Question

Assume the CAPM holds and the return on the market portfolio is 10%, its standard deviation is 10% and the risk-free rate is 5%. Can each of the following assets exist in equilibrium? Explain.

a) A bond with expected return 0% and standard deviation 1%

b) A put option with expected return 50% and standard deviation of 100%

c) A stock with an expected return of 10% and the standard deviation of 9%

d) A call option with Sharpe ratio expected to return 15% and standard deviation 20%

Answer 1

Based on the sharpe ratio of market portfolio, we will conclude if the four assets exist in equillibrium or not.

First calculating sharpe ratio for the market =

Sharpe ratio = [return on portfolio - risk free rate] / standard deviation

Sharpe ratio for market = [10 - 5] / 10 = 5/10 = 0.5

a. Sharpe ratio for a bond = [0 - 5] / 1 = -5

b. Sharpe ratio for put option = [50 - 5] / 100 = 45/100 = 0.45

c. Sharpe ratio of stock = [10 - 5] / 9 = 5/9 = 0.55

d. Sharpe ratio for call option = [15-5] / 20 = 10/20 = 0.5

When comparing hese assets with market portfolio ,

Bond is a not in equillibrium because it is too far from that of market portfolio,

Put option and stock is most likely to be in equillibrium

call option is in equillibrium because sharpe ratio is exactly that of market portfolio.