investmentquestions

FIN 5401: Investments
Problem Set 2
1. Assume that all stock returns have the market index as a common factor, and that all stocks in the economy have a beta of 1 on the market index. The firm-specific components of stock returns have a standard deviation of 30%. Suppose that an analyst studies 50 stocks, and finds that one-half have an alpha of
2.6%, and the other half have an alpha of -4%. Suppose the analyst buys $1 million of an equally weighted portfolio of the positive alpha stocks, and sells $1 million of an equally weighted portfolio of the negative alpha stocks.
a.What are the expected profit (in dollars) and the standard deviation of the analyst’s profit
(in dollars)?
b.What would your answer be if the number of stocks was 100 instead of 50? Explain your
results.
2. The excel file Data for PS2.xls contains monthly returns for Disney (RET), from 1995 to 2005. The file also contains the monthly series of T-bill rates (RF), excess return on the market (MKTRF), and Fama-French factors SMB and HML. Estimate alphas and factor loadings for the following asset pricing models and comment on your results:
a.The CAPM model, using all the data in the series.
b.The three-factor model, using all the data in the series.
c.The three-factor model, using data until December 2000.
3. A security is expected to pay a constant dividend in perpetuity. It is currently trading at $100 and its expected return is 14%. The risk free rate is 6 %. What will be the new price of this security if its correlation with the market portfolio doubles (all other variables remain unchanged)?
4. The expected return on a zero beta portfolio is 5%. Suppose you consider buying a share of stock at $100. It is expected to pay $4 dividend next year and you expect it to sell then for $106. The stock has a market beta of -0.
5. Is the stock over-priced or underpriced? The expected market rate of return is 12%.
5. You have gathered following information about stock X and Y.
Stocks Forecast Return Std Dev Beta
X 14% 36% 0.8
Y 17% 25% 1.5
Market Index 14% 15% 1.0
Risk Free rate 5%
a.Calculate expected return and alpha for each stock.
b.Identify and justify which stock would be more appropriate for an investor who wants to
a.add this stock to a well-diversified equity portfolio.
b.hold this stock as a single-stock portfolio.。