Alpha Stability

his article builds on my article in the last month's issue (Alpha in the Box). Just like any other measurement statistic, the alpha coefficient of a mutual fund is a snapshot (based on historical data) at a particular moment in time. At a later moment in time, the alpha coefficient will be different. This study measures the volatility of alpha coefficients over a 10-year period within each of the nine Morningstar style boxes.

As a reminder, alpha is "a measure of the difference between a portfolio's actual returns and its expected performance, given its level of risk as measured by beta. A positive alpha figure indicates the portfolio has performed better than its beta would predict. In contrast, a negative alpha indicates the portfolio has underperformed, given the expectations established by beta." (Morningstar)

The U.S. equity mutual funds included in this analysis were extracted from Morningstar's Principia database. There were a number of stringent filters employed in the selection of funds. First, only distinct funds were considered (i.e. only one share class of multiple share class funds was included). Index funds, enhanced index funds, and exchange traded funds were omitted inasmuch as they shouldn't be generating an alpha coefficient of any consequence if they are faithfully tracking their respective index. Sector funds were excluded. Funds chosen for analysis had to have at least 80% of their portfolio in U.S. stock and have a 10-year performance history as of 12/31/05. Finally, only funds with an Equity Style Consistency Rating of "High" were included. In the end, 343 funds were analyzed (35 large cap value, 76 large cap blend, 88 large cap growth, 10 mid cap value, 18 mid cap blend, 41 mid cap growth, 18 small cap value, 17 small cap blend, and 40 small cap growth).

The calculation of alpha for each fund followed the format outlined in last month's article. However, in this analysis, four alpha coefficients (each one covering a period of 30 months) were calculated using monthly data for each fund over the 10-year period. The first 30-month period was from January, 1996 to June 1998, the second period was from July 1998 to December, 2000, the third period spanned from January, 2001 to June, 2003, the last period was from July, 2003 to December, 2005. Unlike the analysis last month, alpha coefficients in this analysis were not asset-weighted due to the fact that obtaining monthly net asset figures over the 10-year period was not feasible.

In order to demonstrate the steps in this analysis, detailed results for the 35 large cap value funds are shown in the table "Large Value Funds". The funds in the table are ranked in descending order by their mean alpha. Let's examine a specific fund--Vanguard Equity Income. During the first 30 month period (January 1996 to June 1998) its alpha coefficient was 0.26. During period 2, its alpha was 2.09, and so on. The average of the four alphas over the 10-year period was 0.43. The standard deviation of the four alphas was 1.32. The average of the 35 "mean alphas" for this group of large cap value funds was -0.62% and the mean of the 35 standard deviations of the was 2.47%. The results for each of the remaining eight Morningstar style boxes are presented in the figure "Alpha Summary".

As shown in "Alpha Constellation" (essentially a graph of risk-adjusted alpha coefficients) large value funds had the lowest alpha volatility (as measured by standard deviation) followed by large blend funds and small cap value funds. However, large value funds also had the second lowest average alpha (-0.62) over this 10-year period. Small cap blend funds had the highest average alpha and the 6th highest alpha standard deviation.

The efficient alpha frontier (highlighted in red) consists of the large value (LV), large blend (LB), small value (SV), and small blend) SB style boxes. In other words, the style boxes closest to the northwest corner. Mid value (MV), large growth (LG), and mid blend (MB) style boxes (in blue) represent a slightly suboptimal frontier on the basis of risk-adjusted alpha. Mid growth (MG) funds and small growth (SG) funds (in yellow) are two equity styles that generated high alpha volatility without compensatory high alpha over this particular 10-year period. In essence, they represent the least efficient frontier of risk-adjusted alpha as they are closest to the southeast corner of the graph.

In the case of small growth (SG) funds, an average alpha of 0.87 was impressive, but the alpha volatility of 8.05 informs us that the average alpha was highly variable. Indeed, the average alpha among the 40 SG funds during period one was 3.27, 4.99 during period two, -1.58 in period three, and -3.20 during period four. Mid growth funds had the worst of both-low average alpha and high volatility of alpha. This suggests that active management was relatively ineffectual, or at best sporadically successful, among mid cap growth funds.

To summarize, alpha for small growth funds was about three times more volatile than alpha among large value and large blend funds during the period being studied. Said differently, the alpha of large value and large blend funds exhibited about 30% of the volatility of the alpha among small growth funds. This isn't all bad. Small growth funds generated high average alpha during the first two periods. But, the fortune of SG funds shifted during the latter two time periods as reflected in negative average alpha.

Over this 10-year period the alpha coefficient of large cap value and large cap blend funds fluctuated within a significantly smaller "bandwidth" than the alpha coefficient of small cap growth funds (and growth funds in general). However, despite the greater fluctuation in alpha among small growth funds, SG funds generated the third highest average alpha among the nine style boxes. Small blend funds, arguably a style box that is easily overlooked, had the highest risk-adjusted alpha in this study.

In general, growth funds had inferior risk-adjusted alpha compared to blend funds and value funds over this 10-year period. Compared to value and blend funds, growth funds appear to have greater alpha volatility, effectively reducing our confidence in the usefulness of using alpha as a selection criterion among growth funds-precisely because alpha tends to be a moving target among growth funds (this was particularly true among mid growth funds and small growth funds).

Growth funds have, if you will, distinctive risk-adjusted alpha characteristics whereas the risk-adjusted alpha of value funds and blend funds is more similar (particularly among large cap funds). This may suggest that-on average-choosing between a value fund and a blend fund is a less significant decision than choosing between a blend fund and a growth fund. During the past 10 years, the boundary between value and blend funds was thinner than the boundary between blend and growth funds-at least in terms of risk-adjusted alpha.

Large Value Funds

Alpha Summary

Alpha Constellation

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Craig L. Israelsen, Ph.D. is an associate professor at Brigham Young University. He teaches family finance in the Department of Home and Family Living. His research interests include mutual fund analysis. He writes monthly for Financial Planning magazine. Learn more about Craig Israelsen at http://familyliving.familylife.byu.edu/faculty/israelsen.htm