Frank Bellamy, aged 61, wants to know whether the manager of one sleeve of his diversified portfolio added value beyond what its market exposure alone would have delivered. Over the measurement period the sleeve returned 12.2 percent a year, the broad market index returned 9.5 percent a year, the risk-free rate averaged 3.0 percent a year, and the sleeve's beta against that index was 1.20. Using the capital asset pricing model to set the required return, and rounding to one decimal place, what is Jensen's alpha for the sleeve?
- Aplus 2.7 percent
- Bminus 2.2 percent
- Cplus 9.2 percent
- Dplus 1.4 percent Correct
Why A is wrong: This subtracts the market return of 9.5 percent from the sleeve's 12.2 percent, which implicitly treats beta as 1.00 and so gives the manager credit for the extra return that the sleeve's above-market beta of 1.20 was expected to produce.
Why B is wrong: This applies beta to the whole market return rather than to the market risk premium, giving 3.0 plus 1.20 multiplied by 9.5, which is 14.4 percent, because the 3.0 percent risk-free rate was not subtracted from the 9.5 percent market return.
Why C is wrong: This is the sleeve's excess return over the risk-free rate, 12.2 less 3.0, which is the numerator of Sharpe and Treynor but is not alpha, because nothing has yet been deducted for the return the sleeve's market exposure was expected to earn.
Why D is correct: The capital asset pricing model required return is 3.0 plus 1.20 multiplied by (9.5 less 3.0), which is 3.0 plus 7.8, or 10.8 percent, and the sleeve returned 12.2 percent, so alpha is 12.2 less 10.8, which is 1.4 percent.