Question

If the simple CAPM is valid, is the situation below possible? You need to provide explanation for it, just yes or no is not acceptable.

Portfolio	Expected return	Standard deviation
Risk free	8%	0
Market	18%	24
Portfolio A	20%	22

Answer 1

Given that,

Risk free rate Rf = 8%

Expected return on market Rm = 18%

Standard deviation on market SDm = 24%

Expected return on portfolio A Ra = 20%

Standard deviation of portfolio A SDa = 22%

So, reward-to-volatility ratio of market and portfolio A is calculated using formula:

reward-to-volatility ratio = (E(r) - Rf)/SD(r)

for portfolio A, reward-to-volatility ratio = (20-8)/22 = 0.5455

for market portfolio, reward-to-volatility ratio = (18-8)/24 = 0.4167

Since reward-to-volatility ratio is lower for Market portfolio, this condition is not possible according to CAPM, since CAPM predicts the market portfolio as the most efficient portfolio.