Question

Market portfolio has an expected return of 11% and volatility of 20%. Risk-free rate is 3%. Security X and Y have betas of 1.4 and 0.9 respectively.

a) According to CAPM, what are the expected return of X and Y?

E(rm)-rf = 11% - 3% = 8%

3% +1.4*8% = 14.2%

3% +1.4 *8% = 10.2%

b) What should be X worth today, if X pays a dividend of $1.2 one year from today and is priced at 30 one year from today? The required rate of return is the expected return using CAPM from part a).

c) If security X has expected return of 15%, is it underprice/overprice/fairly priced according to CAPM? What is its alpha?

d) Plot SML and label X, Y and Market portfolio on the line.

e) What is the beta of a portfolio with 50% in X and 50% in Y?

f)What is the beta of a portfolio with 55% in Market portfolio and 45% in risk-free asset?

g) You are investing in a complete portfolio. The complete portfolio is composed of risk-free asset and a risky portfolio, P, constructed with 20% in X and 80% in Y. It turns out that your complete portfolio has an expected rate of return of 9.4%. What is the beta of your complete portfolio? (hint: you may or may not use all information to solve this problem)

Q2. Stock A has a beta of 1 and standard deviation of 50%. Market portfolio has a standard deviation of 20%. What is the correlation of stock A with the market portfolio? How much of stock A’s total risk is due to market risk?

Q3. Assume the risk-free rate is 8% and the expected rate of return on the market is 18%. A stock has an expected return of 6%. What is its beta?