NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return
Portfolio A has a return of 15%, standard deviation of 20% and beta of 1.2. Portfolio B has a return of 13%, standard deviation of 12% and beta of 0.8. The risk-free rate is 7%. Which statement is correct?
Portfolio B has the higher Sharpe ratio: 0.50 against 0.40 for A. Sharpe is excess return over the 7% risk-free rate divided by standard deviation: A is 8/20 = 0.40 and B is 6/12 = 0.50, so B gives more return per unit of total risk.
- AA has the higher Sharpe ratio, 0.40 versus 0.50 for B
- BB has the higher Sharpe ratio, 0.50 versus 0.40 for ACorrect
- CA has the higher Treynor ratio, 6.67 versus 6.00 for B
- DBoth have the same Sharpe ratio of 0.40
Explanation
Sharpe A = (15-7)/20 = 0.40; Sharpe B = (13-7)/12 = 0.50, so B is higher. Treynor A = 8/1.2 = 6.67 and B = 6/0.8 = 7.5, so B is also higher on Treynor, which makes the third option false. The first option reverses the ranking.
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