State of economy Probability of state of economy return on stock X Return on stock Y Return on Stock Z

Boom 10% .3 .2 -.05

Normal 70% .12 .1 .15

Poor 20% .05 -.15 .1

Use at least 6 decimal places when you calculate variances and covariances to avoid significant rounding errors.

a. Find the expected return, variance of returns, and standard deviation of returns of each stock.

b. Find the covariance and correlation of returns for each pair of stock.

c. You form a portfolio using stock X and stock Y. Compute the expected return, variance, and standard deviation of the portfolio with 40 percent of its fund invested in stock X and 60 percent in stock Y.

d. You form a portfolio using stock X, stock Y, and stock Z. You invest $10,000 in stock X, $15,000 in stock Y, and $25,000 in stock Z. Calculate the expected return, variance, and standard deviation of the portfolio.

e. Suppose the risk-free rate is 5 percent and the market portfolio has expected return of 11 percent (i.e., the market risk premium is 11 5 = 6 percent). If the betas of stock X, stock Y, and stock Z are 0.75, 1.20, and 1.80, respectively, use the Capital Asset Pricing Model (CAPM) to find the expected return of each stock. If the estimated returns are 12 percent, 10 percent, and 17 percent for stock X, stock Y and stock Z, respectively, compute alpha for each stock. Also indicate whether each stock is undervalued or overvalued according to the Capital Asset Pricing Model (CAPM).

f. Find the beta of the portfolio that has 20 percent invested in stock X, 30 percent in stock Y, and 50 percent in stock Z. The betas of stock X, stock Y, and stock Z are 0.75, 1.20, and 1.80 (same betas as part (e)), respectively. What is the expected return on the portfolio according to the CAPM? The risk-free rate is 5 percent and the market risk premium is 6 percent.