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Jensen's Alpha

This is a risk-adjusted measure used to gauge the extent to which a manager has added value to the returns that could have been expected from a benchmark portfolio with the same degree of sensitivity to movements in the market (Beta). It is calculated by subtracting the fund's Beta from its average return in excess of the notional risk-free rate, then multiplying the result by the benchmark's average return in excess of the risk-free rate.
It is designed to be a test of whether a fund has achieved a better performance than its Beta would suggest: a positive Jensen Alpha indicates an active management style with superior stock-picking ability; a negative figure is produced if returns are less than the fund's Beta, and thus falling short of the benchmark. In effect, the measurement determines how much extra has been generated from active management, by comparison with returns that would have been achieved anyway, while carrying the same level of market risk. Finally, since Jensen's Alpha is calculated by reference to a fund's Beta, a strong R-squared correlation between the fund and its benchmark is important if the measure is to have any significance.

Worked Example: Jensen's Alpha – What do you expect?
Positive Jensen's Alpha is a measure of how much return a fund has generated over and above what it could have been expected to make. By extension, a negative Jensen will quantify by how much a fund has failed to meet the expected return. But how do we establish the amount of return we should expect?
This is done by reference to the fund's benchmark. It is reasonable to assume that matching a benchmark's return is no great feat; further, if the exercise is to be worthwhile, the fund's return should beat the benchmark by a margin that could have been earned from a risk-free investment.
The starting point, then, is the benchmark return in excess of a notional risk-free rate (in our examples we are using a RFR of 3.5%). Then, acknowledging the effect of the fund's sensitivity to benchmark movements, the excess return is multiplied by the fund's Beta. This produces Jensen's Alpha. As a practical example, we can look at the following ratios table:

Table 9. Ratios table over 36 months (from 31 Aug 2002 to 31 Aug 2005) against benchmark "UT Europe Excluding UK" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Ann Volatility Beta Sharpe Jensen's Alpha R-Squared
Credit Suisse MMgr European 14.65 0.81 0.78 2.44 0.86
Insight European Discovery EUR 16.99 0.93 0.39 -3.6 0.83
New Star European Portfolio 13.49 0.75 1.14 7.09 0.86
Scottish Widows European Gth 14.51 0.83 0.73 1.41 0.9
Taube Hodson Stonex Ptnrs Eurpn 14.49 0.79 0.73 1.86 0.82
Sector: UT Europe Excluding UK 16.67 1 0.67 0 1

Here we can see that the all-important R-squared correlation between the funds and their sector benchmark is strong in each case. The Betas suggest varying degrees of sensitivity to benchmark movements, and this is taken into account in the range of Jensen's Alphas that is evident. Our next table shows how this translates into performance.

Table 10. Total Return - Standard performance table from Unit Trust/OEIC universe
Name 1m 3m 6m 1y 3y
New Star European Portfolio TR 3.71 12.13 13.54 33.33 86.5
Credit Suisse MMgr European TR 3.45 11.36 12.73 33.08 71.75
Sector: UT Europe Excluding UK TR 2 9.76 11.66 28.01 70.16
Scottish Widows European Growth TR 3.24 10.8 15.52 31.87 65.9
Taube Hodson Stonex Partners European TR 1.11 6.99 9.77 24.77 62.96
Insight European Discovery EUR TR 2.36 9.48 14.06 28.25 54.39

Looking at three-year returns, Insight's negative Jensen is borne out by the fund's underperformance of the sector. Given its Beta of 0.93, one would expect performance to be more in line with the benchmark but, alas, no. This suggests some active management bets that have not prospered, and that simply tracking the sector would have yielded better results.
Conversely, New Star, with the highest Jensen, has comfortably outperformed. Active management has succeeded in adding value, and the Jensen reflects the risk-adjusted return over what could have been expected from this sector.
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