Analyzing Fund Performance: Beta Neutral Strategies and Jensen’s Alpha

Consider two funds A and B in country. Fund A gives a return of 13% with a standard deviation of 25%, Fund B gives a return of 18% with a standard deviation of 33%. If risk free rate is 4%, the return of the market portfolio is 14% and has a standard deviation of 20%. Consider the following information. Fund A uses beta neutral strategy i.e. it buys (long) on some stocks or sell (short) on some stocks. Fund B has a beta of 1.2. A beta neutral strategy means that the beta of zero.  Use knowledge of capital asset pricing model to understand which of the funds performed better. Use Jensen’s Alpha to perform the analysis.

The question is inspired from the research paper – Perold, André, F. 2004. “The Capital Asset Pricing Model.” Journal of Economic Perspectives, 18 (3): 3–24. 

First, here there is no need to calculate a superior return using the Sharpe ratio. Fund A is beta neutral, so its beta is zero. If we use the Sharpe ratio without taking the investment style, the comparison will not be judicious. Market Neutral Strategy is used by hedge fund managers and requires shorting of stock.

Fig 1: Comparison Chart | The middle Road 

Fund B on the other hand is employing a long-only strategy. In this case, one needs to compare returns generated to the respective benchmark. If we compare the alpha generated, for Fund A it will be on the risk-free rate of 4%. Since the beta of the fund is zero, its performance is judged against the risk-free rate.

Fund A alpha is 13% – 4% = 9%.

Expected Return = Risk-Free Rate + Beta * (Excess return of the fund over risk-free rate)
Excess return of the fund over risk free rate = Market Premium

Fund B Expected Return = 4% + (18%- 4%) * 1.2 = 4% + 16.8% = 20.8%
Fund B Alpha = 18% -20.8% = -2.8%

Fund A is a better performer than Fund B. However, if we had looked at Sharpe Ratio ==> Sharpe Ratio of Fund A is 0.36 and Fund B is 0.42, Fund B is giving superior risk adjusted return.

Suggested Reference Read 

Perold, André, F. 2004. “The Capital Asset Pricing Model.” Journal of Economic Perspectives, 18 (3): 3–24

Disclaimer
This question and analysis are inspired by Dr. Andre Perold’s research paper, The Capital Asset Pricing Model. The content has been developed independently by The Middle Road as part of its proprietary educational offerings. Any resemblance to original materials is incidental, and this document is not affiliated with or endorsed by Dr. Andre Perold or his publisher. The Middle Road asserts its ownership over the original aspects of this material while acknowledging the academic influence of the referenced work.