What is the expected return on an efficient portfolio with a standard deviation of 15%? Assume the risk-free rate is 6% and the expected return on the market portfolio is 14.8% with a standard deviation of 20%.
A)8.20%
B)12.60%
C)16.50%
D)17.73%

Question

Quizplus · Accepted Answer

The expected return on an efficient portfolio can be calculated using the Capital Asset Pricing Model (CAPM) formula: Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate). However, without the beta, we use the concept of the Security Market Line (SML) which is derived from CAPM and represents expected return as a function of systematic risk (beta). Given the information, we can also approach this through the concept of the Sharpe ratio, which is a measure for calculating risk-adjusted return. It is the ratio of the difference between the return of the investment and the risk-free rate, divided by the standard deviation of the investment. The Sharpe ratio of the market can be calculated as (Market Return - Risk-Free Rate) / Market Standard Deviation = (14.8% - 6%) / 20% = 0.44. Assuming the portfolio is efficient, it should have the same Sharpe ratio as the market. Thus, we can find the expected return of the portfolio by rearranging the Sharpe ratio formula: Expected Return = Risk-Free Rate + (Portfolio Standard Deviation * Sharpe Ratio of the Market) = 6% + (15% * 0.44) = 6% + 6.6% = 12.6%.

What Is the Expected Return on an Efficient Portfolio with a Standard