assignment1solutions - Stat 371 Assignment 1 Solutions...

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1 Stat 371 Assignment 1 Solutions Spring 2007 1. A company that manages part of a pension fund is responsible for investing in equities outside North America. To justify the fees, the pension fund trustees require that the company achieve returns better than a benchmark portfolio, here the so-called EAFE index, by 200 basis points (2%). In reporting to their client , the company’s portfolio review contained the following statement about the control of risk. “We define and control risk through statistically based measurements such as R 2 . This ensures that we maintain an appropriate level of diversification given each client’s portfolio objectives. A minimum R 2 of .80 would be acceptable; however the R 2 in our portfolio has typically been meaningfully higher. … In this way, a well diversified portfolio can be achieved without resorting to the more common country, economic or industry diversification approaches which tend to limit stock selection flexibility.” In the file pension.txt , you will find the monthly returns (% change from the previous month) for the portfolio and the EAFE index for a period from month end March 2001 until month end March 2005. The variate names are Month, EAFE and portfolio. a) Use R to plot the portfolio returns against the index. Fit a line and add the fitted line to the plot. I used the following R code to create the plot on the next page and to add the fitted line. Note that I chose to fit a model with an intercept a<-read.table('',header=T) attach(a) b<-lm(portfolio~EAFE) summary(b) plot(portfolio~EAFE, xlab=’EAFE monthly returns’,ylab=’portfolio monthly returns’, main=’Plot of Portfolio vs EAFE returns March 2001 to March 2005’) abline(b) The summary output: R code summary(b) is Call: lm(formula = portfolio ~ EAFE) Residuals: Min 1Q Median 3Q Max -4.9592 -0.6717 0.0491 0.7127 3.7005 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -0.02855 0.22557 -0.127 0.9 EAFE 0.88279 0.05398 16.355 <2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
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2 Residual standard error: 1.578 on 47 degrees of freedom Multiple R-Squared: 0.8505, Adjusted R-squared: 0.8474 F-statistic: 267.5 on 1 and 47 DF, p-value: < 2.2e-16 The plot is shown below. b) Was the volatility of the portfolio greater than that of the index? Explain.
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This note was uploaded on 05/12/2011 for the course STAT 371 taught by Professor Ahmed during the Fall '09 term at Waterloo.

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assignment1solutions - Stat 371 Assignment 1 Solutions...

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