assignment1solutions

assignment1solutions - Stat 371 Assignment 1 Solutions...

This preview shows pages 1–3. Sign up to view the full content.

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('http://www.math.uwaterloo.ca/~rjmackay/pension.txt',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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/12/2011 for the course STAT 371 taught by Professor Ahmed during the Fall '09 term at Waterloo.

Page1 / 8

assignment1solutions - Stat 371 Assignment 1 Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online