To see how this happens, consider a fund that outperforms its benchmark by five percentage points in January, when the benchmark return is zero, and is dead even with the benchmark every other month of the year. The correct alpha in this case is, of course, 5%. But thats not what gets reported. To illustrate, assume a funds value rose in January to 105 from 100 and assume the benchmark return over the balance of the year is 40%. The funds value rises to 147 (a 40% gain on the 105 value at the end of January). The conventional alpha magically rises to 7% (the 47% full-year return minus the 40% benchmark return).
But what if the benchmark drops 40% over the balance of the year and the funds value declines by the same 40% from 105 to 63? The conventional alpha shrivels to 3% (a 37% loss on the funds original value of 100 minus the 40% decline in the benchmark). The degree of distortion, from 5% to 7% or from 5% to 3%, is the same 40% as the percentage return of the benchmark.
Once again, the true alpha in both cases is 5%. That is the percentage difference between 140 and 147 and between 60 and 63. It also is exactly the percentage difference between an investors terminal wealth position and what the investor would have had with a benchmark investment at zero transaction costs and zero fees. As such, it is a properly scaled percentage measure of the managers contribution to the investors wealth.
It makes no difference, by the way, when the manager achieves its five-percentage-point superiority over the benchmark; it could come in any month, or be spread evenly or irregularly over the year. The end result is the same alpha expands or shrinks by the percentage change in the benchmark over the full year. And the same type of distortion also occurs in the calculation of a risk-adjusted Jensens alpha.
Happily, there is a simple methodology to correct this distortion and compute what I call a market-adjusted alpha. Simply divide the conventionally calculated alpha for any period by one plus the percentage total return on the benchmark over the same period. The result always equals the managers percentage contribution to an investors wealth. Market-adjusted alphas have another neat property: The market-adjusted alphas for subperiods (days or months) compound to the same answer as the calculation for the market-adjusted alpha for the full period (year or quarter). Conventional subperiod alphas never compound to the same value as the alpha for a full period.
While the effect on conventional alphas of a given percentage change in the benchmark is symmetric whether it is up or down, the relative impact of changing to market-adjusted alphas is not. In the case above, for example, market adjusting changes the up-market alpha from 7% to 5%. Thats a reduction of 29%. But the same two-percentage point increase in the down-market alpha, from 3% to 5%, boosts it by a whopping 67%.