Question

Suppose that the market portfolio has an expected return of 10%, and a standard deviation of returns of 20%. The risk-free rate is 5%.

b) Suppose that stock A has a beta of 0.5 and an expected return of 3%. We would like to evaluate, according to the CAPM, whether this stock is overpriced or underpriced. First, construct a tracking portfolio, made using weight K on the market portfolio and 1 − K on the risk-free rate, which has the same beta as stock A. What should K be?

c) Now, compute the expected return on the tracking portfolio. Is it higher or lower than the expected return on stock A? If we are holding the market portfolio, how should we adjust our portfolio to increase its Sharpe ratio?

d) Suppose that stock F has a standard deviation of returns of 30%. If the CAPM holds, can we say anything about the expected return on stock F? i.e. what are the maximum and minimum possible expected return for stock F?

Answer 1

(b) Return as per CAPM of Stock A = RF + Beta(RM - RF)

• RF = Risk free rate
• Beta
• RM = Return as per market

=5 + 0.5 (10 - 5 )

=7.5%

Expected return as per market is 3%

Expected beta is 0.5

0.5 = (0.2 * k) + (0 * 1-k)

0.5 = 0.2k

k = 2.5

Amount to be invested in Market portfolio and Risk free securities is 2.5:(-1.5)

(c) Expected return of tracking portfolio = (10%* 2.5) + (5% * -1.5) = 17.5%

It is higher comparing to return as per CAPM

To increase the sharp ratio, investor should consider investing in market portfolio.

(d)

Standard Deviation(SD) of Stock F is 30%

Maximum possible expected return of Stock F

• When R is 1

Beta = (R*SD of Security)/SD of Market

=1.5

Return as per CAPM = RF + Beta ( RM - RF)

= 5 + 1.5(10-5)

=12.5%

Minimum possible expected return on Stock F

• When R is -1

Beta = -1.5

Return as per CAPM = RF + Beta (Rm - RF)

=5 + (-1.5)(10-5)

= -2.5%