Estimate the expected excess return for allseven stocks

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Reference no: EM132168298

Part -1: Efficient Equity Portfolios

Problem 1

Write an Rprogram to find the efficient frontier, the tangencyPortfolio, and the minimum variance portfolio, and plot on "reward-riskspace" the location of each of the six stocks, the efficient frontier, the tan-gency portfolio, and the line of efficient portfolios. Use the constraints that-0.1≤wj≤0.5for each stock. The first constraint limits short sales but does not rule them out completely. The second constraint prohibits more than50 % of the investment in any single stock. Assume that the annual risk-freerate is 3 % and convert this to a daily rate by dividing by 365, since interestis earned on trading as well as nontrading days.

Problem 2

If an investor wants an efficient portfolio with an expected daily return of 0.07 %, how should the investor allocate his or her capital to the sixstocks and to the risk-free asset? Assume that the investor wishes to use thetangency portfolio computed with the constraints -0.1≤wj≤0.5,not theunconstrained tangency portfolio.

Part -2:

In this lab, you will fit model (17.20). The S&P 500 index will be a proxy forthe market portfolio and the 90-day Treasury rate will serve as the risk-freerate.This lab uses the data setStock_Bond_2004_to_2006.csvwhichis available on the book's website. This data set contains a subset of the data inthe data set Stock_Bond.csvused elsewhere.

TheRcommands needed to fit model (17.20) will be given in small groupsso that they can be explained better. First run the following commands toread the data, extract the prices, and find the number of observations:

dat = read.csv("Stock_Bond_2004_to_2006.csv", header = TRUE)
prices = dat [ , c(5, 7, 9, 11, 13, 15, 17, 24)]
n = dim(prices)[1]

Next, run these commands to convert the risk-free rate to a daily rate, compute net returns, extract the Treasury rate, and compute excess returns for themarket and for seven stocks. The risk-free rate is given as a percentage so thereturns are also computed as percentages.

dat2 = as.matrix(cbind(dat[(2:n), 3] / 365,
100 * (prices[2:n,] / prices[1:(n-1), ] - 1)))
names(dat2)[1] = "treasury"
risk_free = dat2[,1]
ExRet = dat2[ ,2:9] - risk_free
market = ExRet[ ,8]
stockExRet = ExRet[ ,1:7]

Now fit model (17.20) to each stock, compute the residuals, look at a scatter-plot matrix of the residuals, and extract the estimated betas.fit_reg = lm(stockExRet ~ market)
summary(fit_reg)
res = residuals(fit_reg)
pairs(res)
options(digits = 3)
betas = fit_reg$coeff[2, ]

Problem 1
Would you reject the null hypothesis that alpha is zero for any of the seven stocks? Why or why not?

Problem 2
Use model (17.20) to estimate the expected excess return for allseven stocks. Compare these results to using the sample means of the excess re-turns to estimate these parameters. Assume for the remainder of this lab thatall alphas are zero. (Note: Because of this assumption, one might considerreestimating the betas and the residuals with a no-intercept model. However, since the estimated alphas were close to zero, forcing the alphas to be ex-actly zero will not change the estimates of the betas or the residuals by much.Therefore, for simplicity, do not reestimate.)

Attachment:- Problems.rar

Reference no: EM132168298

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