Sharpe ratio
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1. Mark Harrywitz proposes to invest in two different stocks, X and Y. He expects a return of 12% from X and 8% from Y. The standard deviation of returns is 20% for X and 10% for Y. The correlation coefficient between the returns is .2.
a. Compute the expected return and the standard deviation of the following portfolios:
Portfolio Percentage in X Percentage in Y
1 50 50
2 25 75
3 75 25
b. Sketch the set of portfolios composed of X and Y on a graph with E(r) on the vertical axis and the portfolio standard deviation on the horizontal axis.
c. Suppose that Mr. Harrywitz can also borrow or lend at an interest rate of 5 percent. Show on your sketch how this alters his opportunities. Given that he can borrow or lend, approximately what proportions of the common stock portfolio should be invested in X and Y?
2. You create a portfolio with 25 stocks and put 4 percent of your money in each of the 25 securities. Each of the stocks has an expected return of 13 percent, a standard deviation of 40 percent, and a common (pairwise) correlation coefficient of .5. What is the expected return and standard deviation of this equally weighted portfolio? If T-bills yield 7 percent, what is the Sharpe ratio for this portfolio (the slope of the CAL?
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Sharpe ratio is discovered.
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