Alpha in the Box

he search for Shangri La pales in comparison to the quest for funds that consistently deliver high alpha. Fundamental question: does alpha differ across the nine Morningstar style boxes? In other words, do funds in some style boxes tend to deliver more alpha than funds in other style boxes?

Morningstar calculates alpha over a three-year period using monthly returns. Desiring a longer time period, this study calculated alpha within each of the nine different Morningstar style boxes using annual performance data over the 10-year period from 1996 to 2005.

Morningstar describes alpha as "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."

The equation for alpha used in this analysis was:

Alpha = (Annual Fund Return - Annual T Bill Return) - [Beta * (Benchmark Indexes Return - T Bill Return)]

Or, in reduced form, alpha can be expressed as:

Alpha = Annual Excess Return of Fund - [(Beta * (Annual Excess Return of Benchmark Return)]

Take the Dodge & Cox Stock fund for example. Dodge and Cox Stock is categorized by Morningstar as a large-cap value fund, hence its performance will be compared with the average performance of five large-cap value indexes-S&P 500/Citigroup Value, Dow Jones Large Value, Russell 1000 Value, Russell Top 200 Value and the Wilshire Large Value-as shown in "Benchmark Averages" on page tk. (More about benchmark averages in a moment.)

In "Creating Alpha," the annual returns of the three-month T-Bill (i.e. cash) are subtracted from the annual returns of the Dodge & Cox Stock fund for an annual excess return (17.01% in 1996, 23.09% in 1997, etc.). The annual return of cash was then subtracted from the average annual returns of five large-cap value indexes resulting in the annual excess return for the benchmark indexes (16.14% in 1996, etc.). Over the 10-year period from 1996 to 2005, the average annual excess return for Dodge & Cox Stock was 11.43% (in green) and 7.15% (in pink) for the five large-cap value indexes.

Next, the beta coefficient is calculated using the "@Slope" function in Excel. Beta describes the relationship between the annual returns of the Dodge and Cox fund and the average annual returns of the Large Value (LV) indexes over this particular 10-year period. The result was 0.67 (in blue), which can be interpreted as meaning that the Dodge & Cox Stock Fund was 67% as volatile as the average annual performance of the five LV indexes. Finally, the alpha coefficient (in gray) is calculated as [11.43% - (0.67 * 7.15%)] = 6.64%.

COMBINING BENCHMARKS

Why use averaged performance of several indexes? In any given year, there can be significant disparity in annual performance among prominent indexes within the same style box. Therefore, comparing the performance of actively managed funds against the average performance of several benchmark indexes, rather than just one, minimizes the risk of distortions when calculating "excess return." The annual returns of the three-month T-Bill are also reported in "Benchmark Averages."

The funds included in this study had to meet several criteria. First, they had to be distinct U.S. equity funds with at least a 10-year return as of Dec. 31, 2005. The term "distinct" indicates that redundant share classes were removed. Sector funds, index funds, exchange-traded funds and enhanced index funds were removed. Finally, each fund needed to have at least 66% of its portfolio in U.S. equities. Morningstar Principia was the data source for this study.

ASSET WEIGHTING

The results shown in "Alpha Raw and Cooked" are summarized in the graph "The Bigger the Better." In seven of the nine style boxes, the asset-weighted alpha was higher than the raw alpha. In fact, the average "bump" in alpha created by asset weighting was 77 basis points. When comparing the average alpha within each style box (which is an aggregate comparison), asset-weighting each fund's alpha coefficient is critically important because funds have dramatically different in size (i.e. net assets). Aggregate analysis that does not weight fund characteristics by net assets makes the assumption that all funds have the same amount of net assets-which is clearly not the case.

These asset-weighted results suggest that larger funds (those with more assets) tend to have higher alpha. This isn't terribly surprising since funds that perform well (generate positive alpha) tend to accumulate more assets. These results also serve as a reminder that the raw averages found in mutual fund data (historical return, alpha, expense ratios, etc.), can differ dramatically from asset-weighted averages. Asset weighting is a more accurate reflection of reality because the performance characteristics of a $25 billion fund have more impact on investors than the performance of a $25 million fund.

Mid- and small-cap funds told another story during this particular 10-year period. Actively managed mid-cap funds-particularly mid-cap growth-had more difficulty generating alpha (i.e. creating excess return superior to the excess return of their benchmark indexes) than did large- and small-cap funds. In general, small-cap funds had the highest average alpha (raw and asset-weighted) suggesting that active management is potentially more fruitful among small cap stocks.

Large-cap growth (LG), as an equity category, also demonstrates reasonably high raw and asset-weighted alpha indicating the potential for adding value through active management. Understandably, this 10-year period includes a three-year period (2001 to 2002) in which the three growth style boxes (LG, MG, SG) experienced consecutive negative returns. It is during such periods that some actively managed funds demonstrate superiority to passive indexes-which of course translates into positive alpha.

For instance, the average three-year return of the five LG indexes was -24.2% from 2000 to 2002, whereas the average three-year return among the top 50% of the 177 LG funds (when ranked by 10-year raw alpha from highest to lowest) was -17.4%. From 2000 to 2002, the average three-year return of the four MG indexes was -16.8%, but only -9.4% among the top half of the MG funds (when ranked by alpha from high to low). Small caps were no different. The average three-year return of the four SG indexes was -17.8%, but -8.7% among the top half of the SG funds (when ranked by alpha).

Outperforming the benchmark indexes during down years, rather than outperforming indexes during up years, appears to be an important key in generating positive alpha among actively managed funds. In other words, adding value (i.e. creating positive alpha) is more difficult during a bull equity market-as the rising tide is lifting all boats. Conversely, during downturns in the equity market is when managerial value manifests itself-by navigating around the storm to a greater or lesser extent. Simply put, alpha is created when it is most needed-during market turbulence.

Finally, the five funds in each style box with the highest alpha over the 10-year period are listed in "Fab Five". The funds in this box represent funds that added value to investors during a turbulent period in the U.S. equity market marked by dramatic annual gains and losses. The highlighted funds are not necessarily short-list candidates because alpha isn't the only consideration when selecting funds. However, alpha is a reasonable place to start. Among other things, the Greeks knew that too.

Creating Alpha

Year	Annual Return of Dodge & Cox Stock (%)	Annual Return of three-month T-Bill  (%)	Annual Excess Return of Dodge & Cox Stock (%)	Average Annual Return of five LV Indexes (%)	Annual Excess Return of LV Indexes (%)
1996	22.27	5.26	17.01	21.40	16.14
1997	28.4	5.31	23.09	33.39	28.08
1998	5.4	5.01	0.39	16.38	11.37
1999	20.21	4.87	15.34	8.13	3.26
2000	16.31	6.32	9.99	5.37	-0.95
2001	9.33	3.67	5.66	-8.07	-11.74
2002	-10.54	1.68	-12.22	-17.96	-19.64
2003	32.34	1.05	31.29	29.23	28.18
2004	19.17	1.43	17.74	14.87	13.44
2005	9.37	3.34	6.03	6.67	3.33
10-Year Average			11.43		7.15
10-Year Beta	0.67

                             Alpha =  11.43% – (.67 * 7.15%)  =  6.64%.

Benchmark Averages

Annual Returns (%) from 1996-2005
Year à	1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	10 Year Annualized Return
Large-Cap Value Indexes (S&P 500/Citigroup Value, Dow Jones Large Value, Russell 1000 Value, Russell Top 200 Value, Wilshire Large Value)
Average Annual Return of 5 LV Indexes	21.4	33.4	16.4	8.1	5.4	-8.1	-18.0	29.2	14.9	6.7	9.87
Large-Cap Blend Indexes (Morningstar Large Cap, Russell 1000, S&P 500, Wilshire Large Cap 750)
Average Annual Return of 4 LB Indexes	22.8	33.5	28.7	21.2	-9.8	-13.1	-22.2	28.5	10.7	5.4	8.88
Large-Cap Growth Indexes (S&P 500/Citigroup Growth, Dow Jones Large Growth, Russell 1000 Growth, Russell Top 200 Growth, Wilshire Large Growth)
Average Annual Return of 5 LG Indexes	24.2	33.5	42.8	32.4	-25.3	-19.9	-27.2	27.4	5.6	3.0	6.59
Mid-Cap Value Indexes (S&P Midcap 400/Citigroup Value, Dow Jones Midcap Value, Russell Midcap Value, Wilshire Midcap Value)
Average Annual Return of 4 MV Indexes	20.5	34.8	3.5	-1.3	25.5	5.9	-9.6	40.4	22.1	11.6	14.31
Mid-Cap Blend Indexes (Morningstar Midcap, Russell Midcap, S&P Midcap 400, Wilshire Midcap 500)
Average Annual Return of 4 MB Indexes	18.6	27.5	9.7	20.3	9.8	-3.2	-16.6	39.3	18.8	12.2	12.63
Mid-Cap Growth Indexes (S&P Midcap 400/Citigroup Growth, Dow Jones Midcap Growth, Russell Midcap Growth, Wilshire Midcap Growth)
Average Annual Return of 4 MG Indexes	16.8	23.4	18.9	52.4	-9.3	-14.6	-25.7	39.1	15.5	12.8	10.54
Small-Cap Value Indexes (S&P Smallcap 600/Citigroup Value, Dow Jones Small Value, Russell 2000 Value, Wilshire Small Value)
Average Annual Return of 4 SV Indexes	24.1	33.7	-6.2	-1.2	22.7	12.5	-10.4	45.2	21.0	7.2	13.60
Small Cap Blend Indexes (Morningstar Small Cap, Russell 2000, S&P Smallcap 600, Wilshire Small Cap 1750)
Average Annual Return of 4 SB Indexes	18.2	23.1	-2.4	19.4	4.1	3.5	-19.1	45.3	19.9	6.5	10.61
Small-Cap Growth Indexes (S&P Smallcap 600/Citigroup Growth, Dow Jones Small Growth, Russell 2000 Growth, Wilshire Small Growth)
Average Annual Return of 4 SG Indexes	14.8	16.1	4.2	44.2	-15.4	-8.3	-28.4	44.6	17.0	6.8	7.23
Annual Returns of 3-Month T-Bill	5.26	5.31	5.01	4.87	6.32	3.67	1.68	1.05	1.43	3.34	3.78

Data source:  Morningstar Principia

Alpha Raw and Cooked

The Bigger the Better

Fab Five

Morningstar Equity Style Box	Value	Blend	Growth
Large Cap	Dodge & Cox Stock Allianz OCC Value Instl Excelsior Val & Restruct Weitz Value TCW Galileo Div Focus N	Mairs & Power Growth Thompson Plumb Growth FMC Select Century Shares Trust Inst AIM Basic Value A	Smith Barney Aggr Grth A Amer Funds Grth Fund A Janus Olympus Janus Growth & Income Fidelity Contrafund
Mid Cap	Delafield Lord Abbett Mid-Cap ValA Goldman Sachs Mid Val Is Marshall Mid-Cap Val Inv Franklin Bal Sh Invmt A	Meridian Value Ariel Ariel Appreciation Maxim Ariel Small Cap Val First Eagle Fund of Am Y	Wasatch Core Growth Bridgeway Aggr Inv 1 Baron Partners Meridian Growth Touchstone Emerging Gr A
Small Cap	Franklin MicroCap Val A Janus Sm Cap Val Instl Evergreen Special Val A Mainstay Small Cap Opp I DFA U.S. Small Value II	Royce Trust Shares Inv Keeley Small Cap Value Lord Abbett Sm-Cap Val A ICM Small Company T. Rowe Price Small Value	Wasatch Micro Cap Bridgeway Ultra-Small Co First Amer Sm Cp Gr Opp Y Sentinel Small Company A Schroder US Opport Inv

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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.