Comparing Hedge Fund Performance based on Alpha
Team Latte
August 16, 2007
There's a lot of talk about "Alpha" these days. In light of the recent debacle in the credit markets and consequent losses in some of the large and well know hedge funds (which followed an "alpha" strategy) many are questioning the wisdom behind alpha.
We would talk in detail about alpha elsewhere in the site but for the moment a stylized case study would be in order to show how exactly is alpha calculated (a bit of "back of the envelope" method here) and we can use this for comparing the performance of various hedge funds.
Alpha is simply the excess return generated over what is predicted by the Capital Asset Pricing Model (CAPM) and that is really what every hedge fund is after.
Let's look at a three year return data for each fund.
Assume that the U.S. Dollar risk free rate in the economy is 5%. Also, assume that all fund returns are in dollar terms. The following are the data for the funds:
| Return Data of the Funds |
|
|
|
| |
Fund |
Fund |
Market |
| |
A |
B |
Index |
| year 1 |
23% |
14% |
12% |
| year 2 |
-15% |
-8% |
-6% |
| year 3 |
17% |
15% |
8% |
| Annualized Fund Returns = |
6.95% |
6.45% |
4.37% |
| Volatility of the Market Return = |
|
|
9.45% |
From the above return data and the three year annualized return computation it seems that though both the funds beat the market index in terms of return, Fund A did better than Fund B in terms of absolute return.
Market index had a (historical) realized volatility of 9.45%. The volatility is calculated simply as the standard deviation of returns. To calculate beta we need the correlation of the fund returns with the market return. That is easy to compute given the three year historical data. Also, once we compute the realized volatility of the individual funds from the above data we can easily calculate the Sharpe ratio. The results are as shown here:
| Quant Analysis |
|
|
| |
Fund |
Fund |
| |
A |
B |
| Volatility of Fund Returns = |
20.43% |
13.00% |
| correlation with Market Returns = |
0.9978 |
0.9685 |
| Sharpe Ratio = |
9.53% |
11.12% |
| Beta = |
2.16 |
1.33 |
| Alpha = |
-2.48% |
0.62% |
From the above we can see that even though in absolute return terms Fund A outperformed Fund B (a total return of 6.95% versus 6.45%) it neither generated a higher Sharpe ratio nor could generate a higher alpha. In fact, Fund A's alpha is negative (a value of minus 2.48%). Fund B generated a positive and a superior alpha.
A negative alpha means that the portfolio lies below the SML (Security Market Line) as given by the CAPM model. Any portfolio lying below the SML is an inferior portfolio and subject to high unsystematic risk.
  
Any comments and queries can be sent through our web-based form. |
a d v e r t i s e m e n t
