1. Suppose that in 2021, there are three possible growth rates for the US economy: 8%, 6% and 4%. Suppose that the three scenarios are equally likely to occur. Further assume that the return on the stock market during the year will be 20%, 10%, and 0% respectively in these three scenarios, and the return on the 10-year T-bond will be -1%, 2%, and 5% in these three scenarios. What are the standard deviations of stocks' and bonds' returns in 2021? What is the correlation coefficient between stocks' and bonds' returns?

2. You, a pension fund manager, are considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a risk-free rate of 2%. The expected returns and standard deviations of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	10%	15%
Bond fund (B)	4%	8%

The correlation coefficient between the returns of stock fund and bond fund, is 0.1

1. You invest 50% in the T-bill money market fund and 50% in the bond fund. What is your expected return and standard deviation?
2. You invest only in the stock fund and bond fund. You want an expected return of 8%. What is the standard deviation of your portfolio?
3. You invest in all three funds. Use the formula for the weights of the optimal risky portfolio to compute the optimal portfolio weights. What is the Sharpe ratio of the best CAL? You manage $1000 for your client and your client wants an expected return of 8%. How much money do you invest in each of the three funds?
4. Is the standard deviation of your complete portfolio from C higher or lower than that in B?

3. Suppose that the yield on short-term government securities (perceived to be risk-free) is 2%. Suppose also that the expected return required by the market for a portfolio with a beta of 1.0 is 10% over the next year. You consider buying one share of a company's stock. The stock is expected to pay a dividend of $3 one year later and to sell then for $41. The stocks beta is 0.8. What must be the price of the stock according to the capital asset pricing model?

4. Assume that CAPM holds. Suppose that the expected return of the market portfolio is 7% in 2021 and the standard deviation of market return in 2021 is 12%. Assume that the covariance of Walmart's stock return with the market is 0.00144, and the covariance of Alphabet's stock return with the market is 0.01512. The standard deviations of Walmart and Alphabet stock return are 6% and 20%, respectively. What proportion of Alphabets and Walmarts risk (variance) can be diversified away?