdB5IOTNTRJWUk++C4w7+IyIh/Yqem3SZrKVvkgeJGBWBr5wCEfnKyhScrKyvlAeRRfOh+U+Ljzsix/fAR53NvKPpBlOZGaKfTbS/5HnEW9pkbZNvKBM/Cr2sDNrr86TWXDfLD7vuKi+WDtUmMf+nXgsmRx5mB948yqR3WpjUWPDnyaSTwU/9DT7uchyQeAOZFrCLbqg4MC+SDiUhuLHp3MB5GXf2XnJx+8GTx51WmTOm22vmy38nyT/CsKxT3BRQXzQfDzUVx/4DC/cLKGJikrz6wueDXSst17/fmFrXHAfdp5t23kgzeDna/TJnXabH3ZbmXzfLBsvHUgH/jIBydraJKyMns+2B0N/LKtC5bJBz8uNfahayfnF3br9eu1q/APsgAWZLwaafcPU1d0gN1DjuEAHUl6vU/NE/rlWMUPsuASyAeVML9gp6bfJmkqszTJnyPc7brKw3ig+YXiP8hisO9Zq6FJysqTq0udbVx+TyhuXa3M/MIP8oGdmn6bpKkkH5Rn4gdZBj4cOm12/dVpKtvmg/U//UrywRv5wE5Nv03SVNbPB7urc5Wj5AMTP8gy8OHQabPrr05T2SQfiCWQD3aQD+zU9NskTWWuJk3TRD7IZQop9yWYSTXLsvwZ+2JWTQ23lfvqZD+ZPl+omrG/KevJB29jv6pZq+m3SZpK8kENhT+/YLDvWauhScrK5ucPIpUXPX+Q+naB29y2dvt1cNZcbz/5gM8v4ELOfAYh13rzLDDv4jJiOEBfti48rrBG84p/fgGwg3xQHPMLdmr6bZKmMnuTmF9Y4fML7WtokrLy/OoKXa2sXG9GdscX8oGdmn6bpKkkH9TA5xda19AkZSX54LvAvIv7+J45dJclTeL9w56exj5gWZaNb1AvvbqLuNTGomvML8R98oE/w7g+xRjFcIDukA/KudTGoneVhwJ/pTkXmHdxH+9c8BsJan+cSVk28Pm0gZutL9utzNuk3UP0ovMLpzG/cLKGJikrs6zu9WnnvKPBbn1H+WCa5vvzeb/5+SDf+QODna/TJnXabH3ZbiX5oAvkg5M1NElZST74LjDv4n68Lz2Y78/X7bQLEMgHdmr6bZKmknzQBfLByRqapKwkH3wXmHdxGZEP7NT02yRNJfmgC+SDkzU0SVlpcC+5yoHzAdcfWGxSp83Wl+1Wkg+6QD44WUOTlJUG95KrHDgfpLnU2IdhdP1xJssutbEYQP0eSz4A8HapY+RSGwscMGw+SP19ptdplt3fsPnjJ1bHva3sA1mWU7m/Kdd7qZdM5hdO1tAkZaXBvbQwvyAEEwMAX+vDtJ7WexroQOaDLu/iPh63cOMTrk+Me+2I//77z//v64YoEzXuv+tFaWrWlc2bVLnZL6aaFFldpLJVk5Kanf2AH5XBvleoSdaardw0C3syUtmqSanNrjwglFvZ45b6iwspDHY+8oHBPRmpbNUk8kEJBvse+cDanoxUtmrSZfNB2YRgsPORDwzuyUhlqyaRD0ow2PfIB9b2ZKSyVZMunA9KMtj5yAcG92SkslWTyAclGOx75ANrezJS2apJV80H7nedv5ccpH0/UpzBzkc+MLgnI5WtmkQ+KMFg3yMfWNuTkcpWTbpmPnje508WeNw+GYF8UKRJlZv9YqpJkdVFKls1iXxQgsG+Rz6wticjla2adM18IKLA65/kgyJNqtzsF1NNiqwuUtmqSeSDEgz2PfKBtT0ZqWzVpGvmg+d9FpcmPm7zPOfLBwAAoJyy1x/8xIHvRAMAADCNs5cAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAAJPIBAACQyAcAAEAiHwAAAIl8AAAApEr54HGb5vsz/e+e93l6uz2+y/q9I734cfPu+JSEFqls46Ft07TNW0eLTXMr39rA8EPhNlh5vrzlHHvelmUJN/7zwGqxjbfUoGEHhOFHg2XMAYHRIKhKPnje59v9Pidv1fM+f3aFu/l5Hr3HEotf+9n98/AB7a34yAI0bfuuoc2m7S4m8NBvG749XI507TfqUJ/cbrz7lxxoGm+pQQMPCMOPBvEldTogMBpsqJEPXh3h6e/+532eb7fZC0Pfe8JP0nv3fPdSbH9tF79a4XXN1bCSzF+2WN3zPt9u4Xc3mrY13zTNBv48CZFNiG1X/Y3a6JOrrvUO7bHBw6t+d+LIcdzg6bNn5AFh+NFgdxs7HBAYDbZUyAefjfS7zvM+T25HTLeHf090Id4e2+5fu8W/D8zzfOa0TfxoeS901VhN25pvmmYD904nLu8YHWlC/Y3a6JPyKHUnHR+3zbV92/b6s2jOb/H0mTP0gDD8aLC7jf0NCIwGm4rnA38HyZ3n34ztSG9uaH840BT//uv5dC05sudVR8tq846MCNU3LWEDRTsDa7PyfO33ycDW7Tc+vksabalBgw8Iw48G2m0UTbU7IDAaRJTOB4/vRRUvsmPtDQfibUT8dKK2OPz8RrPetsDR8vjOJ221NrFtbTYtYQN96ja02ajdPhnYukALfhv//F509F1k6y01aPQBYfjRQLuNPssDAqNBTOF8EDix9NnX69OJ641+riddHqFLOVKLw4EtNZe9/9Q/Wtx5qt0RQdO2dpuWvoGBv9u+2XKjon3yd+siZxQDjReLM7ClBo07IAw/GiRuY+Dvtm+22y5Gg6ii+SC0Ia/tfN5DlyPJjiWi3TfPhWZhUop/OoX7w+RQtlr4+w53VUr8zY2ibc02LXkDk9vQaKO2++R667533W43eeBuvT8Ijv1tnj5zhh4Qhh8N0rYxuRkttovRYEej70ca6IQpLoD+Whg7GN24UGclHwBbvlmf3loWAwKsu+JowPcrAwAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfAAAAiXwAAAAk8gEAAJDIBwAAQCIfjO5xm6Zpmu/P97+f99n9+/WYz9VFHpLLlm6Pn1Vt/zkAwCzywfher+LvV+3HzXutftz8l/OfwshDa8/7vAoAPyt6R4WtvwcAWEM+uAL3Wi1eyEUI8F/TIw+trfPBupyEAAA9IR9cw+v1ep4DL/riJMH7RT3y0NoqH4TKCQgA0BHywUV8rgX4eX0+e/3Bz8K9x8NRIJ4xAACWkA+u4XupoP+qLU4SvItuj/hDG0snHwDAQMgHV/B5vZav2/IiA+8lPPLQxvKZXwCAgZAPLkBeduhepIvlA65PBIDOkQ+GJz6aGPkQo/LzC+tX+s3PN7oq0gEA9IV8MDj59Ug/X5AU+H6jn1ML4Yd0+WDh+5EAoGPkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEh288EEYE/rwxTAsKyML8Gx79+/f69H//37J27//f0F7xe3//7+TNVwO+NtZR/IspzK/U25XvIBgHLsji/xse81bu7SlNWsMdikTputL9utNLiXXGW8mHwAoBy74wtjH4xr3kWbNwDAwOyOL4x9MK75RQAcIwDKsTu+ML9gp6bfJmkqjzXJ75/uNvMLAIZhd3whH9ip6bdJmsrz+WD5nEsgHwAYRrHx5XFbfRxhvj9TWsbYB5Mi0wqVOy3HCIByCo0vz/s83R6r+1ISAmMfbIr0TPIBgGEUGl8et1U82LhzE/MLdmr6bZKmMrVJkZ7J/AKAYdQ9f0A+sNekTputL9utfD2q7G/nuyX5AEAXio0vz/tc8vqDsV/VrNX02yRNJfkAANbsji/kAzs1HTUp+EXdolJ0LZcPxEcW/XvIBwCupub4kvn6A83g2MurmvGajpoU7BXrqwf8MteX3J3roKDPB7vdknwAoAt2x5fdsY/BEWu7Hztc54PlNxnEl2CqW3IIACjH7viiGfsYH+Hb6g9bJwZ2/3C9EPIBgIsof33id0ohNr8QnDY+8Lu3rxEz++/t5qrhdsbbW30gcvvVqcTt16TA7rp2a5YC/SS+jeQDAOWU/3zj4/bJCPm//yB4lti/sqyXWXPjNb00aavPbH1CwXUS5UUDmjKuPwAwhjrfj/T6Z858EKxZ/5MBdGBbr/dbxZF6ZT+xNudF9wZQTrnzB+LbDh63ec74/UjBsqQXDHQt/nqvrI/cf6ZhGZdmZ10Arqbs9Qc/ceA70aCi/KB5/C1gF2fF7deYalJk8igyvxDJB3n3EvMLAMZgd3whH9ipad6k4LMc/9YjscD4oweadGBFSYtayAcAmir9+87z/eG+aDnh5MFCPrBU07xJwc8Wihdj8gEAZFT4+gN/liHr7zuTDy7V7ODsQFI+yN6kSJmy62qWRj4A0Erpzy8877M7bVDk952D7yzXZZpFVagx2CT7zY5fVbBbtrtS8gEArJX//oOvxy3f+QNRuVXMANpEtU8EKPNBZdVaYmeTAYyn6OcXvDjwuOX9fWdlJQNoEzU/MRg/gdQE+QDAAOyOL/qTtBUuPRvjRP3hmtRF5X1G4pNHmnzA/AIApLI7vmQZZHNdT04+IB/s1izkAwADsTu+5Br7GEPry/ulhMwvNF8RgAuyO76QD/qVMR9olmPtKSYfABiAlfFlCjn/275//L5z9duT4neQz9S728o+kGU5lfubcr3kAwDl2B1fuP7ATk3SopK+kcL/eit3O+PFp5pKrj8AgDW74wv5wE5N0qL0+WBd80oJmusclU3SVJIPAGDN7vhCPrBTk7SoM/nA1WiuYDCbD5b00x7BevIBgIbsji/kAzs1SYvypwziyznzrdj6st3K+vlg68TJupJ8AKAVu+PLpT6/4C7JbN2QDOL5YF02pOB1FetH18XH1gIA2ZX/fuX3Dz1PeX/fOYn9YVS8nNhvcAT5YFlNsqwDgX8P+QCAQeV+n+nz+87uVxfK/L5zXK7rxYqeqA+eWK7WpLzzC8GXveByzn8wwfj8wtZJgnWf3LrN/AKAhgqNL5+fcvZ/3rnM7zvH5Xo1Ih+QD5JWFNy6152iJjL7QD4A0FCp8eXzW87eSYOfrLAv+9hn87z9VpMMNlVjNx8oHx2V3wkjc0nKnXPNfQigjnLjy/M+Tz/Sft65yNhncDwdKR/sXoinfGhsmg0nHwBozu74knd+IbLMhifqt7ZxmI9lbk2dlHhyD1c230tB0zQxvwCgoZrjS8vrDyKLbfVCG5+A7y4fTN73Hvp3BpdDPlAujXwAoBW74wv5oE6TyAfkAwBYszu+jJ0PNFtn/GOZPnFlvrh/vRzygXJp5AMArVgZX6YQO7+3m6vG3X6N7OdrjNyeNn6jOXh/ru1S9oEsy6nc35TrJR8AKMfu+FJu7LMwqma8iL251M8x9rJd9rEnAZRT7vuRgrJdn3iGhVGVfIDz2JMAyik3vjxuqd948KvoFLW/8PoT+cprD7u4/mB3T4qtyHXppb5st5LrDwBgreT4ci4hkA9cmbWvbfBp8kGJva0v260kHwDAmt3xpfTY13BsTf12PLMvA/qGuZRgdlt6xM4EUE6x8eV9BcJ8f7jvWW72+85Nln9+1cbzwYFWiXMJOImdCaCcQuOL9/vOLhe0+33n+CqMzy9svaY2abbfkq3vNqjZJE3ZbiXzCwCwVu7zC69U4P9oo4nvV16vwn4+WGy8GPt5xUhk0ZTtVpIPAGCt3PmDdRb4/OazToV8sGx8K/B67a1eQiLT9mZjTc0macp2K8kHALBWbHx53mf/0wuPW+oPPDfMB+v3xyPlgwObtpAPyAcALsbu+FInH6xrglcF9psP1lnnwAcOF/IB+QDAxdgdX2qOfcHL7go1IGmxJz8WuN6Ww0vjpcggnhQA5dgdX+zng2klUhNcl75h51/RRTJIXSAvRQbxpAAox8r4sn6tncz/fuP0+zuEu8txG6X87b7F+/1Dsa7d21v1qcuxfFvZB7Isp3J/U66XfACgHLvjS+XrD4In3t0/g9cw7q4ruAmp1x/oV7der1+z3sBp9fHOyD6veW0B1x+4Sq4/ANCK3fGl8tgXzwdb9ZF7srT/2MTEVuVuC5O2F83xpAAox+74YiEfRJqxdbXB7h8eJhae1LCth87kITTHkwKgHLvji4X5BXePcn5Bkw9Ofm+BSwYHvtsguHViLmMr9zC/kKtJzC8A6ILd8cVyPti6sKB0PvCXeeySiMi6yAd1mkQ+ANCFYuPL8/Ozjd+vWTb3+wt+TdKr424+qHOh3+7sQJZ8EDldcWZ1J2v0ZbuV5AMAWCs0vni/v/C4fTKC6XywbE/qd5EPznxWwk8G5IPSTSIfAOhCofFFRIHXP7vPB5FzDEvn+SCyKPJB3iaRDwB0odz5A/FrTI/bPAd+03Fb/bEvfvW+uDxwt7KCjB+X2FoUr0CW8ewAKKfs9Qc/ceA70aBiLR/oF0I+QB08OwDKsTu+NJlfOL+c3SE770n43SmPA+sKzpIwv5CrScwvAOhCzfGlg+sPsiwnY5N2a8gH5ysNPrmuknwAoBW74wtjn0Y8H5xZZvbFIjueIADl2B1fGPs0SuSDpe5VFDiM5whAOVbGlynEzu/t5qrJfvv1CpF9+VPi71A3ua3sA1mWU7m/KddLPgBQjt3xpf71BxVqsq+uxPUHwQV2uic1lQafXFfJ9QcAWin3/UhBpq9PrFBTYnUlLqskH5RrEvkAQBfKjS+P2yS+IikN+UBZ0+PHLqo1SVNpcC+5SvIBgFZKji/nEgL5QFlDPjhZaXAvuUryAYBW7I4vjH1K7KjL4qkHUE6x8eV9BcJ8f3x+6Dnl4oOFsQ/YwzECoJzCv8/k/wrD+jeb4i1jfsFMTb9N0lQa3EuukvkFAK2U/n3n5312pw2Sv18ZQFyJoxcAlpLnD9ZZ4HE79YGGH6+R8b///vP/+7ohykSN++96UZqadWXzJlVu9oupJkVWF6ls1aSkZpMAALRS9PedvTjwuE3nPu4okA/IB+QDACin19GHfEA+IB8AQDm9jj7kA/IB+QAAyul19CEfkA/IBwBQTq+jD/mAfEA+AIByGH0AAIBEPgAAABL5AAAASOQDAAAgkQ8AAIBEPgAAABL5AAAASOQDAAAgkQ8AAIBEPgAAABL5AAAASOQDAAAgkQ8AAIBEPgAAABL5AAAASOQDAAAgkQ8AAIBEPgAAABL5AAAASOQDAAAgkQ8AAIBUKR88btN8f6b/3fM+T2+3x3dZv3ekFz9u3h2fktAilW08tG2atnnraLFpbuVbGxh+KNwGK8+Xt5xjz9uyLOHGfx5YLbbxlgLAAVXywfM+3+73OXmMe97nz8Dobn5Gde+xxOLXqOv+efjl3VvxkQVo2vZdQ5tN211M4KHfNnxf72Tuab9Rh/rkduPdv2TsaLylAHBIjXzwemV4+oPx8z7Pt9vsvTX63hMest+D5XfMjI2e28WvVnivVauckcxftljd8z7fbuHTHZq2Nd80zQb+PAmRTYhtV/2N2uiTq671fgsfixJe9bsTR17VGzx9AHBIhXzwGfL815LnfZ7csDjdHv490YV44+f2C85u8e8D8zyfOYkbf/l8L3TVWE3bmm+aZgP35heWz+n17SbU36iNPilfs90UxOO2ubZv215/Fn3X3+LpA4BDiucDf7iUQ6l/MzasejPF+/lAU/z7r+fTteTIOKx6+Vxt3pF8UH3TEjZQtDOwNivP136fDGzdfuPju6TRlgLAYaXzgXeJ1Yt8pdnLB+K8Qnx+QVscHu0PzvcGXj692eWt1ia2rc2mJWygT92GNhu12ycDWxdowW/jn99LEL+LbL2lAHBc4XwQONPsTryv5hfWQ2BgCnbz+sSU4vDbt9R3ae8/9V8+3Vnr3XygaVu7TUvfwMDfbd9suVHRPvm7dZH5he2LAzZiUIstBYATiuaD0LDmLgwLXJ8oX2nEG73vu7vQnGxKcfhTZMlv0VYLf9/hrlGLn+1QtK3ZpiVvYHIbGm3Udp9cb933rtvtJl/Gt84WBJNgm6cPAE5o9P1InDBFT+ivAC6HfABs+b7zp7cCuBq+XxkAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACARD4AAAAS+QAAAEjkAwAAIJEPAACA9D9zInwL0m3UxwAAAABJRU5ErkJggg==" width="400" /> <br />
<br />
Even Canadian bonds (XBB.TO) got hit! For Canadian investors, there was no where to run and no where to hide.<br />
<br />
Here are what the updated expected shortfall values look like. For the ES calculations I calculate one day ES at a 99% confidence interval.<br />
<img alt="" height="345" 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To the right of the chart ES violations are evident for each of the three ES values. Lets take a closer look at the last 30 trading days.<br />
<span style="font-size: x-small;"><br /></span>
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<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-08-27<span> </span>0.0173129171
-0.01797793 -0.01302212 -0.01568852<span>
</span>0<span> </span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-08-28<span> </span>0.0011453308
-0.01797793 -0.01307287 -0.01584518<span> </span><span> </span>0<span>
</span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-08-31 -0.0050855477 -0.01797793 -0.01303772 -0.01572148<span> </span>0<span>
</span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-01 -0.0176022569 -0.01797793 -0.01304444 -0.01575105<span> </span>0<span>
</span>1</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-02<span> </span>0.0068626662
-0.01822957 -0.01311513 -0.01578005<span>
</span>0<span> </span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-03<span> </span>0.0035217033
-0.01822957 -0.01311116 -0.01577722<span>
</span>0<span> </span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-04 -0.0086586215 -0.01822957 -0.01303865 -0.01570228<span> </span>0<span>
</span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-08<span> </span>0.0099768929
-0.01822957 -0.01305171 -0.01570694<span>
</span>0<span> </span>0</span></span></div>
<span style="font-size: x-small;">
</span><div class="MsoNormal" style="background: white none repeat scroll 0% 0%; line-height: normal; margin-bottom: 0.0001pt;">
<span style="font-size: x-small;"><span style="color: black; font-family: "Lucida Console";">2015-09-09 -0.0055476529 -0.01822957 -0.01306676 -0.01569068<span> </span>0<span>
</span>0</span></span></div>
<span style="font-size: x-small;">
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<br />
ES calculated using the historical method results in hits (portfolio return less than ES) on August 21 and 24. ES calculated using the modified approach results in hits on August 21,24, and September 1. The ES is calculated using a confidence interval of 99%. So 99% of the time the actual loss should be no larger than the ES value. There is a 1% chance of losing more than the ES value. For daily data this works out to a "hit" or exceedance once every 100 days. According to the modified ES calculation we have had 3 hits in the past 30 days. Poisson clumping? Perhaps, but certainly beyond what the models predicted. <br />
<br />
<br />
Here is the R code.<br />
<br />
#########################################################<br /># Economic forecasting and analysis<br /># Perry Sadorsky<br /># ES for a Canadian portfolio<br /># September 2015<br />##########################################################<br /><br />rm(list=ls())<br />library(fpp)<br />library(quantmod)<br />library(PerformanceAnalytics)<br /><br /><br /><br /><br />symbols = c(<br /> "XIU.TO", # Canadian equities, <br /> "XRE.TO", # Canadian REITS, <br /> "XSP.TO", # US equities (SP500), <br /> "XIN.TO", # EAFE equities, <br /> "XBB.TO" # Canada bonds, <br />)<br /><br /><br /><br />getSymbols(symbols, from="1970-01-01")<br />m = length(symbols)<br />Y = Ad(XIU.TO)<br />for (i in 2:m) Y = cbind(Y, Ad(get(symbols[i])))<br />head(Y)<br />tail(Y)<br /><br /><br /><br />par(mfrow = c(3, 2))<br />for (i in 1:m) plot(tail (Y[, i], 100), main = symbols[i])<br />par(mfrow = c(1, 1))<br /><br /><br /><br />## returns<br />y.ret <- (na.omit(1 * diff(log(Y)) ))<br /><br /><br />par(mfrow = c(3, 2))<br />for (i in 1:m) {qqnorm(y.ret[, i], main = c("QQ Normal Plot",symbols[i]))<br /> qqline(y.ret[, i])}<br />par(mfrow = c(1, 1))<br /><br /><br />head(y.ret)<br />tail(y.ret)<br />weights <- c(0.3, 0.1, 0.2, 0.1, 0.3)<br />##########################################################<br /><br /><br />w.e = 1000<br />p.v = 0.99<br />port.ret = weights[1]*y.ret[,1] + weights[2]*y.ret[,2] + weights[3]*y.ret[,3]+ weights[4]*y.ret[,4] + weights[5]*y.ret[,5]<br />names(port.ret) = c("Portfolio")<br /><br /><br /><br />## create custom function<br />bt_p_ES <- function(x, p, w) {<br /> modified.ES = as.numeric ( ES(x, p=p, method="modified", portfolio_method = "component", weights = w)$MES)<br /> historical.ES = as.numeric (ES(x, p=p, method="historical", portfolio_method="component", weights = w)$`-r_exceed/c_exceed`)<br /> gaussian.ES = as.numeric ( ES(x, p=p, method="gaussian", portfolio_method = "component", weights = w)$ES)<br /> ans = c(historical.ES, gaussian.ES, modified.ES)<br /> names(ans) = c("Historical", "Gaussian", "Modified")<br /> return(ans)<br />}<br /><br /><br />## rolling analysis<br />tic <- Sys.time()<br />ret.es_1 <- rollapply(y.ret, width = w.e, FUN = bt_p_ES, p=p.v, w=weights, by.column = FALSE,<br /> align = "right" )<br />toc <- Sys.time()<br />toc - tic<br /><br />View(ret.es_1)<br />tail(ret.es_1)<br /><br /><br />## all three together with actual portfolio returns<br />ES.results = lag(ret.es_1, k=1)<br />chart.TimeSeries(merge(port.ret, -ES.results), legend.loc="topright")<br />tail(-ES.results)<br /><br /># identify exceedances<br />hit_hist = port.ret < -ES.results[,1]<br />hit_mod = port.ret < -ES.results[,3]<br /><br />colnames(hit_hist) = "hit_hist"<br />colnames(hit_mod) = "hit_mod"<br /><br />tail(merge(port.ret, -ES.results, hit_hist, hit_mod),30)<br /><br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-50696205085044903372015-07-09T15:43:00.002-04:002015-07-09T15:43:45.950-04:00Expected Shortfall for a Canadian ETF PortfolioIn the past few weeks we have seen a lot of volatility in the financial markets. Greece is on the verge of a bailout, leaving the Euro currency, or something in between. China's stock markets, after an impressive run up over the past year have come crashing down. At times like these it is always a good idea to quantify portfolio risk. I take the position of a Canadian investor who invests in a portfolio of broad based ETFs who wants to know their risk exposure as measured by expected shortfall (ES). ES is related to value at risk (VaR) but whereas VaR provides a measure of the minimum loss for a particular time period and coverage, ES calculates the average expected loss and is therefore closer to what an investor might expect to loose on average. <br />
<br />
I use a portfolio of five broad asset classes: Canadian equities, Canadian REITs, US equities, Europe and Far East (EAFE) equities, and Canadian bonds. I use daily data sourced from Yahoo Finance. The ticker symbols and asset classes are as follows.<br />
<br />
"XIU.TO", # Canadian equities, <br /> "XRE.TO", # Canadian REITS, <br /> "XSP.TO", # US equities (SP500), <br /> "XIN.TO", # EAFE equities, <br /> "XBB.TO" # Canada bonds,<br />
<br />
Here is how each of the ETFs have performed.<br />
<br />
<img alt="" height="342" 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" width="400" /><br />
<br />
Except for XBB, the other ETFs experienced large drops during the 2008 - 2009 financial crisis. The Canadian bond market, however, just kept on chugging along.<br />
<br />
Here are what the QQ plots look like for the daily continuously compounded returns.<br />
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<img alt="" height="342" 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" width="400" /><br />
The plots indicate heavy tails for each of the asset returns. This would indicate that assuming normally distributed returns is probably not the best assumption to make when measuring risk.<br />
<br />
Now on to calculating expected shortfall (ES). For comparison purposes, ES is calculated three ways (Historical, Gaussian, Modified). ES is calculated using a fixed width moving window of 1000 days. At the end of the day, the current ES is shifted forward by one day to provide a forecast for the next day's shortfall. Coverage is set at 99% which means that ES is calculated as the average loss over the first percentile of the return distribution. As we have seen from the QQ plots, the Gaussian approach is likely to lead to underestimating the expected shortfall because it does not account for heavy tails. In these situations, Modified often works well because it takes into account skewness and excess kurtosis.<br />
<br />
The first portfolio I consider is a diversified portfolio with the following portfolio weights.<br />
<br />
XIU 30%<br />
XRE 10%<br />
XSP 20%<br />
XIN 10%<br />
XBB 30%<br />
<br />
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<img alt="" height="342" 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" width="400" /><br />
Expected shortfall calculated from the Historical or Modified versions is very similar. In comparison, ES calculated from the Gaussian approach results in more violations.<br />
<br />
Here are what the recent daily ES values look like.<br />
<br />
<span class="Apple-style-span" style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #e1e2e5; border-collapse: separate; color: black; font-family: 'Lucida Console'; font-size: 24px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: 2; text-align: -webkit-left; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;"></span><br />
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="-webkit-user-select: text; border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap !important; word-break: break-all;" tabindex="0"> <span style="font-size: small;"> Historical Gaussian Modified
2015-06-30 -0.02057 -0.01398 -0.02016
2015-07-02 -0.02057 -0.01398 -0.02016
2015-07-03 -0.02057 -0.01398 -0.02016
2015-07-06 -0.02057 -0.01397 -0.02016
2015-07-07 -0.02057 -0.01395 -0.02018
2015-07-08 -0.02057 -0.01395 -0.02017</span></pre>
<br />
<br />
<br />
The ES modified value for July 8, 2015 indicates that on that day there was a 1% chance of loosing an average of 2.017% of the portfolio. In other words, the average daily loss on a $100,000 portfolio is $2017. <br />
<br />
For comparison purposes, I also estimate expected shortfall for a traditional 60/40 portfolio (60% XIU and 40% XBB).<br />
<br />
<img alt="" height="342" 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" width="400" /><br />
As in the previous case, the Historical and Modified ES values are similar while the Gaussian ES values lead to more rejections. The most recent value for the Modified ES indicates an average portfolio loss of 1.676% at 99% coverage. The average loss on a $100,000 portfolio is $1676. Notice that the ES values from the 60/40 portfolio are smaller in absolute value than those from the 5 asset portfolio. Interestingly, the Canadian 60/40 portfolio provides less risk than the diversified five asset portfolio.<br />
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<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="-webkit-user-select: text; border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; font-family: 'Lucida Console'; font-size: 18pt !important; line-height: 1.2; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap !important; word-break: break-all;" tabindex="0"> <span style="font-size: small;">Historical Gaussian Modified
2015-06-30 -0.0164 -0.01278 -0.01682
2015-07-02 -0.0164 -0.01278 -0.01681
2015-07-03 -0.0164 -0.01278 -0.01680
2015-07-06 -0.0164 -0.01278 -0.01680
2015-07-07 -0.0164 -0.01277 -0.01676
2015-07-08 -0.0164 -0.01277 -0.01676</span></pre>
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While the most recent volatility in the financial markets has been a concern, there has been no breaching of the Historical or Modified expected shortfall values in either the five asset portfolio or the 60/40 portfolio.<br />
<br />
<br />
The R code is provided below. It takes about 12 minutes to complete one rolling ES calculation.<br />
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#########################################################<br /># Economic forecasting and analysis<br /># Perry Sadorsky<br /># ES for a Canadian portfolio<br /># July 2015<br />##########################################################<br /><br />rm(list=ls())<br />library(fpp)<br />library(quantmod)<br /><br /><br /><br /><br />symbols = c(<br /> "XIU.TO", # Canadian equities, <br /> "XRE.TO", # Canadian REITS, <br /> "XSP.TO", # US equities (SP500), <br /> "XIN.TO", # EAFE equities, <br /> "XBB.TO" # Canada bonds, <br />)<br /><br /><br /><br />getSymbols(symbols, from="1970-01-01")<br />m = length(symbols)<br />Y = Ad(XIU.TO)<br />for (i in 2:m) Y = cbind(Y, Ad(get(symbols[i])))<br />head(Y)<br />tail(Y)<br /><br /><br /><br />par(mfrow = c(3, 2))<br />for (i in 1:m) plot(Y[, i], main = symbols[i])<br />par(mfrow = c(1, 1))<br /><br /><br /><br />## returns<br />y.ret <- (na.omit(1 * diff(log(Y)) ))<br /><br /><br />par(mfrow = c(3, 2))<br />for (i in 1:m) {qqnorm(y.ret[, i], main = c("QQ Normal Plot",symbols[i]))<br /> qqline(y.ret[, i])}<br />par(mfrow = c(1, 1))<br /><br /><br />head(y.ret)<br />tail(y.ret)<br />weights <- c(0.3, 0.1, 0.2, 0.1, 0.3)<br />##########################################################<br /><br /><br />w.e = 1000<br />p.v = 0.99<br />port.ret = weights[1]*y.ret[,1] + weights[2]*y.ret[,2] + weights[3]*y.ret[,3]+ weights[4]*y.ret[,4] + weights[5]*y.ret[,5]<br />names(port.ret) = c("Portfolio")<br /><br /><br /><br />## create custom function<br />bt_p_ES <- function(x, p, w) {<br /> modified.ES = as.numeric ( ES(x, p=p, method="modified", portfolio_method = "component", weights = w)$MES)<br /> historical.ES = as.numeric (ES(x, p=p, method="historical", portfolio_method="component", weights = w)$`-r_exceed/c_exceed`)<br /> gaussian.ES = as.numeric ( ES(x, p=p, method="gaussian", portfolio_method = "component", weights = w)$ES)<br /> ans = c(historical.ES, gaussian.ES, modified.ES)<br /> names(ans) = c("Historical", "Gaussian", "Modified")<br /> return(ans)<br />}<br /><br /><br />## rolling analysis<br />tic <- Sys.time()<br />ret.es_1 <- rollapply(y.ret, width = w.e, FUN = bt_p_ES, p=p.v, w=weights, by.column = FALSE,<br /> align = "right" )<br />toc <- Sys.time()<br />toc - tic<br /><br />View(ret.es_1)<br />tail(ret.es_1)<br /><br /><br />## all three together with actual portfolio returns<br />ES.results = lag(ret.es_1, k=1)<br />chart.TimeSeries(merge(port.ret, -ES.results), legend.loc="topright")<br />tail(-ES.results)<br /><br /><br />##########################################################<br />##### comparison with 60/40 portfolio<br />##########################################################<br />port.ret.b = 0.6*y.ret[,1] + 0.4*y.ret[,5]<br />names(port.ret.b) = c("Portfolio 60/40")<br />y.ret.b = y.ret[,c(1,5)]<br />tail(y.ret.b)<br /><br /><br /><br />## rolling analysis<br />tic <- Sys.time()<br />ret.es_1.b <- rollapply(y.ret.b, width = w.e, FUN = bt_p_ES, p=p.v, w=c(.6,.4), by.column = FALSE,<br /> align = "right" )<br />toc <- Sys.time()<br />toc - tic<br /><br />View(ret.es_1.b)<br />tail(ret.es_1.b)<br /><br /><br />## all three together with actual portfolio returns<br />ES.results.b = lag(ret.es_1.b, k=1)<br />chart.TimeSeries(merge(port.ret.b, -ES.results.b), legend.loc="topright")<br />tail(-ES.results.b)<br /><br /><br />
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-31642139322243801472015-07-02T17:42:00.001-04:002015-07-02T17:51:44.573-04:00Correlations Between Canadian ETFsJune was a difficult month for world equity markets. China was down double digits and most European markets fell between 3% and 5%. Canadian equity markets got caught up in the downdraft.<br />
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We know that equity correlation increased during the 2008-2009 financial crisis, but how does current equity correlation compare with the past. In order to investigate further, I took the position of a Canadian investor with a diversified portfolio of ETFs. For the analysis, I used daily data pulled from Yahoo Finance.<br />
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"XIU.TO", # Canadian equities, <br />
"XRE.TO", # Canadian REITS, <br />
"XSP.TO", # US equities, SP500<br />
"XIN.TO", # EAFE equities,<br />
"XBB.TO" # Canada bonds, <br />
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<br />
Here is how the ETFs have performed. Except for bonds, the other assets took a big hit during the financial crisis.<br />
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<img alt="" height="291" 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" width="400" /><br />
<br />
<br />
Here are what the correlations look like from 2002 until the end of June 2015. Bonds are negatively correlated with each of the equities with the largest negative correlation with the US. The largest positive correlation is between the US and other developed markets.<br />
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<img alt="" height="291" 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" width="400" /><br />
<br />
Here are what the correlations look like from 2002 until the end of December 2007. Each equity correlation is smaller (in absolute value) than the corresponding value over the full sample indicating greater diversification benefits over this first sub-sample. Notice that during this time period, bonds correlated positively with REITs.<br />
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<img alt="" height="291" 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" width="400" /><br />
<br />
Here are what the correlations look like during the financial crisis. Notice that correlations between equity ETFs were much higher during the financial crisis then during the previous period (2002 - 2007). For example, the correlation between XIU and XIN went from 58.6% to 85.9%!<br />
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<img alt="" height="291" 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" width="400" /><br />
<br />
Here are what the correlations look like over the post-crisis period (July 2009 until the end of June 2015). Correlations for the equity ETFs are smaller than they were during the financial crisis, but they have not yet returned to pre-crisis values. In some cases, bonds have actually gotten more negatively correlated with equities. The correlations between Canada and the US or Canada and developed international markets are very high (over 70%) <br />
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<img alt="" height="291" 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" width="400" /><br />
<br />
The overall takeaway is that in the post-crisis period, correlations between Canada, the US, and other developed markets remains high. This makes it difficult to diversify risk between these asset classes. The correlation between bonds and equities in the post-crisis period has, in some cases, gotten even more negative (possibly in anticipation of Central Bank interest rate increases).<br />
<br />
<br />
<br />
Here is the R code. <br />
<br />
#########################################################<br />
# Economic forecasting and analysis<br />
# Perry Sadorsky<br />
# Heat Map for a Canadian ETF portfolio<br />
# June 2015<br />
##########################################################<br />
<br />
<br />
rm(list=ls())<br />
library(fpp)<br />
library(quantmod)<br />
library(gplots)<br />
<br />
<br />
<br />
## define symbols<br />
symbols = c(<br />
"XIU.TO", # Canadian equities, <br />
"XRE.TO", # Canadian REITS, <br />
"XSP.TO", # US equities, SP500<br />
"XIN.TO", # EAFE equities,<br />
"XBB.TO" # Canada bonds, <br />
)<br />
<br />
<br />
## get data<br />
getSymbols(symbols, from="1970-01-01")<br />
m = length(symbols)<br />
Y = Ad(XIU.TO)<br />
for (i in 2:m) Y = cbind(Y, Ad(get(symbols[i])))<br />
head(Y)<br />
tail(Y)<br />
<br />
<br />
## plots<br />
par(mfrow = c(3, 2))<br />
for (i in 1:m) plot(Y[, i], main = symbols[i])<br />
par(mfrow = c(1, 1))<br />
<br />
<br />
## returns<br />
ret <- (na.omit(1.0 * diff(log(Y)) *<br />
100))<br />
colnames(ret) = c("XIU", "XRE", "XSP", "XIN", "XBB")<br />
head(ret)<br />
tail(ret)<br />
<br />
<br />
## helper function from<br />
## http://blog.revolutionanalytics.com/2014/08/quantitative-finance-applications-in-r-8.html<br />
generate_heat_map <- function(correlationMatrix, title)<br />
{<br />
<br />
heatmap.2(x = correlationMatrix, # the correlation matrix input<br />
cellnote = correlationMatrix, # places correlation value in each cell<br />
main = title, # heat map title<br />
symm = TRUE, # configure diagram as standard correlation matrix<br />
dendrogram="none", # do not draw a row dendrogram<br />
Rowv = FALSE, # keep ordering consistent<br />
trace="none", # turns off trace lines inside the heat map<br />
density.info="none", # turns off density plot inside color legend<br />
notecol="black") # set font color of cell labels to black<br />
<br />
}<br />
<br />
<br />
<br />
<br />
# Convert each to percent format<br />
corr1 <- cor(ret) * 100<br />
corr2 <- cor(ret['2002-10/2007-12']) * 100<br />
corr3 <- cor(ret['2008-10/2009-05']) * 100<br />
corr4 <- cor(ret['2009-07/2015-06']) * 100<br />
<br />
heatmap.2(corr1)<br />
<br />
corr1 = round(corr1, digits = 1)<br />
corr2 = round(corr2, digits = 1)<br />
corr3 = round(corr3, digits = 1)<br />
corr4 = round(corr4, digits = 1)<br />
<br />
par(cex.main=.8)<br />
<br />
generate_heat_map(corr1, "Correlations of Canadian ETF Returns, Oct 2002 - June 2015")<br />
generate_heat_map(corr2, "Correlations of Canadian ETF Returns, Oct 2002 - Dec 2007")<br />
generate_heat_map(corr3, "Correlations of Canadian ETF Returns, Oct 2008 - May 2009")<br />
generate_heat_map(corr4, "Correlations of Canadian ETF Returns, July 2009 - June 2015")<br />
par(cex.main=1.0)<br />
<br />
<br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-5981049628846883962015-06-21T21:50:00.000-04:002015-06-21T21:50:46.985-04:00A Closer Look at the Oil Price - Gasoline Price Relationship in OntarioIn a recent <a href="http://www.r-bloggers.com/what-a-gas-the-falling-price-of-oil-and-ontario-gasoline-prices/">post</a>, Myles Harrison investigated the relationship between Ontario average gasoline prices and US oil prices. He concluded by showing a strong positive relationship between the two. The recent drop in oil prices has led to a drop in gasoline prices, but my question is whether gas prices are as low as they should be given that oil is currently a few cents below $60 per barrel.<br />
<br />
In this post, I will conduct further analysis by extending his work in several directions. First, Myles loaded the gasoline price data from the Ontario government website using a call to wget. This is certainly an easy way to pull down data from websites. The only drawback is that two separate programs are being used: one to load the data, and another to analyze the data. I will load the data directly into R. In addition I will load additional data on oil prices, exchange rates, and the Canadian CPI. My approach results in code that is more lengthy than Myles, but has the advantage of being contained in one program. The data set is monthly starting in January 1990 and continuing until March of 2015. Second, I will investigate the gasoline price - oil price relationship using 4 different specifications of the data. From these relationships I will make a forecast of current gasoline prices based off of current oil prices. Third, I will provide some tests for residual stationarity to ensure that the the variables are cointegrated.<br />
<br />
The gasoline price <a href="http://www.energy.gov.on.ca/en/fuel-prices/">data</a> comes from an Ontario government website. Additional data on oil prices, exchange rates, and Canadian consumer price index (CPI) comes from the Federal Reserve of St. Louis database (<a href="http://research.stlouisfed.org/fred2/">FRED data</a>).<br />
<br />
First. here are some plots of Ontario gasoline prices and US oil prices. As expected, the two series move together closely.<br />
<br />
<img alt="" height="352" 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" width="400" /> <br />
<br />
I estimate four specifications.<br />
<br />
S1: gasoline prices ~ oil prices (nominal values not adjusted for exchange rates)<br />
S2: log(gasoline prices) ~ log(oil prices) (nominal values not adjusted for exchange rates)<br />
S3: gasoline prices ~ oil prices (adjusted for exchange rates and inflation)<br />
S4: log( gasoline prices) ~ log(oil prices) (adjusted for exchange rates and inflation)<br />
<br />
Specification S1 is the most basic and does not adjust for inflation or different currencies. Notice the strong positive correlation between gasoline prices and oil prices. The simple correlation between the two is 0.973. <br />
<br />
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="border-color: initial; border-style: none; border-width: initial; font-family: "Lucida Console"; line-height: 1.2; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important; word-break: break-all;" tabindex="0"><span style="font-size: small;"><span class="Apple-style-span" style="background-color: #e1e2e5; border-collapse: separate; color: black; font-family: "Lucida Console"; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: 2; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;"><span style="font-size: x-small;"> </span></span></span></pre>
<span style="font-size: small;"><span class="Apple-style-span" style="background-color: #e1e2e5; border-collapse: separate; color: black; font-family: "Lucida Console"; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: 2; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;">
</span></span>
<img alt="" height="353" 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" width="400" /><br />
<br />
Using this specification to forecast gas prices (for oil prices of
$50, $55, $60, $65, labelled as points 1 through 4 respectively) results
in the following table. For example, at oil prices of $60 (point 3) the forecast of average
Ontario gasoline prices is 90.9 cents/liter. The most recent actual
value is $1.16 which is beyond the upper 95% confidence level. Based on
this analysis, gas prices are too high. <br />
<div class="MsoNormal">
<br /></div>
<br />
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="border-color: initial; border-style: none; border-width: initial; font-family: "Lucida Console"; line-height: 1.2; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important; word-break: break-all;" tabindex="0"><span style="font-size: small;">Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
1 82.5 74.3 90.6 70.0 95.0
2 86.7 78.5 94.9 74.2 99.2
3 90.9 82.8 99.1 78.4 103.4
4 95.1 87.0 103.3 82.6 107.7</span></pre>
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="border-color: initial; border-style: none; border-width: initial; font-family: "Lucida Console"; line-height: 1.2; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important; word-break: break-all;" tabindex="0"><span style="font-size: small;"> </span></pre>
<br />
Also notice the increase in variability towards the right of the plot.
This can be controlled for by estimating a log - log specification (S2).<br />
<br />
Specification 4 is the one that is most consistent because each variable is expressed in real Canadian dollars. The log - log specification accounts for changing variability in the data.<br />
<br />
<img alt="" height="353" 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" width="400" /><br />
<br />
<br />
Here is a table comparing the gasoline price forecasts from each of the four specifications.<br />
<br />
<br />
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="border-color: initial; border-style: none; border-width: initial; font-family: "Lucida Console"; line-height: 1.2; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important; word-break: break-all;" tabindex="0"><span style="font-size: small;"> S1 S2 S3 S4
Oil coefficient 0.845 0.477 0.702 0.439
t stat 72.871 81.483 55.576 51.631
R-squared 0.946 0.957 0.911 0.899
Forecast (oil=50) 82.472 86.766 86.606 88.295
Forecast (oil=55) 86.696 90.801 90.116 92.068
Forecast (oil=60) 90.921 94.648 93.626 95.653
Forecast (oil=65) 95.146 98.330 97.136 99.074</span></pre>
<br />
<br />
The estimated coefficient on the oil price variable is positive and statistically significant in each specification. The dependent variable in each specification is different so it is not possible to compare across models, but clearly for each specification, oil prices have a statistically significant positive impact on Ontario gasoline prices. The gasoline price forecast for oil prices at $60 range between 90.9 cents/liter to 95.7 cents/liter. The interesting point is that the current price of gasoline at $1.16 per liter is higher than the upper 95% confidence bound in all cases.<br />
<br />
Lastly, the table below shows the p-values from an ADF test on the residuals from each specification. The residuals from each specification are stationary at 5% which is consistent with a cointegrating relationship between gasoline prices and oil prices.<br />
<span style="font-size: small;"><span style="font-family: inherit;"><br /></span></span>
<span style="font-family: inherit;"><span class="Apple-style-span" style="background-color: #e1e2e5; border-collapse: separate; color: black; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: 28px; orphans: 2; text-indent: 0px; text-transform: none; white-space: pre-wrap; widows: 2; word-spacing: 0px;"></span></span><br />
<pre class="GFKJRPGCGCB" id="rstudio_console_output" style="border-color: initial; border-style: none; border-width: initial; line-height: 1.2; margin: 0px; outline-color: initial; outline-style: none; outline-width: initial; white-space: pre-wrap ! important; word-break: break-all;" tabindex="0"> S1 S2 S3 S4
Residuals adf p value 0.000867 0.000264 0.000044 0.0464</pre>
<br />
<br />
The main take-away is that Ontario gasoline prices and oil prices are cointegrated and this is robust to several different regression specifications. Based on this analysis, gasoline prices are higher than the upper 95% confidence band.<br />
<br />
<br />
<br />
Here is the R code.<br />
<br />
#########################################################<br />
# Economic forecasting and analysis<br />
# Perry Sadorsky<br />
# June 2015<br />
# Forecasting Ontario gasoline prices<br />
##########################################################<br />
<br />
## basic reference is from this post<br />
## http://www.r-bloggers.com/what-a-gas-the-falling-price-of-oil-and-ontario-gasoline-prices/<br />
<br />
<br />
# load libraries<br />
library(fpp)<br />
library(quantmod)<br />
library(reshape2)<br />
library(urca)<br />
<br />
<br />
##########################################################<br />
## collect data from Ontario government<br />
##########################################################<br />
<br />
furl = c("http://www.energy.gov.on.ca/fuelupload/ONTREG1991.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1992.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1993.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1994.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1995.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1996.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1997.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1998.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG1999.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2000.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2001.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2002.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2003.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2004.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2005.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2006.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2007.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2008.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2009.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2010.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2011.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2012.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2013.csv",<br />
"http://www.energy.gov.on.ca/fuelupload/ONTREG2014.csv" <br />
)<br />
<br />
gasp = c(1,2,3,4,5,6,7,8,9,10,11,12)<br />
xx = read.csv("http://www.energy.gov.on.ca/fuelupload/ONTREG1990.csv",skip=1) <br />
xx = head(xx,-3)<br />
xx = tail(xx,12)<br />
xx = xx[,"ON.Avg"]<br />
gasp = cbind(gasp,xx)<br />
<br />
<br />
for (i in 1:24) {<br />
xx = read.csv(furl[i],skip=1)<br />
xx = head(xx,-3)<br />
xx = tail(xx,12)<br />
xx = xx[,"ON.Avg"]<br />
gasp =cbind(gasp,xx)<br />
}<br />
<br />
## output is a nice matrix<br />
View(gasp)<br />
<br />
<br />
## stack the data into a column<br />
s_gasp = melt(gasp)<br />
s_gasp = s_gasp[-c(1:12),] <br />
View(s_gasp) <br />
<br />
<br />
on_avg = s_gasp[,3]<br />
tail(on_avg)<br />
View(on_avg)<br />
<br />
<br />
## append 2015 data <br />
# "http://www.energy.gov.on.ca/fuelupload/ONTREG2015.csv"<br />
<br />
yy = read.csv("http://www.energy.gov.on.ca/fuelupload/ONTREG2015.csv",skip=1) <br />
yy = head(yy,-3)<br />
yy = tail(yy,6)<br />
yy= yy[,"ON.Avg"]<br />
yy<br />
<br />
on_avg_a = append(on_avg,yy)<br />
tail(on_avg_a)<br />
View(on_avg_a)<br />
<br />
gas = ts(on_avg_a, start=1990, end=c(2015,3), frequency=12)<br />
plot(gas,main="Ontario gas prices (cents per liter)", xlab="",ylab="")<br />
<br />
<br />
##########################################################<br />
## now load data on oil prices and FX<br />
##########################################################<br />
<br />
# load data from FRED into new environment<br />
symbol.vec = c("MCOILWTICO" , "EXCAUS", "CANCPIALLMINMEI")<br />
data <- new.env()<br />
getSymbols(symbol.vec, src="FRED", env = data)<br />
<br />
<br />
(data$MCOILWTICO["1990-01-01::"])-> oil<br />
(data$EXCAUS["1990-01-01::"])-> fx<br />
(data$CANCPIALLMINMEI["1990-01-01::"])-> cpi<br />
<br />
# rebase cpi<br />
tail(cpi,14)<br />
cpi2014 = mean( cpi[(300-11):300] )<br />
cpi_2014 = cpi/cpi2014 * 100<br />
mean( cpi_2014[(300-11):300] )<br />
<br />
<br />
par(mfrow = c(3, 1))<br />
plot(oil,main="Oil prices")<br />
plot(fx,main="$C/$US")<br />
plot(cpi_2014,main="CPI")<br />
par(mfrow = c(1, 1))<br />
<br />
<br />
df_fred = cbind(oil,fx,cpi_2014)<br />
head(df_fred)<br />
tail(df_fred)<br />
## latest cpi value is for March<br />
<br />
df_fred_1 = ts(df_fred, start=1990, end=c(2015,3), frequency=12)<br />
nrow(df_fred_1)<br />
length(gas)<br />
<br />
oil_n = df_fred_1[,1]<br />
<br />
par(mfrow = c(2, 1))<br />
plot(gas,main="Ontario gas prices (cents per liter)", xlab="",ylab="")<br />
plot(df_fred_1[,1],main="Oil prices ($/bbl)", xlab="",ylab="")<br />
par(mfrow = c(1, 1))<br />
<br />
cor(gas,df_fred_1[,1])<br />
<br />
<br />
##########################################################<br />
## linear regressions<br />
##########################################################<br />
<br />
table = matrix( NA, nrow=7, ncol=4)<br />
table2 = matrix( NA, nrow=1, ncol=4)<br />
<br />
lm1 = lm(gas ~ oil_n)<br />
<br />
lm1s = summary(lm1)<br />
table[1,1] = lm1s$coefficients[2,1]<br />
table[2,1] = lm1s$coefficients[2,3]<br />
table[3,1] = lm1s$r.squared<br />
<br />
<br />
plot(gas ~ oil_n,<br />
ylab="Ontario gas prices (cents per liter)", xlab="WTI oil prices ($/bbl)")<br />
abline(lm1)<br />
adf1 = ur.df(lm1$residuals, type="drift",selectlags="AIC", lags=12)<br />
adf1@testreg$coefficients <br />
table2[1,1] = adf1@testreg$coefficients[2,4]<br />
<br />
## some forecasting<br />
fcast <- forecast(lm1, newdata=data.frame(oil_n=c(50, 55, 60, 65)))<br />
fcast<br />
plot(fcast)<br />
<br />
<br />
table[4,1] = fcast$mean[1]<br />
table[5,1] = fcast$mean[2]<br />
table[6,1] = fcast$mean[3]<br />
table[7,1] = fcast$mean[4]<br />
table<br />
<br />
<br />
<br />
## log- log specification<br />
lm2 = lm(log(gas) ~ log(oil_n))<br />
summary(lm2)<br />
<br />
lm2s = summary(lm2)<br />
table[1,2] = lm2s$coefficients[2,1]<br />
table[2,2] = lm2s$coefficients[2,3]<br />
table[3,2] = lm2s$r.squared<br />
<br />
plot(log(gas) ~ log(oil_n),<br />
ylab="Log of Ontario gas prices (cents per liter)", xlab="Log of WTI oil prices ($/bbl)")<br />
abline(lm2)<br />
adf2 = ur.df(lm2$residuals, type="drift",selectlags="AIC", lags=12)<br />
adf2@testreg$coefficients <br />
table2[1,2] = adf2@testreg$coefficients[2,4]<br />
<br />
## some forecasting<br />
fcast <- forecast(lm2, newdata=data.frame(oil_n=c(50, 55, 60, 65)))<br />
fcast<br />
plot(fcast)<br />
<br />
exp(fcast$mean)<br />
<br />
table[4,2] = exp(fcast$mean[1])<br />
table[5,2] = exp(fcast$mean[2])<br />
table[6,2] = exp(fcast$mean[3])<br />
table[7,2] = exp(fcast$mean[4])<br />
<br />
<br />
<br />
## now do this in real Canadian dollars<br />
gas_r = gas/df_fred_1[,3]*100<br />
oil_r = (df_fred_1[,1]*df_fred_1[,2])/df_fred_1[,3]*100<br />
<br />
<br />
lm3 = lm(gas_r ~ oil_r)<br />
summary(lm3)<br />
<br />
lm3s = summary(lm3)<br />
table[1,3] = lm3s$coefficients[2,1]<br />
table[2,3] = lm3s$coefficients[2,3]<br />
table[3,3] = lm3s$r.squared<br />
<br />
plot(gas_r ~ oil_r,<br />
ylab="Ontario real gas prices (cents per liter)", xlab="Real oil prices ($/bbl)")<br />
abline(lm3)<br />
adf3 = ur.df(lm3$residuals, type="drift",selectlags="AIC", lags=12)<br />
adf3@testreg$coefficients <br />
table2[1,3] = adf3@testreg$coefficients[2,4]<br />
<br />
## some forecasting<br />
fcast <- forecast(lm3, newdata=data.frame(oil_r=c(50, 55, 60, 65)))<br />
fcast<br />
plot(fcast)<br />
<br />
table[4,3] = fcast$mean[1]<br />
table[5,3] = fcast$mean[2]<br />
table[6,3] = fcast$mean[3]<br />
table[7,3] = fcast$mean[4]<br />
<br />
<br />
<br />
## log- log specification in real Canadian dollars<br />
lm4 = lm(log(gas_r) ~ log(oil_r))<br />
summary(lm4)<br />
<br />
lm4s = summary(lm4)<br />
table[1,4] = lm4s$coefficients[2,1]<br />
table[2,4] = lm4s$coefficients[2,3]<br />
table[3,4] = lm4s$r.squared<br />
<br />
<br />
plot(log(gas_r) ~ log(oil_r),<br />
ylab="Log of real Ontario gas prices (cents per liter)", xlab="Log of real oil prices ($/bbl)")<br />
abline(lm4)<br />
adf4 = ur.df(lm4$residuals, type="drift",selectlags="AIC", lags=12)<br />
adf4@testreg$coefficients <br />
table2[1,4] = adf4@testreg$coefficients[2,4]<br />
<br />
## some forecasting<br />
fcast <- forecast(lm4, newdata=data.frame(oil_r=c(50, 55, 60, 65)))<br />
fcast<br />
(fcast$mean)<br />
(fcast$lower)<br />
(fcast$upper)<br />
# plot(fcast)<br />
exp(fcast$mean)<br />
exp(fcast$lower)<br />
exp(fcast$upper)<br />
<br />
fcast4 = cbind(exp(fcast$mean),exp(fcast$lower), exp(fcast$upper))<br />
colnames(fcast4) = c("Forecast", "Lo 80", "Lo 95", "Hi 80", "Hi 95")<br />
fcast4<br />
<br />
table[4,4] = exp(fcast$mean[1])<br />
table[5,4] = exp(fcast$mean[2])<br />
table[6,4] = exp(fcast$mean[3])<br />
table[7,4] = exp(fcast$mean[4])<br />
<br />
<br />
colnames(table) = c("S1", "S2", "S3", "S4")<br />
rownames(table) = c("Oil coefficient", "t stat", "R-squared", "Forecast (oil=50)", "Forecast (oil=55)", "Forecast (oil=60)", "Forecast (oil=65)")<br />
<br />
options(digits=3, scipen=10) <br />
table<br />
<br />
<br />
colnames(table2) = c("S1", "S2", "S3", "S4")<br />
rownames(table2) = c("Residuals adf p value")<br />
table2<br />
<br />
<pre style="background: #ffffff; color: black;"></pre>
Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-69423932907631484032015-06-05T12:41:00.000-04:002015-06-05T12:41:04.784-04:00Forecasting Ontario Housing Starts<br />
With all of the talk about the housing market in Ontario, I decided to forecast Ontario housing starts using many of the methods that I teach in my Economic Forecasting and Analysis course. These methods are all covered in Rob Hyndmans's textbook <a href="https://www.otexts.org/fpp">Forecasting: Principles and Practice</a> which I use as a textbook for my course.<br />
<br />
Forecasting housing starts is important for the real estate market because housing starts are one of the key drivers of the real estate market.<br />
<br />
Here are what Ontario housing starts look like over a 65 year period. Notice two peaks in the housing starts data: one in the early 1970s and the other in the late 1980s. The data comes from CANSIM. <br />
<br />
<img alt="" height="192" src="data:image/png;base64,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" width="400" /><br />
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The two peaks in housing starts are unlikely to be repeated in the near future so for forecasting, a shorter time frame is desirable. For the forecasts, the training period was set as 1994 quarter 1 to 2010 quarter 4. The test period was set as 2011 first quarter to 2015 first quarter. Forecasts were produced for each model and their accuracy measures compared.<br />
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Here are what the forecast accuracy measures look like. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBRnVoUODx5dRkz5TJR25cvSijY38eLJxWh7rzJw5p5ZRC3qwepo8HAemz9pf5Dlyi93EBB6JNHm1NkpqcHcW8IS0OColZk53X_ssopptelme-7zr9DAhAjW-J4AIKqSRB-7mVxwTlhhI/s1600/ontario_hs.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBRnVoUODx5dRkz5TJR25cvSijY38eLJxWh7rzJw5p5ZRC3qwepo8HAemz9pf5Dlyi93EBB6JNHm1NkpqcHcW8IS0OColZk53X_ssopptelme-7zr9DAhAjW-J4AIKqSRB-7mVxwTlhhI/s400/ontario_hs.jpg" width="351" /></a></div>
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For model comparison, I like to focus on the out-of-sample or test values. From the table, Seasonal Naive has the lowest MASE among the test value, indicating that based on MASE this is the best forecasting method. The next best methods are STL and ARIMA. Notice, that from the MPE values there may be some opportunity to combine forecasts, but I do not do this here.<br />
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<img alt="" height="192" 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" width="400" /><br />
The Seasonal naive method produces forecasts for Ontario housing starts of 59,688 units for each of 2015, 2016, and 2017. By comparison, Canada Mortgage and Housing Corporation (CMHC) forecasts Ontario housing starts of 61,700 and 60,600 for 2015 and 2016 respectively. Both sets of forecasts agree that Ontario housing starts are likely to remain flat for the next few years. Flat housing starts combined with strong demand for houses implies upward pressure on house prices. This is especially the case in the GTA. A good time for sellers, but not such a good time to be a buyer. The forecasts are also useful for helping predict future sales for any company that is directly linked to housing starts.<br />
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The R code is posted below. The data you have to source yourself from CANSIM (CANSIM data label is v730423).<br />
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#########################################################<br /># Economic forecasting and analysis<br /># Perry Sadorsky<br /># Forecasting Ontario housing starts<br />##########################################################<br /><br /><br /># load libraries<br />library(fpp)<br /><br /><br /># import data <br />ontario.housing.starts <- read.csv("C:/house prices/ontario housing starts.csv")<br />View(ontario.housing.starts)<br /><br /> <br /># tell R that data set is a time series<br />df = ts(ontario.housing.starts, start=1948, frequency=4)<br />df<br /><br />hist(df[,"hs"], breaks=100)<br /><br /><br /># create a named variable<br />y = df[,"hs"]<br /> <br /> <br /># some graphs<br />hist(y)<br />plot(y)<br />Acf(y)<br /><br /><br /># add labels to the plot<br />plot(y, main="Ontario housing starts", xlab="", ylab="",col = 'blue', lwd=4)<br /><br /><br /><br />##########################################################<br />##########################################################<br /># set training data, test data, out of sample<br />train <- window(y,start=c(1994, 1),end=c(2010, 4))<br />train<br />plot(train)<br /><br />test <- window(y, start=2011)<br />both <- window(y,start=c(1994, 1))<br />h=17<br /><br />##########################################################<br />##########################################################<br /><br /><br />##########################################################<br />## forecast with benchmarks<br />##########################################################<br /><br />fit1 <- meanf(train, h=h)<br />fit2 <- naive(train, h=h)<br />fit3 <- snaive(train, h=h)<br /><br />plot(fit1)<br />plot(fit2)<br />plot(fit3)<br /><br /><br /># make a nice plot showing the forecasts<br />plot(fit1, plot.conf=FALSE,<br />main="Forecasts for Ontario housing starts")<br />lines(fit2$mean,col=2)<br />lines(fit3$mean,col=3)<br />legend("topleft",lty=1,col=c(4,2,3),<br />legend=c("Mean method","Naive method","Seasonal naive method"),bty="n")<br /><br /><br /># plot with forecasts and actual values<br />plot(fit1, plot.conf=FALSE,<br /> main="Forecasts for Ontario housing starts")<br />lines(fit2$mean,col=2)<br />lines(fit3$mean,col=3)<br />lines(hs)<br />legend("topleft",lty=1,col=c(4,2,3),<br /> legend=c("Mean method","Naive method","Seasonal naive method"),bty="n")<br /><br /><br /><br />##########################################################<br /># exponential smoothing approaches<br />##########################################################<br /><br /># simple exponential moving averages<br />fit4 <- ses(train, h = h)<br />summary(fit4)<br />plot(fit4)<br /><br /><br /># holt's linear trend method<br />fit5 <- holt(train, h=h) <br />summary(fit5)<br />plot(fit5)<br /><br /><br /># holt's exponential trend method<br />fit6 <- holt(train, exponential=TRUE, h=h) <br />summary(fit6)<br />plot(fit6)<br /><br /><br /># holt's damped trend method<br />fit7 <- holt(train, damped=TRUE, h=h) <br />summary(fit7)<br />plot(fit7)<br /><br /><br /># holt winter's method<br />fit8 <- hw(train, seasonal="multiplicative", h=h) <br />summary(fit8)<br />plot(fit8)<br /><br /><br /># ETS method<br />y.ets <- ets(train, model="ZZZ") <br />summary(y.ets)<br />fit9 <- forecast(y.ets, h=h)<br />summary(fit9)<br />plot(fit9)<br /><br /><br /># STL method<br />y.stl <- stl(train, t.window=15, s.window="periodic", robust=TRUE)<br />summary(y.stl)<br />fit10 <- forecast(y.stl, method="rwdrift",h=h)<br />summary(fit10)<br />plot(fit10)<br /><br /><br /># trend plus seasonal<br />tps <- tslm(train ~ trend + season)<br />summary(tps) <br />fit11 = forecast(tps,h=h)<br />plot(fit11)<br /><br /><br /># arima modelling and forecasting<br /># test for unit root <br />adf.test(train, alternative = "stationary")<br />kpss.test(train)<br />ndiffs(train)<br /><br /><br />y.arima <- auto.arima(train)<br />fit12 <- forecast(y.arima, h=h)<br />plot(fit12)<br /><br /># take logs to reduce variability<br />y.arima.lambda <- auto.arima(train, lambda=0)<br />fit13 <- forecast(y.arima.lambda, h=h)<br />plot(fit13)<br />tsdiag(y.arima.lambda)<br /><br /><br />## ANN<br />ann <- nnetar(train, repeats=100,lambda=0)<br />fit14 = forecast(ann,h=h)<br />plot(fit14)<br /><br />## bats<br />bats_fit <- bats(train)<br />fit15 = forecast(bats_fit,h=h)<br />plot(fit15)<br /><br /><br /><br /># accuracy measures<br />a1 = accuracy(fit1, test)<br />a2 = accuracy(fit2, test)<br />a3 = accuracy(fit3, test)<br />a4 = accuracy(fit4, test)<br />a5 = accuracy(fit5, test)<br />a6 = accuracy(fit6, test)<br />a7 = accuracy(fit7, test)<br />a8 = accuracy(fit8, test)<br />a9 = accuracy(fit9, test)<br />a10 = accuracy(fit10, test)<br />a11 = accuracy(fit11, test)<br />a12 = accuracy(fit12, test)<br />a13 = accuracy(fit13, test)<br />a14 = accuracy(fit14, test)<br />a15 = accuracy(fit15, test)<br /><br /><br />#Combining forecast summary statistics into a table with row names<br />a.table<-rbind(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15)<br /><br />row.names(a.table)<-c('Mean training','Mean test', 'Naive training', 'Naive test', 'S. Naive training', 'S. Naive test' ,<br /> 'ES training','ES test', 'Holt linear training', 'Holt linear test', 'Holt ES training', 'Holt ES test' ,<br /> 'Holt dampled training','Holt damped test', 'Holt Winters training', 'Holt Winters test', 'ETS training', 'ETS test' , <br /> 'STL training','STL test','linear trend training','linear trend test',<br /> 'ARIMA training', 'ARIMA test',<br /> 'ARIMA training (log)', 'ARIMA test (log)',<br /> 'ANN training', 'ANN test',<br /> 'BATS training', 'BATS test'<br /> )<br /><br /># order the table according to MASE<br />a.table<-as.data.frame(a.table)<br />a.table<-a.table[order(a.table$MASE),]<br />a.table<br /><br /># write table to csv file<br />## write.csv(a.table, "C:/house prices/atable.csv")<br />##########################################################<br />##########################################################<br /><br /><br />## based on MASE to choose model, forecast hs periods into the future<br />hs = 11<br /><br />fit.os.1 <- snaive(both, h=hs)<br />plot(fit.os.1, include=48)<br />fit.os.1<br /><br /><br />fit.os.2 = stl(both, t.window=15, s.window="periodic", robust=TRUE)<br />fit.os.2.f <- forecast(fit.os.2 , method="rwdrift",h=hs)<br />plot(fit.os.2.f, include=48)<br /><br /><br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-91795798041705371782015-05-21T20:30:00.000-04:002015-05-21T20:30:54.798-04:00Carbon Trading Coming to OntarioI recently gave an interview to 360 Energy about the newly announced plan to start a cap and trade<br />
program for carbon dioxide trading in Ontario.<br />
<br />
Here is the <a href="http://www.360energy.net/2015/05/exclusive-360-energy-interview-with-dr-perry-sadorsky/">link</a> to the interview.<br />
<br />
In the interview I cover some of the pros and cons of carbon trading and provide some thoughts on other carbon related topics. <br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-4098860465495925672015-03-13T16:15:00.000-04:002015-03-13T16:15:26.122-04:00Oil Prices at $20 a Barrel?I recently read an interesting article by Anatole Kaletsky on $50 a barrel representing a new ceiling for oil prices. In the <a href="http://www.project-syndicate.org/commentary/oil-prices-ceiling-and-floor-by-anatole-kaletsky-2015-01">article</a>, he describes the tradeoff between competition and monopoly power as prime drivers of oil prices. Over the past 40 years real (inflation adjusted) oil prices have traded in two regimes: 1) a high price regime associated with monopoly power, and 2) a low price regime associated with competitive market power. The dividing line between the two regimes is an oil price of approximately $50 a barrel. Consider the following chart of real oil prices with 2014 as the base year. Oil priced at $50 a barrel does seem to represent a dividing line between high priced monopoly regimes and low priced competitive regimes.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW7YyJCqvUtUxIPcJfxgmKgz7GqFgpxhm8i7UmMDWPLojq_cLIDHHISC31f8hSIZI_nf3PJRg0yqQ1k5w_1MoTLqsePTM2YJc_J7ZfI6EVy7mW1k1V5O6wUskhyphenhyphenx3uTopbzjFqTLi62As/s1600/rop.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW7YyJCqvUtUxIPcJfxgmKgz7GqFgpxhm8i7UmMDWPLojq_cLIDHHISC31f8hSIZI_nf3PJRg0yqQ1k5w_1MoTLqsePTM2YJc_J7ZfI6EVy7mW1k1V5O6wUskhyphenhyphenx3uTopbzjFqTLi62As/s1600/rop.jpeg" height="301" width="400" /></a></div>
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From 1974 to 1985 the oil market operated in a monopoly pricing regime as OPEC exerted its monopoly power. Between 1986 and 2004 oil prices were determined by competitive pricing. During this time period, new oil from the North Sea and Alaska helped to restore more competition in the world oil market. More recently, from 2005 until the summer of 2014, oil prices were again determined by monopoly pricing power as oil demand increased faster than supply. If $50 is the divideing line between the competitive and monopolistic regimes, it also looks like $20 is the floor for oil prices in the competitive regime. It is thus possible that if oil prices have switched into a competitive regime, then we could see prices bottom out at $20.<br />
<br />
In a competitive market, the price of oil is determined by the marginal cost of production. According to Kaletsky, the marginal cost of production for conventional oil is around $20 per barrel, while the marginal cost of production from US fracking is around $50 per barrel. If we have entered a new competitive pricing regime, then US frackers are the new "swing producers".<br />
<br />
This led me to think about a way to empirically determine the threshold price for oil. In response, I estimated a self exciting threshold autoregressive (SETAR) model for real oil prices. SETAR models are designed to model data that changes its pattern depending upon what regime it is in. The SETAR approach chose $57.42 as the threshold value. This is slightly higher than $50 but consistent with what the marginal cost of US fracking could be. Here is what the regime switching plot looks like.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikdMujlz40AMyvMfWg8HFFddcANJOBQNf4Zw2rEomS0h9P0wwSSQh3kXmQSMqNPNDOtKCwVbjgcdt_-K5Vbne0Kmo6MfmOyIJVlHn43i2FpH3efqETWsyjOqb0FkfBZXGEiW1vVepzFBs/s1600/Rplot.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikdMujlz40AMyvMfWg8HFFddcANJOBQNf4Zw2rEomS0h9P0wwSSQh3kXmQSMqNPNDOtKCwVbjgcdt_-K5Vbne0Kmo6MfmOyIJVlHn43i2FpH3efqETWsyjOqb0FkfBZXGEiW1vVepzFBs/s1600/Rplot.jpeg" height="301" width="400" /></a></div>
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According to the plot, oil prices are still in a high price regime. Remember, one sudden drop in prices does not indicate a regime switch. If, however, oil prices do continue to stay below $57 a barrel signifying a switch into a low price regime, then $20 looks like a price floor.<br />
<br />
<br />
The R code is posted below. The monthly oil price and CPI data comes from <a href="http://research.stlouisfed.org/fred2/">FRED</a>. Notice, that the oil price series needs to be constructed by splicing the old FRED oil price series (OILPRICE) with the more recent one (MCOILWTICO). The resulting SETAR model fits well and the residuals show no discernible pattern.<br />
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#########################################################<br /># Economic forecasting and analysis<br /># Perry Sadorsky<br /># March 2015<br /># SETAR model of oil prices<br />##########################################################<br /><br /><br /># load libraries<br />library(fpp)<br />library(tsDyn)<br /><br /><br />##########################################################<br />## read in data and prepare data<br />##########################################################<br /><br /><br /># import data on monthly oil prices<br />cpi_oil <- read.csv("C:/oil prices/cpi_oil.csv")<br />View(cpi_oil)<br /><br /><br /># tell R that data set is a time series<br />cpi_oil = ts(cpi_oil, start=1947, frequency=12)<br />cpi_oil<br /><br /><br />oil = cpi_oil[,"OILPRICE"]<br />cpi = cpi_oil[,"CPIAUCSL"]<br /><br /><br />oil =window(oil,start=1973)<br />cpi =window(cpi,start=1973)<br /><br /><br /># rebase cpi <br />tail(cpi,14)<br />cpi2014 = mean( cpi[(816-11):816] )<br />cpi_2014 = cpi/cpi2014 * 100<br /><br /><br />## http://www.project-syndicate.org/commentary/oil-prices-ceiling-and-floor-by-anatole-kaletsky-2015-01<br />rop = oil/cpi_2014 *100<br />plot(rop,main="Real oil prices ($/bbl)",xlab="",ylab="",xaxt="n",lwd=4)<br />axis(1,at=c(seq(from=1974,to=2014,by=2)), las=2)<br />abline(h=50)<br />abline(h=20)<br /><br /><br />rop.ret = 100* diff(log(rop))<br />plot(rop.ret)<br />tsdisplay(rop.ret)<br /><br /><br /><br />#### SETAR model<br /># select model<br />selectSETAR(rop, m=6, d=2, nthresh=1)<br /><br /><br /># estimate model<br />mod.setar <- setar(rop, m=6, thDelay=0, th= 57.42232 , mL=6, mH=3)<br />mod.setar<br />summary(mod.setar)<br />plot(mod.setar)<br />par(mfrow=c(1,1))<br /><br /><br />
<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-73227055819329065582015-03-03T14:25:00.002-05:002015-03-03T14:38:10.437-05:00A Wavelet Analysis of Oil Prices and the Canadian DollarIn a previous <a href="http://perrysadorsky.blogspot.ca/2015/02/correlations-between-oil-prices-and.html">post</a>, I investigated the time series relationship between oil prices, the Canadian dollar, and Canadian stock prices (measured using the TSX composite index). A rolling analysis was used to show how the relationship between these variables changes across time. <br />
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">In
this post, I use a wavelet analysis to further explore relationships between
oil prices, the Canadian dollar, and Canadian stock prices. Wavelet analysis is
a frequency – time domain approach with origins stemming from Fourier analysis
and spectral density analysis. Fourier analysis and spectral filtering methods
impose strong restrictions on the data structure and in doing so lose
information about the time dimension. By comparison, wavelets combine information
from the time dimension and frequency dimension. Wavelets do not make strong assumptions
about the data generating process. Gencay et al. (2002) and Ramsey (2002) are excellent
references on the application of wavelets to economic and financial data.</span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Below,
I apply a wavelet coherence approach to monthly returns on oil prices ($US/barrel)
and the $US/$C exchange rate which I denote as FX. </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih8c275C6fJlzUS5Q68ZwOcmddilFyMu_upKJp37pq1m8eNJdMNzd0dGbbXzLxkrqqBsMMUbAR00LOe1mSL8JFkdIkFb2SIRVaal-tkfxaLgqzfJilggvmz8XlqwIQao7eQFwk9PcTUZU/s1600/wtcfxoil.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih8c275C6fJlzUS5Q68ZwOcmddilFyMu_upKJp37pq1m8eNJdMNzd0dGbbXzLxkrqqBsMMUbAR00LOe1mSL8JFkdIkFb2SIRVaal-tkfxaLgqzfJilggvmz8XlqwIQao7eQFwk9PcTUZU/s1600/wtcfxoil.jpeg" height="268" width="400" /></a></div>
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The stronger the relationship (coherence) between the two variables, the more red the colour. Both period and time are measured in months. The cone of influence is indicated by the dashed white line beyond which the estimates are unreliable. It is also, in some cases, possible to assign directionality to the relationship. This is done through the use of phase arrows. The phase arrows are interpreted as follows, where X is FX and Y is oil.<br />
<br />
<ul>
<li style="margin-top: 0;">right: in-phase</li>
<li>left: anti-phase</li>
<li>down: X leading Y by 90°</li>
<li>up: Y leading X by 90°</li>
</ul>
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The strongest coherence occurs on the time scale between months 250 (October 2006) and 300 (December 2012). Around 11 months on the period scale, the phase arrows are mostly pointing up. This indicates that oil is leading FX. Around month 23 on the period scale, however, the phase arrows are pointing down, indicating that FX is leading oil. The wavelet analysis shows the strongest relationship between FX and oil occurred relative recently with the directionality depending upon the month. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgULG-u1gaDas3OPHjfsLopTg3Xa2O4kNjrPKzdP7lzUQHrSbCHRjcMnvIPbkRQu7Ij6MZ2vkoAItEW8RD8hMqYJWXSCNtd1EvFjYZK1qSrOv8ALQ1SMi4djuDYt8GEIQUFQYPv5s_Nhi8/s1600/wtctsxoil.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgULG-u1gaDas3OPHjfsLopTg3Xa2O4kNjrPKzdP7lzUQHrSbCHRjcMnvIPbkRQu7Ij6MZ2vkoAItEW8RD8hMqYJWXSCNtd1EvFjYZK1qSrOv8ALQ1SMi4djuDYt8GEIQUFQYPv5s_Nhi8/s1600/wtctsxoil.jpeg" height="268" width="400" /></a></div>
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The wavelet coherence between oil prices and the TSX show several pockets of high coherence (around 50 months on the time scale (February 1990), 200 months (August 2002), and 250 - 300 months). All three regions show strong coherence between 8 and 11 periods (months). In the first two regions, the phase arrows are mostly down indicating that the TSX is leading oil. In the 250 to 300 month time period the phase arrows are up between period 8 and 11 indicating that oil leads the TSX. </div>
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This analysis presents further results that the relationship between FX and oil prices is complicated and that when using standard time series approaches one should not be surprised to fail to find strong linear relationships between these two variables.</div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">References</span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Ramsey
JB. Wavelets in economics and finance: past and future. Studies in Nonlinear Dynamics
& Econometrics 2002;6(3):1–27.</span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Gencay R, Selcuk F, Whitcher B.
An introduction to wavelets and other filtering methods in finance and
economics. San Diego,London and Tokyo: Academic Press; 2002.</span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Here is the R script.</span></div>
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#########################################################<br />
# Economic forecasting and analysis<br />
# Perry Sadorsky<br />
# February 2015<br />
# wavelets between FXcan and oil prices<br />
##########################################################<br />
<br />
<br />
# load libraries<br />
library(fpp)<br />
library(quantmod)<br />
library(biwavelet)<br />
<br />
<br />
##########################################################<br />
## read in data and prepare data<br />
##########################################################<br />
<br />
# load data from Yahoo<br />
symbols <- c( "^GSPTSE" )<br />
getSymbols(symbols, from="1986-01-01", src='yahoo')<br />
tsx = GSPTSE[, "GSPTSE.Adjusted", drop=F]<br />
nrow(tsx)<br />
<br />
<br />
# load data from FRED into new environment<br />
symbol.vec = c("DCOILWTICO" , "DEXCAUS")<br />
data <- new.env()<br />
getSymbols(symbol.vec, src="FRED", env = data)<br />
<br />
<br />
# fix up FRED data<br />
na.locf(data$DCOILWTICO["1986-01-01::"])-> oil<br />
1/na.locf(data$DEXCAUS["1986-01-01::"])-> fx<br />
<br />
<br />
fred.merged = merge(oil,fx,join = "inner") <br />
View(fred.merged)<br />
nrow(fred.merged)<br />
<br />
<br />
series.merged <- merge(fred.merged,tsx,join = "inner") <br />
tail(series.merged)<br />
tail(tsx)<br />
tail(fx)<br />
colnames(series.merged) <- c("oil", "fx", "TSX")<br />
<br />
<br />
##########################################################<br />
## now convert to monthly data<br />
##########################################################<br />
<br />
series.merged.monthly <- series.merged[ endpoints(series.merged, on="months", k=1), ]<br />
View(series.merged.monthly)<br />
y.m = series.merged.monthly<br />
<br />
<br />
# plot monthly data<br />
par(mfrow=c(3,1))<br />
plot(y.m[,1],main="Oil prices ($/bbl)")<br />
plot(y.m[,2],main="$US/$C")<br />
plot(y.m[,3],main="TSX")<br />
par(mfrow=c(1,1))<br />
<br />
<br />
##########################################################<br />
# wavelet analysis<br />
##########################################################<br />
# wtc works better with numeric data<br />
<br />
<br />
oil = as.numeric(y.m[,1])<br />
fx = as.numeric(y.m[,2])<br />
tsx = as.numeric(y.m[,3])<br />
<br />
<br />
# compute returns<br />
fx.ret = diff(log(fx)) * 100<br />
oil.ret = diff(log(oil)) * 100<br />
tsx.ret = diff(log(tsx)) * 100<br />
lh = length(oil.ret)<br />
<br />
<br />
tsdisplay(fx.ret)<br />
tsdisplay(oil.ret)<br />
tsdisplay(tsx.ret)<br />
par(mfrow=c(1,1))<br />
<br />
<br />
# bind in time dimension<br />
x1 = cbind(1:lh,fx.ret)<br />
x2 = cbind(1:lh,oil.ret)<br />
x3 = cbind(1:lh,tsx.ret)<br />
<br />
<br />
# wavelet coherence<br />
wtc.fxoil = wtc(x1,x2, nrands=1000)<br />
par(oma=c(0, 0, 0, 1), mar=c(5, 4, 4, 5) + 0.1)<br />
plot(wtc.fxoil, plot.cb=TRUE,plot.phase=TRUE,arrow.size.head=0.15,ylim=c(4,32),main="Wavelet coherence of FX and oil")<br />
<br />
<br />
wtc.tsxoil = wtc(x3,x2, nrands=1000)<br />
par(oma=c(0, 0, 0, 1), mar=c(5, 4, 4, 5) + 0.1)<br />
plot(wtc.tsxoil, plot.cb=TRUE,plot.phase=TRUE,arrow.size.head=0.15,ylim=c(4,32),main="Wavelet coherence of TSX and oil")<br />
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Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com2tag:blogger.com,1999:blog-6991386370942322529.post-54424531119327527632015-02-16T16:20:00.000-05:002015-02-16T16:20:24.606-05:00Correlations between Oil Prices and the Canadian DollarThe past several months have been difficult for watchers of the Canadian dollar and oil prices. Given that the Canadian economy is heavily reliant on natural resources and that oil is one of the largest exports, it seems reasonable to expect a strong relationship between commodity prices in general and oil prices in particular and Canadian exchange rates. Oil prices, which are priced in US dollars, can impact exchange rates through two different channels: the terms of trade effect or the wealth effect. <br />
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The chart below shows how many US dollars one Canadian dollar buys. Daily data from January 2, 1986 to February 6, 2015 are used to construct the chart.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjljLoL7ORCke2uZtYipIVLhKe-QWAipK5q0u6fYpdNEZvbx3RXLcLEoAlcxyvQ792D5dWJhLnKZJo8DLW63r2Cfw-0jLkRkXeTT-vDDkmM1oL2s1ATT825qCH1l_ZCIXtP5UFGFdpLfD4/s1600/fx.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjljLoL7ORCke2uZtYipIVLhKe-QWAipK5q0u6fYpdNEZvbx3RXLcLEoAlcxyvQ792D5dWJhLnKZJo8DLW63r2Cfw-0jLkRkXeTT-vDDkmM1oL2s1ATT825qCH1l_ZCIXtP5UFGFdpLfD4/s1600/fx.jpeg" height="286" width="320" /></a></div>
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The Canadian dollar has been fairly volatile over this time period, ranging from a low of 62 cents on January 18, 2002 to a high of $1.09 on November 7, 2007. As recently as September 2014, the Canadian dollar was trading over 90 cents. Once oil prices began to fall the Canadian dollar followed and within a few months was down below 80 cents.<br />
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For comparison purposes, here are what oil prices ($US/barrel) look like.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoo6erNoM7aih6yJF6rzlzOerAYMy2CKRyCCmwBAziFCuw4VD6FTa9eRCaGD3ADfr1hojd-lp-3ch9QwdDESYEnnD_fwypifGstQdk4yvgYkVpMjeIQz9Sr7kICoNyeNU0LZQE-ZYtLmw/s1600/oil.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgoo6erNoM7aih6yJF6rzlzOerAYMy2CKRyCCmwBAziFCuw4VD6FTa9eRCaGD3ADfr1hojd-lp-3ch9QwdDESYEnnD_fwypifGstQdk4yvgYkVpMjeIQz9Sr7kICoNyeNU0LZQE-ZYtLmw/s1600/oil.jpeg" height="286" width="320" /></a></div>
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Before the year 2000, the oil price - Canadian dollar relationship was not as obvious. Since 2000, however, the relationship between the two has become much more pronounced. This correlation has given rise to the labeling of the Canadian dollar as a "petro-currency".<br />
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For completeness, here is a chart of the Toronto Stock Exchange (TSX). Notice that since 2000, the pattern of the TSX is similar to that of oil prices and exchange rates.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj01bQpgvDnYV7Yl8x1c5axU__f1GISW2VIA6qNjFB2bkIodLI-N1ylkTCBi5j7Qtt-JYbMYdbscs4L8udW_wgPb7-sE-3P1ALMIOV8LGdrM720Oh4Z938luMHRXukm9inEl6Bl_l9olIw/s1600/tsx.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj01bQpgvDnYV7Yl8x1c5axU__f1GISW2VIA6qNjFB2bkIodLI-N1ylkTCBi5j7Qtt-JYbMYdbscs4L8udW_wgPb7-sE-3P1ALMIOV8LGdrM720Oh4Z938luMHRXukm9inEl6Bl_l9olIw/s1600/tsx.jpeg" height="286" width="320" /></a></div>
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In order to more fully explore the relationship between oil prices and exchange rates, I conducted some rolling correlation analyses. A fixed window of 1260 days (approximately 5 years of trading days) was used to estimate the correlation between the daily returns of the exchange rate and oil prices. A rolling correlation analysis allows for sudden changes or jumps in the relationship between the two variables. A roiling analysis is a convenient way to see how stable a relationship is across time.<br />
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A chart of the rolling correlations between the Canadian dollar and oil prices (both measured in daily returns) shows how the relationship has strengthened across time. Across the sample period, the correlation between these two variables is mostly positive. In the 1990s, the correlation was never above 0.1. This indicates a fairly weak correlation between oil prices and the Canadian dollar. The relationship strengthened in the mid 2000s and after the 2008 - 2009 financial crisis. Today, the relationship remains moderate (between 0.4 and 0.5).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwaVuHrUKSOysyCTyIlx0MM9bGleBi_FGmloQck2rnFFg8GxDMFIPVd6068eiHBwTWvjUeGgTMDOQ6Isp8QuNYPKaomyRc2o-mFpN95Yr4NS7LsKqsKZ4Okv2atdMWK4ALMJ2s-NHR0m0/s1600/rollfxoil.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwaVuHrUKSOysyCTyIlx0MM9bGleBi_FGmloQck2rnFFg8GxDMFIPVd6068eiHBwTWvjUeGgTMDOQ6Isp8QuNYPKaomyRc2o-mFpN95Yr4NS7LsKqsKZ4Okv2atdMWK4ALMJ2s-NHR0m0/s1600/rollfxoil.jpeg" height="286" width="320" /></a></div>
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Here are what the rolling correlations look like for the other pairs of data. notice how the correlations have strengthened after the 2008 - 2009 financial crisis. The higher degree of correlations between different assets is one of the lasting effects of this crisis.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkLDj2dfhIme5ePdZTAEcGOUAguVyY-1O_BvMdD2dGbPXqKJAWVv4ie0jd5g7U1Aw6v_0iJkMOsjsYDSJoDV_unuWKhfCPkwpWOcNRw2iWi8tGuW_wfeUH40e92yqKjt3QPE-r2otXC8Q/s1600/rolloiltsx.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkLDj2dfhIme5ePdZTAEcGOUAguVyY-1O_BvMdD2dGbPXqKJAWVv4ie0jd5g7U1Aw6v_0iJkMOsjsYDSJoDV_unuWKhfCPkwpWOcNRw2iWi8tGuW_wfeUH40e92yqKjt3QPE-r2otXC8Q/s1600/rolloiltsx.jpeg" height="286" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr_vVMkHSfeVzMdbMP1qvv75Kn9y961us2fP4hAbPQhlUZyLq-oM8RVpsxkkLOodaF8ihPiid3OfIIwTWwAPcn3mxUhKLqsg29-bmD5ysWMpEN2PO9csITIZm4RqEbDXJO4_PpaqFdwl4/s1600/rollfxtsx.jpeg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr_vVMkHSfeVzMdbMP1qvv75Kn9y961us2fP4hAbPQhlUZyLq-oM8RVpsxkkLOodaF8ihPiid3OfIIwTWwAPcn3mxUhKLqsg29-bmD5ysWMpEN2PO9csITIZm4RqEbDXJO4_PpaqFdwl4/s1600/rollfxtsx.jpeg" height="286" width="320" /></a></div>
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As a further analysis, I investigate the possibility of Granger causality from oil prices to exchange rates. A vector autoregression with 11 lags is used for the analysis. This model was stable and the residuals were approximately random. I use the same data set as in the previous charts. A rolling analysis is carried out on the causality test and the p values are plotted below. The purple line denotes a p value of 0.05. From the plot, evidence of causality from oil prices to exchange rates occurred at the beginning and end of the sample period. Overall, there does not seem to be much evidence of Granger causality running from oil prices to the Canadian dollar. The relationship between the two is probably more of a contemporaneous nature than a causal nature.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg093qDPeiNs0FJ3d0L-_XSyrGrl9LhwUt6QkahPeqP3QBtP9JJDCq2lVD3bTMvzYTxZpF85Qj9qZ7VsI6NTwMkxQncPnqckdgLM69MqQnH9ge1pIV8NaAQKElrjMsj9kT_c0f0MmYx7YU/s1600/causoiltofx.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg093qDPeiNs0FJ3d0L-_XSyrGrl9LhwUt6QkahPeqP3QBtP9JJDCq2lVD3bTMvzYTxZpF85Qj9qZ7VsI6NTwMkxQncPnqckdgLM69MqQnH9ge1pIV8NaAQKElrjMsj9kT_c0f0MmYx7YU/s1600/causoiltofx.jpeg" height="286" width="320" /></a></div>
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In summary, the relationship between oil prices and the Canadian dollar changes across time.This has implications for modelling, forecasting, and portfolio diversification.<br />
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Here is the R code to conduct the analysis. The rolling p value calculation takes about 15 minutes to complete.<br />
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#########################################################<br /># Economic forecasting and analysis<br /># Perry Sadorsky<br /># February 2015<br /># rolling correlations between FXcan and oil prices<br /># load data directly from FRED and Yahoo and merge<br />##########################################################<br /><br /># load libraries<br />library(fpp)<br />library(quantmod)<br /><br /><br /># load data from Yahoo<br />symbols <- c( "^GSPTSE" )<br />getSymbols(symbols, from="1986-01-01", src='yahoo')<br />tsx = GSPTSE[, "GSPTSE.Adjusted", drop=F]<br />nrow(tsx)<br /><br /><br /># load data from FRED into new environment<br />symbol.vec = c("DCOILWTICO" , "DEXCAUS")<br />data <- new.env()<br />getSymbols(symbol.vec, src="FRED", env = data)<br /><br /><br /># fix up FRED data<br />na.locf(data$DCOILWTICO["1986-01-01::"])-> oil<br />1/na.locf(data$DEXCAUS["1986-01-01::"])-> fx<br /><br /><br />fred.merged = merge(oil,fx,join = "inner") <br />View(fred.merged)<br />nrow(fred.merged)<br /><br /><br />series.merged <- merge(fred.merged,tsx,join = "inner") <br />tail(series.merged)<br />tail(tsx)<br />tail(fx)<br />colnames(series.merged) <- c("oil", "fx", "TSX")<br /># View(series.merged)<br /><br /><br /># plot prices<br />par(mfrow=c(3,1))<br />plot(series.merged[,1], main="OIL ($US/bbl)")<br />plot(series.merged[,2], main="$US/$C")<br />plot(series.merged[,3], main="TSX")<br />par(mfrow=c(1,1))<br /><br /><br /># find min and max of fx<br />fx.min = which.min(series.merged[,2])<br />series.merged[fx.min,2]<br /><br />fx.max = which.max(series.merged[,2])<br />series.merged[fx.max,2]<br /><br /><br /># calculate returns<br />ret = diff(log(series.merged)) * 100<br />tail(ret)<br /><br /><br /># plot returns<br />tsdisplay(ret[,1],main="Returns of oil")<br />tsdisplay(ret[,2],main="Returns of FX")<br />tsdisplay(ret[,3],main="Returns of TSX")<br />par(mfrow=c(1,1))<br /><br /><br /># 5 year rolling correlations, approximately 1260 days <br />rollout2 = rollapply(ret, 1260 ,function(x) cor(x[,1],x[,2]), by.column=FALSE,align="right")<br />rollout2 = na.omit(rollout2) <br />plot(rollout2,main="Rolling 5 year correlations between returns of FX and Oil")<br /><br /><br />rollout3 = rollapply(ret, 1260 ,function(x) cor(x[,1],x[,3]), by.column=FALSE,align="right")<br />rollout3 = na.omit(rollout3) <br />plot(rollout3,main="Rolling 5 year correlations between returns of Oil and TSX")<br /><br /><br />rollout4 = rollapply(ret, 1260 ,function(x) cor(x[,2],x[,3]), by.column=FALSE,align="right")<br />rollout4 = na.omit(rollout4) <br />plot(rollout4,main="Rolling 5 year correlations between returns of FX and TSX")<br /><br /><br />##########################################################<br />## some var modelling <br />##########################################################<br />library(vars)<br />ret = na.omit(ret)<br /># VAR modelling, select appropriate lag length<br />var1.s = VARselect(ret, lag.max = 26, type = "const")<br />str(var1.s)<br />lag = var1.s$selection[1]<br /><br /><br />var1 <- VAR(ret, p = lag, type = "const")<br />summary(var1)<br />roots(var1)<br />plot(var1)<br />par(mfrow=c(1,1))<br /><br /><br /># Granger causality tests<br />causality(var1, cause = "oil")<br />causality(var1, cause = "fx")<br />causality(var1, cause = "TSX")<br /><br /><br /># impulse response functions<br />var1.irf <- irf(var1, n.ahead = 20, boot = TRUE, cumulative= TRUE)<br />plot(var1.irf)<br />par(mfrow=c(1,1))<br /><br /><br />library(MSBVAR)<br />gt1 = granger.test(ret,p=11)<br />str(gt1)<br />gt1[3,2]<br /><br /><br />roll.gt = function(x) {<br /> gt1 = granger.test(x,p=lag)<br /> gt.p = gt1[3,2]<br /> return(gt.p)<br /> }<br /><br /><br />tic <- Sys.time()<br />roll.gt.pvals = rollapply(ret, width=1260,<br /> by.column=FALSE,<br /> FUN=roll.gt, <br /> align="right")<br />toc <- Sys.time()<br />( toc - tic )<br /><br /><br />roll.gt.pvals = na.omit(roll.gt.pvals)<br />plot(roll.gt.pvals,main="Causality p values (oil > fx)")<br />abline(h=0.05,col="purple")<br /><br /><br /><br />
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Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com2tag:blogger.com,1999:blog-6991386370942322529.post-52144062135034677612014-02-12T15:36:00.002-05:002014-02-12T15:36:40.022-05:00The European Debt CrisisHere is a great <a href="http://www.ritholtz.com/blog/2014/02/european-debt-crisis-visualized/">video presentation</a> of the European Debt Crisis.Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-43081023946887974592014-02-02T13:41:00.003-05:002014-02-02T13:44:58.301-05:00The Big Mac IndexThe <a href="http://www.economist.com/content/big-mac-index">Big Mac Index</a> has come a long way since it was first published by The Economist in 1986. The new and improved version comes with an interactive map. According to the latest numbers, the Canadian dollar is slightly overvalued.Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-60454540785362490092013-11-17T21:01:00.000-05:002013-11-17T21:01:36.808-05:00What a Difference a Ph.D. Makes: More than Three Little LettersFor those working in quantitative finance, this has been expected for a while. Now, there is some good solid research backing up this claim. The full paper is available <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2344938">here</a>.<br />
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"<span style="font-family: Myriad Roman, Arial, Helvetica, Sans-serif; font-size: x-small;">Several
hundred individuals who hold a Ph.D. in economics, finance, or others
fields work for institutional money management companies. The gross
performance of domestic equity investment products managed by
individuals with a Ph.D. (Ph.D. products) is superior to the performance
of non-Ph.D. products matched by objective, size, and past performance
for one-year returns, Sharpe Ratios, alphas, information ratios, and the
manipulation-proof measure MPPM. Fees for Ph.D. products are lower than
those for non-Ph.D. products. Investment flows to Ph.D. products
substantially exceed the flows to the matched non-Ph.D. products.
Ph.D.s’ publications in leading economics and finance journals further
enhance the performance gap."</span>Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com2tag:blogger.com,1999:blog-6991386370942322529.post-32897997059960449362013-09-29T12:40:00.000-04:002013-09-29T12:40:49.987-04:00A Tribute To BlackBerryFrom the <a href="http://www.nytimes.com/interactive/2013/09/29/technology/when-blackberry-reigned-the-queen-got-one-and-how-it-fell.html?_r=0">NYT</a><br />
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-28449640016251888272013-09-15T13:40:00.000-04:002013-09-15T13:40:58.011-04:00The Cleveland Financial Stress IndexA new coincident indicator of <a href="http://www.clevelandfed.org/research/trends/2013/0913/02banfin.cfm">financial stress</a>.<br />
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"The level of the <a href="http://www.clevelandfed.org/research/data/financial_stress_index/">Cleveland Financial Stress Index (CFSI)</a>
has decreased in the past few months, indicating a lower level of
systemic financial stress. Although the most recent reading of the index
from September 4 is in Grade 2 or a “normal stress period,” the index
had been in a Grade 1 or “low stress period” for 49 days since June 1.
The index currently stands at −0.43, which is up 0.63 points from a
recent low on July 15, 2013. (The points refer to the standardized
distance from the mean or the z-score). The index is down 1.32 points
over the past year and is 3.52 points lower than its historical peak in
December 2008."<br />
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Check out how this <a href="http://www.clevelandfed.org/research/data/financial_stress_index/">indicator</a> moved into the Grade 4 category in late 2007, and remained in upper Grade 3 or Grade 4 throughout most of 2008.</div>
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Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com3tag:blogger.com,1999:blog-6991386370942322529.post-61596745849236271412013-08-03T17:28:00.002-04:002013-08-03T21:49:53.251-04:00Stock Market Capitalization to GDPStock market capitalization to GDP has been called by some as the best measure of a stock market's valuation (<a href="http://greenbackd.com/2013/03/25/warren-buffett-and-john-hussman-on-the-stock-market/">see here</a>)and (<a href="http://www.hussmanfunds.com/wmc/wmc130318.htm">here</a>). The market capitalization to GDP ratio is calculated by dividing stock market capitalization by GDP and multiplying the result by 100. This measure can be thought of as an economy wide price to sales ratio. Higher values indicate higher valuations. In general, values over 100 are indicative of over valuations. Lower values indicate lower valuations, but there is considerable disagreement as to what values represent undervaluation in today's environment. <br />
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Here is how this ratio compares across time for the United States.
While many charts use S&P 500 market cap in the calculation, I have used a more broader measure (non financial corporate business: corporate equity, liabilities) obtained from the Federal Reserve. Notice how the ratio tends to peak before recessions. It wasn't until 1999 that market capitalization to GDP broke above 100% but since that time, it has averaged at a higher value than in the pre 1999 time period. Over the last 10 years, undervaluation seems to occur somewhere in the 60% to 80% range. In any case, the current value is high in an historical context, suggesting that at least from the perspective of this measure, the US stock market is approaching overvalued territory.<br />
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<a href="https://research.stlouisfed.org/fred2/graph/fredgraph.png?graph_id=109184&id=MVEONWMVBSNNCB_GDP&scale=Left&range=Max&cosd=1947-01-01&coed=2013-04-01&line_color=%230000ff&link_values=false&line_style=Solid&mark_type=NONE&mw=4&lw=1&ost=-99999&oet=99999&mma=0&fml=a%2Fb&fq=Quarterly&fam=avg&fgst=lin&transformation=lin_lin&vintage_date=2013-08-03_2013-08-03&revision_date=2013-08-03_2013-08-03" imageanchor="1"><img border="0" height="240" src="https://research.stlouisfed.org/fred2/graph/fredgraph.png?graph_id=109184&id=MVEONWMVBSNNCB_GDP&scale=Left&range=Max&cosd=1947-01-01&coed=2013-04-01&line_color=%230000ff&link_values=false&line_style=Solid&mark_type=NONE&mw=4&lw=1&ost=-99999&oet=99999&mma=0&fml=a%2Fb&fq=Quarterly&fam=avg&fgst=lin&transformation=lin_lin&vintage_date=2013-08-03_2013-08-03&revision_date=2013-08-03_2013-08-03" width="400" /></a><br />
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Here is a heat map showing stock market capitalization to GDP for a variety of countries. The data are from the World Bank online data base. The most recent measures show that Canada, the United States, England, Sweden, Switzerland, Chile, Malaysia, Thailand, and South Africa are all overvalued. Rewind the slider scroll bar back to 1988 and push play to see how this ratio changes across time.<br />
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Market capitalization of listed companies (% of GDP)
<iframe height="450" src="http://www.openheatmap.com/embed.html?map=ChaosSulfatizationReentrants" width="580"></iframe>
Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com14tag:blogger.com,1999:blog-6991386370942322529.post-76426090695295457082013-07-31T21:16:00.001-04:002013-07-31T21:16:27.632-04:00The "What Do 7 Billion People Do" ChartThe majority of the global work force works in services. There are fewer entrepreneurs than unemployed.<br />
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com2tag:blogger.com,1999:blog-6991386370942322529.post-17660700298239744992013-06-29T16:56:00.000-04:002013-06-30T10:43:20.202-04:00Canadian REITs and Interest RatesThe past 2 months have been very difficult for Canadian investors. First interest rate worries spooked the banks and REITs, then weak commodity markets torpedoed the resources sector. Gold, the precious metal that is the go-to investment in times of inflation and worry is now trading at a 2 year low. Most recently, Canadian telecoms got whacked on news that Verizon was thinking of moving into Canada.
Real estate investment trusts (REITs) have been good investments for a long time. REITs pay bond size dividends and offer the opportunity for equity like price appreciation. REITs have been so good for so long, that many investors have a sizable portion of their investment portfolio in REITs.
To find out more about what has been happening with REITs, I decided to analyze how sensitive one of Canada's biggest REIT ETFs, the iShares capped REIT index (XRE) is to movements in interest rates.
Here is how XRE has performed since 2008.<br />
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The last recession was hard on XRE, but recovery came quickly.<br />
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Here is how Canadian 3 month T-bills and 10 year government bonds have performed. It seems reasonable to expect that REITs are negatively correlated with T-bill or bond yields, since increases in fixed income yields offer competitive less risky alternatives to investing in REITs. These falling yields have helped push the price of XRE higher.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhArAg_HKoGzB25BpfrybfxaBNSBmhqerPNPY7B8yENe2BivGbdsioWAsO2i5LSglaOPYGHJRImyXjt3DtfPNNa7tu0tWKPaRAR520Ejsjx51843zfqRlNQVXEZFB4Lf56XfcPWmx2-4lQ/s541/cantbillbond.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="291" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhArAg_HKoGzB25BpfrybfxaBNSBmhqerPNPY7B8yENe2BivGbdsioWAsO2i5LSglaOPYGHJRImyXjt3DtfPNNa7tu0tWKPaRAR520Ejsjx51843zfqRlNQVXEZFB4Lf56XfcPWmx2-4lQ/s400/cantbillbond.JPG" width="400" /></a></div>
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I collected monthly data on XRE, 90 day T-bill yields, and the yield on 10 year government of Canada bonds. I calculate the one month return on XRE and denote it as xre_r. I regress one month XRE returns on the yields from T-bills and bonds.<br />
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A regression of xre_r on the 90 day T-bill yield produces the following results.<br />
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xre_r = 1.613 -0.365 tbill<br />
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The estimated coefficient is negative indicating that a 1% increase the tbill yield reduces monthly returns by 0.365%. The sign of this coefficient is as expected, negative, but the estimated coefficient is not statistically significant at conventional levels. The R squared for this regression is 0.0115. Not much going on here.<br />
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A regression of xre_r on the 10 year bond yield produces the following results.<br />
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xre_r = 1.239 -0.105 bond<br />
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As expected the estimated coefficient on the 10 year bond variable is negative. This estimated coefficient is not, however, statistically significant at conventional levels of significance.The R squared from this regression is 0.0005. This is even lower than in the T-bill regression.<br />
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On the face of it, there does not seem to be too much sensitivity of REITs to movements in interest rates. Another possibility is that the relationship between XRE and interest rates is time varying. The regression results reported above assume that the coefficient on the interest rate variable is constant over the sample period. This may not be the case, in which case, a time varying beta approach may be more informative. To investigate this I used a rolling window analysis to estimate the coefficient on the T-bill variable using a rolling window regression approach with a fixed window length of 60 observations.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgM56kMwazcEqV_SsttHO-CuDk2zn6d187pW6U2O7-AeOIXt6_8S_AGTFbOkULwox8dKAOT8ZLdRXVcOtaI72UNHAiVycTiOfBrihvmowwzgMVSQw4LSMG3MhiILh3Dxy69V5TLeVPIn1E/s541/rollingtbillbeta.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgM56kMwazcEqV_SsttHO-CuDk2zn6d187pW6U2O7-AeOIXt6_8S_AGTFbOkULwox8dKAOT8ZLdRXVcOtaI72UNHAiVycTiOfBrihvmowwzgMVSQw4LSMG3MhiILh3Dxy69V5TLeVPIn1E/s400/rollingtbillbeta.JPG" width="400" /></a></div>
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Whoa! Now here is something interesting. Up until the beginning of 2012, the sensitivity of XRE to the T-bill yield was fairly constant. Starting in early 2012, however, the relationship changed with REITs becoming more sensitive to interest rates. The most recent value of the estimated coefficient on the T-bill variable is -5.41. This means that a 1% increase in the T-bill yield decreases monthly returns on XRE by 5.41%. For most of the sample period, REIT investors were not too sensitive to movements in the 90 day T-bill rates. That has clearly changed over the past year. REIT investors have become much more concerned with rising interest rates. With falling REIT prices, the yields on REITs will eventually start to look good on a risk adjusted basis. Given the large sell off in REITs, however, this could take some time.Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com4tag:blogger.com,1999:blog-6991386370942322529.post-69571474070077677712013-04-19T16:51:00.000-04:002013-04-19T16:51:10.269-04:00Seach Interest in the Tar Sands Peaked in 2006Here are some charts showing how Google searches of terms tar sands, oil sands, and fracking compare.
<script type="text/javascript" src="//www.google.com/trends/embed.js?hl=en-US&q=oil+sands%2B+tar+sands,+fracking&cmpt=q&content=1&cid=TIMESERIES_GRAPH_0&export=5&w=500&h=330"></script>
On a regional basis, searches for terms like tar sands or oil sands are mostly from Canada.
<script type="text/javascript" src="//www.google.com/trends/embed.js?hl=en-US&q=oil+sands%2B+tar+sands,+fracking&cmpt=q&content=1&cid=GEO_MAP_0_0&export=5&w=500&h=530"></script>
This is a bit of a surprise, since the assumption here in Canada is that the world is very interested in the tar sands. It appears that there is much more interest in fracking.Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com1tag:blogger.com,1999:blog-6991386370942322529.post-91408780244859416542013-04-19T16:34:00.000-04:002013-04-19T16:34:02.574-04:00What Google Trends is Saying About Renewable Energy and FrackingGoogle searches of the term "renewable energy" peaked in March of 2009. Since then, Google searches for renewable energy having been trending downwards. In comparison, searches of the term "fracking" really started to take off in late 2010 and hit a record high in February of this year.
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<script src="//www.google.com/trends/embed.js?hl=en-US&q=%22renewable+energy%22,+fracking&cmpt=q&content=1&cid=TIMESERIES_GRAPH_0&export=5&w=500&h=330" type="text/javascript"></script>
Here is a regional map of searches for renewable energy. Searchers in Europe, Africa, India, and Australia have shown strong interest in renewable energy.
<script type="text/javascript" src="//www.google.com/trends/embed.js?hl=en-US&q=%22renewable+energy%22,+fracking&cmpt=q&content=1&cid=GEO_MAP_0_0&export=5&w=500&h=530"></script>
Here is a regional map of searches for fracking. Notice how much search interest there is in this term coming from the US and South Africa.
<script type="text/javascript" src="//www.google.com/trends/embed.js?hl=en-US&q=%22renewable+energy%22,+fracking&cmpt=q&content=1&cid=GEO_MAP_1_0&export=5&w=500&h=530"></script>
Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com1tag:blogger.com,1999:blog-6991386370942322529.post-5079961811037019072013-04-17T14:18:00.001-04:002013-04-17T14:18:44.477-04:00Maximum Drawdown for Previous PostIn my previous <a href="http://perrysadorsky.blogspot.ca/2013/04/testing-absolute-momentum-on-tse.html">post</a> I compared several investment strategies for the TSE. Here is an updated table which includes drawdown along with some of the usual risk measures. The seasonal strategy has the highest average annual return (11.35%) and lowest standard deviation. The seasonal strategy has the highest Sharpe Ratio, Sortino Ratio, and Omega Ratio.The seasonal strategy also has the lowest maximum drawdown. <br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-2WL_-uqT7MBr34L4QTjPPAFxrKj80ZRSvXpkRNu_lRsPP0K-0HN3qWf-rFSAzPUUJZTJbQSCO79R5-yBIbr2azQrWRlydyBKWeEyCe8gYVT0M4jllwW4TMIJYY8PXsxsgOsMD5WIvus/s1600/tsxma10march2013_2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="128" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-2WL_-uqT7MBr34L4QTjPPAFxrKj80ZRSvXpkRNu_lRsPP0K-0HN3qWf-rFSAzPUUJZTJbQSCO79R5-yBIbr2azQrWRlydyBKWeEyCe8gYVT0M4jllwW4TMIJYY8PXsxsgOsMD5WIvus/s400/tsxma10march2013_2.JPG" width="400" /></a></div>
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Here is a chart showing how $1000 invested in December of 1970 has performed for each of the strategies.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghipJ36LvRMnrP60G7r5ttXQCyyswpj-gPedjnogu2on8Nkq9b2ZMtwYbYVMgKqTnOptbciQ4AFOLKyT9QwKTjY4JageOv1BBIRnmWhvHunSX9x3Bh0aVzqNB2TiVbA_ZBYVTSSQI2dUY/s1600/comparing1000dollars.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghipJ36LvRMnrP60G7r5ttXQCyyswpj-gPedjnogu2on8Nkq9b2ZMtwYbYVMgKqTnOptbciQ4AFOLKyT9QwKTjY4JageOv1BBIRnmWhvHunSX9x3Bh0aVzqNB2TiVbA_ZBYVTSSQI2dUY/s400/comparing1000dollars.JPG" width="400" /></a></div>
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Overall, the seasonal and moving average strategies provide some downside protection in case things go really bad.Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0tag:blogger.com,1999:blog-6991386370942322529.post-43605985781204067532013-04-10T17:20:00.000-04:002013-04-10T17:22:28.191-04:00Testing Absolute Momentum on the TSEA new research paper by <span style="font-family: Myriad Roman, Arial, Helvetica, Sans-serif; font-size: x-small;"><a class="textlink" href="http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1556771" style="font-size: 14px; font-weight: bold;" target="_blank" title="View other papers by this author">Gary Antonacci</a></span> on <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2244633">absolute momentum</a> piqued my interest.In its simplest form, absolute momentum strategies compare excess asset returns over a pre-defined look back period. If excess returns over the look back period are positive, invest in the asset. If excess returns over the look back period are negative, invest in a 3 month t bill.Antonacci's research shows that absolute momentum strategies work well in a number of markets including US equities, US REITS, US bonds, EAFE, and gold. I thought it would be interesting to see how well an absolute momentum strategy works for the TSE.<br />
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For equity data I use the MSCI Canada total return monthly data (includes dividends). For the risk free rate, I use 3 month Canadian t bills. I choose a look back period of 12 months. 12 months seems to work well for other assets so I choose 12 months for my analysis. This minimizes data snooping. The estimation sample covers the period January 1971 to March 2013. For comparison purposes, I also include buy and hold (B&H), a simple MA(10) switching portfolio, and a seasonal switch strategy (invest in the TSE in the 6 months November through April: invest in 3 month t bills for the 6 months May through October). The calculations do not include trading costs.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMMFP808vwYKZO2CtXgOFTAFiQMh5tuyCYVkwjDgmQ9OqVAkPUlt4t-zFJpY5xuNqJw6OAeSbhljjHCd8vLqPmSRbAy5E7XhFWxuGY4IRZd6CYTA5hFC_HS1axIVGndPiwAEVHooLdbOU/s1600/tseabsmom.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMMFP808vwYKZO2CtXgOFTAFiQMh5tuyCYVkwjDgmQ9OqVAkPUlt4t-zFJpY5xuNqJw6OAeSbhljjHCd8vLqPmSRbAy5E7XhFWxuGY4IRZd6CYTA5hFC_HS1axIVGndPiwAEVHooLdbOU/s400/tseabsmom.JPG" width="400" /></a></div>
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In the case of Canada, there is some evidence that absolute momentum works. Absolute momentum is preferred to buy and hold because it has a higher Sharpe ratio, Sortino ratio, and Omega ratio. One undesirable feature, however, is that absolute momentum has higher downside risk than buy and hold. Notice how the seasonal switch strategy really stands out. The seasonal switch strategy has the highest Sharpe ratio, Sortino ratio, and Omega ratio. The seasonal switch strategy also has the lowest standard deviatiion and downside risk.<br />
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<br />Perry Sadorskyhttp://www.blogger.com/profile/07459686601682036963noreply@blogger.com0