Alpha Goes International

n August we looked at the differential in alpha among the nine Morningstar U.S. equity style boxes. Then, in September's article, the stability of alpha over time was examined. This article addresses both issues (alpha differential and alpha stability) among large cap international equity funds. Large cap funds were the focus of this study inasmuch as there are very few style-specific mid cap and small cap international funds with long term performance histories.

Using 107 representative large cap international funds, this study found that large cap value funds generated an average of 388 basis points of risk-adjusted excess return over the 10-year period from 1996-2005. This excess return is 300+ basis points higher than large cap blend and large cap growth funds, which had 10-year beta coefficients averaging 25% higher than the large cap value funds.

In short, alpha can be looked at as a measure of a fund manager's ability to generate risk-adjusted excess return, where "excess" is defined as the amount of return above the return of the most appropriate benchmark index. The adjustment for risk is captured by utilizing beta in the calculation of alpha.

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." This definition will be important as we look at the results of this study.

The equation for alpha used in this analysis was:
Alpha = (Annual Fund Return - Annual T Bill Return) - [Beta * (Benchmark Indexes Return - T Bill Return)]

In reduced form, alpha can be expressed as:
Alpha = Annual Excess Return of Fund - [(Beta * (Annual Excess Return of Benchmark Return)]

The international (i.e., non-U.S.) equity funds chosen for this study met a number of criteria. First, they had to be in existence as of January 1, 1996 so as to have a performance history from 1996 through 2005. At least 66% of the fund's portfolio needed to be in non-U.S. equities and they had to be classified as large cap funds. Sector funds, exchange traded funds, enhanced index funds, and index funds were excluded. Only one share class was included among funds that have multiple share classes (i.e., the "distinct portfolios" filter in Morningstar Principia was used). Finally, all the funds in the sample needed to have as their "best-fit" index either the Morgan Stanley Capital International Europe, Australasia, Far East Index (MSCI EAFE Index) or the MSCI World ex US Index. There were 126 funds that emerged at this stage of the filtering process. Results were not asset-weighted.

There was one additional filter based on portfolio median market capitalization. The rationale being that only those funds with portfolio market cap similar to the indexes should be included in the analysis. The average market cap of the two indexes (MSCI EAFE and MSCI World ex US) was $28.8 billion as of June 30, 2006. Thus, this final filter isolated only those funds with market cap that was within $10 billion (plus or minus) of $28.8 billion. In the end, 107 funds were included in this present study. Of that total, 23 were classified by Morningstar as large cap value, 61 as large cap blend, and 23 as large cap growth.

Whereas Morningstar calculates alpha over the most recent three-year time period using monthly returns, this study calculated alpha within each of the three Morningstar large cap style boxes (LV, LB, LG) using annual performance data over the 10-year period from 1996 to 2005.

As shown above in the equations above a benchmark index is required to calculate alpha. In this study, two prominent international equity indexes (MSCI EAFE and MSCI World ex US) filled that role. Their annual returns were averaged and are reported below in "Side by Side". Over this ten year period, the average annual return of these two indexes was 6.03%. As a side note, the correlation of the annual returns of these two indexes from 1996-2005 was .999 (as was the R-squared).

As shown in "Colors of the World", the 10-year average annual return for the 23 international large cap value funds was 9.56%, significantly above the average return of the two indexes. The 10-year return for the 61 large blend and 23 large growth funds was much closer to the average of the two indexes (within 50 bps and 28 bps respectively). The correlation between the annual returns of the 23 large cap value funds and the annual returns of Morningstar's International Equity Large Value "Category" was .999. The same was true for the large blend and large growth funds (both had correlations to their respective categories of .999). Thus, the funds in this study are reflective of the aggregate performance of the Morningstar style boxes they represent. The 10-year performance requirement is the primary reason relatively few funds qualified to be included in this study.

Side by Side

Year	MSCI EAFE Index	MSCI World ex US Index	Average of Both Indexes
	TOTAL RETURN (%)
1996	6.05	6.87	6.46
1997	1.78	2.27	2.03
1998	19.93	18.69	19.31
1999	27.03	27.98	27.51
2000	-14.19	-13.36	-13.78
2001	-21.43	-21.39	-21.41
2002	-15.94	-15.80	-15.87
2003	38.59	39.42	39.01
2004	20.25	20.38	20.32
2005	13.54	14.47	14.01
10-Year Ave Annualized Return	5.84	6.22	6.03

The average 10-year alpha for the 23 large cap value funds was 3.88. As noted by R-squared, 94% of the movement in the annual returns of LV funds was explained by the annual returns of two averaged MSCI indexes. The 10-year beta of 0.82 indicates that, on average, LV funds experience only 82% of the volatility of the two MSCI indexes.

The average alpha of the 61 large blend funds was considerably lower (0.81) compared to large value funds, as was the alpha of large growth funds (0.79). This suggests that over this 10-year period, actively managed international equity funds in the large blend and large growth Morningstar categories were less successful in generating residual return above and beyond the "expectations established by beta". Speaking of beta, large blend funds and large growth funds had an average beta that was considerably higher than that of large value funds.

The 10-year alpha coefficient for the large cap value funds of 3.88% was significantly different (at the .999 confidence level) from the alpha of the large cap blend funds and the large cap growth funds. The 10-year alpha of LB funds (0.81) and the LG funds (0.79) were not statistically different. However, the 10-year beta coefficients of each group (LV, LB, LG) were all statistically different from each other at the .98 confidence level or higher.

The highest and lowest alpha for each of the three large cap style boxes is also reported in "Colors of the World". It's worth noting that large value funds had an alpha upside equivalent to large cap growth funds (8.17% compared to 8.41%) but with dramatically better downside (-0.10 vs. -3.69).

The analysis of alpha over this 10-year period will be facilitated by looking at statistics over 3-year rolling periods. In "Rolling Returns" we can see the ebb and flow of performance-in three year increments-from 1996 to 2005. The dark blue line represents the average performance of the 23 large cap value international equity funds, the pink line the average of the 61 large blend funds, and the yellow line the average performance of the 23 large growth funds. The light blue line represents the average performance of the two MSCI indexes.

International large cap value funds (as represented by this sample of 23 funds) never underperformed the index average in any of the eight 3-year rolling periods. Large blend and large growth funds outperformed the combined index performance during the first four 3-year periods (1996-2001) but underperformed in each of the last four 3-year periods (2000-2005). As a side note, over this 10-year period, an average 63% of the LV funds beat the combined index in any given year compared to 48% among blend funds and 45% among growth funds.

A critical component in the calculation of alpha is beta, which is a measure of the magnitude of the association between the returns of two assets. Beta measures the volatility of a fund in relation to the volatility of its benchmark index. As can be seen, over time beta is anything but static. As shown in "Bouncing Beta" it is a dynamic statistic. The rolling beta for large blend and large growth funds tracks in a similar fashion whereas rolling beta for large value funds marches to its own beat. With the exception of the first 3-year period, the fluctuation in beta among LV funds was considerably less than among the LB and LG funds. It's important to have a sense of beta as we attempt to understand the patterns of alpha.

As seen in "Alpha Waves" the alpha for large value funds tends to be much more consistent over time. The average 3-year rolling alpha (there were a total of eight 3-year rolling alphas over the 10-year period) for large value funds was 4.06% with a standard deviation of 2.02%. The average 3-year rolling alpha for large blend funds was 0.34% with a standard deviation of 4.42%. Among international large growth funds, the mean rolling alpha was 0.29% with a standard deviation of 6.22%. In other words, the average alpha of large blend and large growth funds was considerably smaller than the average alpha of large value funds and demonstrated 2-3 times more volatility than the average alpha of large value funds. (The average alphas being discussed here differ slightly from those in "Colors of the World" because these are averages of eight 3-year alphas rather than a single 10-year alpha).

If you compare "Rolling Returns" against "Alpha Waves" you will observe that the average large value alpha declined in the second 3-year rolling period (97-99) despite the average return of LV funds increased during the same period (97-99). This may seem odd-rising returns associated with declining alpha. This answer is demonstrated in "The Making of Alpha". The key to alpha is the degree to which performance exceeds the performance of the benchmark after factoring in the beta coefficient.

For example, in the first 3-year period alpha for LV funds was 6.4% (dark blue solid line) The average annualized 3-year rolling return of the 23 LV funds was 11.4% (dark blue dotted line), well above the 9.0% return of the combined MSCI indexes (light blue line). In the 2nd 3-year period (1997-99) the average return of the large value funds was 15.9%, but the average return of the indexes was 15.8%. The much smaller "excess return" in the 2nd 3-year period combined with a larger beta (on average) causes alpha to fall to 3.2%. In short, performance may rise, but if it doesn't rise beyond that predicted by beta, alpha will decline.

Another example is the 5th 3-year rolling period (2000-02). The average alpha among large value funds hit its highest point (6.83%) despite the fact that the average 3-year rolling return of LV funds was -9.8%. Moreover, the average 3-year rolling beta during the period was nearly 1.0 which "should" cause the funds to behave much like the indexes. (Beta=1.0=identical magnitude of volatility). And yet, on average, LV funds performed much better than the average index return of -17.1%. Bottom line: performing better than expected is the key to generating alpha, particularly during down markets. It was during the market decline of 2000-2002 that international large cap value funds demonstrated a significant alpha advantage over large cap blend and large cap growth international funds.

To summarize, over the 10-year period from 1996-2005, international large cap value funds had a higher and more stable alpha, lower and more stable beta, and returns (on average) that equaled or exceeded the average benchmark performance. Moreover, each group of funds (LV, LB, LG) had a positive 10-year average alpha (see "Colors of the World") suggesting that active management of international funds adds value. It just so happens that a value orientation adds more value.

Colors of the World

Year	International Equity Benchmark Indexes	Actively Managed International Equity Funds
	Average of MSCI EAFE Index and MSCI World xUS Index	Large Value* (23 funds)	Large Blend* (61 funds)	Large Growth* (23 funds)
	Average Annual Return (%)
1996	6.46	15.52	13.37	15.10
1997	2.03	8.62	6.03	5.56
1998	19.31	10.66	13.98	15.79
1999	27.51	30.11	40.98	51.94
2000	-13.78	-4.45	-16.28	-19.48
2001	-21.41	-13.22	-21.21	-23.86
2002	-15.87	-11.47	-16.90	-18.20
2003	39.01	37.96	33.98	32.77
2004	20.32	21.80	16.98	15.28
2005	14.01	13.62	15.31	15.03
Average 10-Year Annualized Return (%)	6.03	9.56	6.53	6.31
Average 10-Year Alpha (%)	--	3.88	0.81	0.79
Std Dev of 10-Year Alpha (%)	--	1.95	2.00	2.86
Median 10-Year Alpha (%)	--	3.52	0.51	0.41
Average 10-Year Beta (%)	--	0.82	1.02	1.11
Average 10-Year R2	--	.94	.92	.86
Highest 10-Yr Alpha (%)	--	8.17	5.67	8.41
Lowest 10-Yr Alpha (%)	--	-0.10	-2.85	-3.69
% of Funds Beating Index Performance over 10 Years		63	48	45

International Rolling Returns

Bouncing Beta

Benchmark Index = MSCI EAFE plus MSCI World xUS

Alpha Waves

Benchmark Index = MSCI EAFE plus MSCI World xUS

The Making of LV Alpha

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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

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Special thanks to Patrick McDonough for his editorial insights.