Finding Consistent Alpha

GLOBAL INVESTMENT RESEARCH

Finding Consistent Alpha Seth J. Masters Chief Investment Officer — Style Blend Equities

Drew W. Demakis Chief Investment Officer — Structured Equities

With future market returns unlikely to match the high levels of the 1990s, generating incremental alpha has become crucial. Our research shows that it’s possible to do so with relative consistency by combining managers effectively.

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For several decades, US pension plans have looked to the stock market to achieve high returns on their assets, and over time, this has been a winning strategy: The return on equities has exceeded the return on long-term government bonds fairly consistently. However, the recent bear market—the worst since the Great Depression—has contributed significantly to a disconcerting shortfall in the funding of pension plan liabilities. The market’s return is bound to revert to the norm over time, but the norm is nothing like the 16.4% returns that funds enjoyed in the 20 years that ended in 2000, when equity returns were boosted by dramatic expansion of price-earnings multiples (Display 1). Without the benefit of multiple expansion, equities are likely to return about 9% a year on average, and bonds, just 5%. Therefore, a typical plan with 60% of its assets in stocks and 40% in bonds would see returns of about 7.3% annually, less than the 8.7% average return assumption. This 1.4 percentage point gap spells trouble. There are several worthwhile strategies for bridging the gap. Since no single one is likely to do the job, most plans should probably consider all of them: raise the equity allocation of the overall fund, globalize investment strategies, add hedge funds and private equity, and increase the alpha on existing assets. Increasing alpha, of course, flies against one of the biggest trends in investing of the last 15 years: the shift to indexed equities. Our research, however, shows that increasing the alpha on existing assets offers great potential: While picking up an additional 1% from alpha

may not have seemed that important when the market was returning 16% a year, with the market returning 9%, that extra 1% becomes critical. In this paper, we will discuss both why achieving alpha is possible and how it can be done with relative consistency.

WHY ALPHA IS POSSIBLE Efficient market theory postulates that alpha shouldn’t exist, and common sense suggests that since the market sums to the index, for a large group of investors to beat the market, others must lag behind. Nonetheless, the median manager in Mercer Investment Consulting’s universe of US large cap managers outperformed the S&P 500 by 0.6% a year on average for the 10 years ending in December 2002; those in the top quartile outperformed by at least 1.9% (Display 2). How is this possible? Our answer is that alpha exists because not all investors seek it, and many of those who do seek it face systematic obstacles. Many investors don’t seek alpha because they have other goals for their equity investments. For example,

Display 1

Display 2

Plans Face a Looming Return Gap

Managers Have Delivered Outperformance

16.4% P/E Expansion

Mercer Manager Universe* vs. S&P 500 (1993–2002)

Annualized Return

6.7 8.9% 7.3%

Earnings Growth

6.2

6.0

Yield

3.5

2.9

8.7%

Gap 1.4%

Information Ratio† 0.3

Median

0.6%

7.5%

0.1

Bottom Quartile

(0.7)%

5.2%

(0.1)

Top Quartile

4.9%

Average 20 Years Forecast Forecast Forecast 1981–2000 Equities Bonds 60% Stocks/ Expected 40% Bonds* Plan Return As of March 31, 2003 *Stocks are represented by the S&P 500 and bonds by the Lehman Aggregate Bond Index. Source: Center for Research in Security Prices (CRSP), Federal Reserve Board, Lehman, Standard & Poor’s Handbook and Bernstein estimates

Finding Consistent Alpha

1.9%

Tracking Error 9.6%

Premium

*Mercer universe of US managers with reported returns from 1993–2002 (351 managers eligible as of February 2003) †Premium/tracking error Source: Mercer Investment Consulting and AllianceBernstein

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many individuals and corporations own large stakes in companies for strategic reasons or to control them; such non-floating positions make up 16% of US market capitalization (Display 3). Obviously, Bill Gates does not actively manage his stake in Microsoft to add value relative to an index on a month-to-month or year-to-year basis. Smaller holdings by individuals, who also tend not to be effective alpha-seekers, comprise another 26% of US market cap. Index funds account for another 9%; by definition, they do not seek to add alpha. The two alpha-seeking groups, mutual funds and other institutional investors, represent slightly less than 50% of market capitalization. That means there is opportunity for them to benefit in aggregate at the expense of the other groups. Of course, not all alpha-seeking professionals succeed in delivering alpha, and many face systematic obstacles to doing so. One systematic obstacle is the tendency of investors to chase performance, as shown in the recent tech bubble. Growth stocks’ massive outperformance during the tech bubble in 1998 and 1999 led to a total of $400 billion in net flows from value mutual funds to growth mutual funds in 1999 and 2000, according to Morningstar. Awash with cash, managers of growth funds were forced to add to their established positions at ever-increasing prices, creating alpha opportunities for other investors. Then, Display 3

Why Alpha Can Exist: Not All Investors Seek It Composition of US Market Capitalization $13.2 Trillion Non-Floating Holdings* “Alpha Seekers” 16% 31% Individual Holdings†

Active Institutional Managers

26% 18% 9% Index Funds

Active Mutual Funds

As of December 31, 2001 *Includes company founders and their heirs and corporate stakes †Includes company employees and other direct investments by individuals that are not professionally managed Source: Federal Reserve, Salomon Smith Barney and AllianceBernstein

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Display 4

Consequently, Market Inefficiencies Persist (%) 50 40 30 20 10 0 (10) (20)

Low P/E Stocks Outperform Average

72

77

(%) 50 40 30 20 10 0 (10) (20)

82

87

92

97

02

97

02

Positive Momentum Stocks Outperform Average

72

77

82

87

92

Through December 31, 2002 Annualized hedged returns of most attractive quintile of stocks relative to the equal-weighted universe of global large-cap developed markets Source: Bernstein analysis

once the bubble burst, soaring fund redemptions forced them to sell positions at ever-decreasing prices, which also created alpha opportunities. Thus, timing decisions by the ultimate investors, rather than alpha-seeking activity by fund managers, drove many purchase and sale decisions at mutual funds. Such market distortions allow alpha-generating inefficiencies to persist even when they are well understood and exploited by active managers. Two well-known examples of such market inefficiencies (or anomalies) are often associated with the value and growth style disciplines, respectively. The cheapest quintile of stocks, ranked by price-to-earnings, systematically outperformed the MSCI World (Display 4, top). So did the quintile of stocks with the highest price momentum (Display 4, bottom). Of course, a key step in choosing an active manager is believing in the anomaly the manager is seeking to exploit and checking that the manager’s process and portfolios are consistent with exploiting that anomaly.

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FINDING ALPHA

THE RISK/RETURN TRADE-OFF

But will active mangers be successful? As our legal advisors insist we always say, past performance isn’t a reliable indicator of future results. This is true for several reasons. First, anomalies such as the long-term outperformance of low P/E and high momentum stocks don’t pay off consistently, so a manager that is disciplined in exploiting such anomalies will tend to have fairly high tracking error. The median tracking error for managers in the Mercer universe of US managers for the 10 years ending 2002 was 7.5%, as Display 2 shows; such a manager would typically underperform in nearly half of all one-year periods. This variability in performance tends to decrease investors’ confidence.

The extremely long time required to have confidence in high alpha managers, statistically speaking, arises because only higher tracking error managers tend to deliver higher alpha. While the highest-alpha decile of US managers in Mercer’s universe with high tracking error delivered annual premiums of at least 3% over the last 10 years, the best performing managers with low tracking error generated only a 1.3% premium (Display 6, top).

Second, even unskillful managers can be lucky. It is only with the passage of time that you can tell whether the good periods outweigh the bad ones and decrease the influence of random outliers. Statistical tests allow us to establish when you can have confidence that performance was due to skill. A manager’s information ratio—the premium divided by tracking error—is a useful measure for such tests, because by definition it relates return to risk. Unfortunately, the statistical evidence indicates that many years of performance are needed to develop a reasonable degree of confidence that a manager’s alpha was due to skill, not luck. For the median manager with an information ratio of 0.1, it would take 271 years to obtain 95% confidence; for a first-quartile manager with an information ratio of 0.3, it would take 31 years (Display 5). Both time periods are too long to be of much practical use when judging real managers. Even the 11 years required to have 95% confidence in a manager with a 0.5 information ratio is long in the context of most investors’— and managers’—careers. Display 5

It Takes Many Years to Distinguish Skill from Luck Information Ratio 1.0

95% Confidence of a Positive Premium

0.5 0.3 0.1 11 31 Source: AllianceBernstein

Finding Consistent Alpha

Years

271

Furthermore, the incremental risk needed to generate greater alpha is large enough that the information ratio declines. Thus, high alpha managers tend to have lower information ratios; managers with high information ratios, however, tend to have both lower tracking error and lower alpha (Display 6, bottom). That is, the managers in whom you can have greater confidence seldom offer high alpha; you can’t have such confidence in managers with high alpha. To understand why there is a declining marginal utility to added risk, let’s look at a simple example: One dollar invested in a stock rises to $2 in the next year as the stock Display 6

High-Risk Managers Have Higher Premiums... Premium for Top-Decile Manager in Mercer Universe* (vs. S&P 500; 1993–2002) 3.0% 2.2% 1.3% Tracking Error:

6%

…but Low-Risk Managers Usually Have Higher IRs Information Ratio (%) Top 0.5 Quartile 0.4 0.3 Median 0.2 0.1 0 Bottom (0.1) Quartile (0.2) Tracking Error:

Mercer Manager Universe* vs. S&P 500 (1993–2002) 0.28%

0.01%

6%

*Mercer US managers with a reported premium and with tracking error between 1% and 9% from 1993 to 2002 (245 managers eligible as of February 2003) Source: Mercer Investment Consulting and AllianceBernstein

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returns 100%, but drops back to $1 again the next year as the stock declines 50%. While the average return for the two years is 25%, the compound growth per year is 0%. The 25% difference between the two is called “risk drag.” It is the damage that volatility inflicts on long-term returns.

However, the probability of outperforming the benchmark in any given 12-month period is greatest for portfolios with 200–300 stocks (Display 10). Although alpha drops as the number of stocks increases from 50 to 250, risk drops Display 7

Risk drag is a function of the square of volatility: It grows geometrically as volatility rises. If you start with a volatility of roughly 10%, similar to the volatility of bonds, the risk drag is about 0.5% (Display 7). If you double the volatility to 20%, about the volatility of most equity indexes, the risk drag quadruples to 2%. If you triple the volatility to 30%, about the volatility of a relatively stable single stock, the risk drag goes up by a factor of nine, to 4.5%. If you raise the volatility six-fold to 60%, which is typical of many small-cap and emergingmarkets stocks, the risk drag rises 36-fold, to 18%. Now, active portfolio management entails taking risks with single stocks in portfolios, so risk drag significantly affects how actively managed portfolios deliver alpha and obtain information ratios. Highly concentrated portfolios are much more volatile than diversified portfolios. As you would expect, a Monte Carlo simulation based on real US stock market returns for the last 30-odd years shows that the more stocks you add to a portfolio, the lower the portfolio’s volatility (Display 8, top). Perhaps surprisingly, however, the more you reduce the portfolio to just a handful of stocks — the more concentration risk you take — the lower your expected return (Display 8, bottom). This is because risk drag slows compound growth. Thus, even if a skillful manager chooses his very best idea for a one-stock portfolio, the alpha produced is likely to be negative, because the risk drag of owning only a single stock overwhelms the manager’s skill at picking stocks. You need tremendous skill to overcome the risk drag of a single-stock portfolio—or even the 20-stock portfolios that have gained some popularity in recent years. Thus, our Monte Carlo simulation shows that the sweet spot for a portfolio aiming to produce high alpha from a 500-stock universe is 40 to 60 stocks (Display 9). When you expand portfolios beyond that, you tend to see a gradual decline in relative return, because your 200th “best idea” isn’t likely to produce the same return as your 50th best idea. And when you get to your 500th best idea (when drawing on a 500-stock index), you’ve given up on active premiums altogether. 4

Risk Drag Grows Geometrically Approximate Risk Drag 18.0% 12.5% 8.0% 4.5% 2.0%

0.5% 10

20

30 40 Volatility (%)

50

60

Source: AllianceBernstein

Display 8

Concentrated Portfolios Have Greater Risk... Volatility (1970–2002)

(%) 40

Volatility of Average Stock

35 30 25

Volatility of Index

20 15 10

1

2

3

5 10 20 50 100 200 500 Number of Stocks

…and Risk Drag Slows Their Compound Growth (%) 14

Compound Return (1970–2002) Index Return

13 Risk Drag

12

Portfolio Return

11 10 9 8 7 1

2

3

5 10 20 50 100 200 500 Number of Stocks

Statistics for each portfolio of a target number of stocks are based on a Monte Carlo simulation in which average statistics were calculated from 1,000 random samples. For each sample, yearly returns were generated based on a strategy of equally allocating capital among the target number of randomly selected stocks in the S&P 500 at the beginning of each calendar year from 1970 to 2002 and holding the portfolio for a year. Annual portfolio reconstitution incurred no transaction costs. Source: Standard & Poor’s and AllianceBernstein

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even faster— so that information ratios and consistency increase. This explains why managers with the highest premiums tend to be less consistent, and managers with the greatest consistency tend to have lower premiums.

Display 11

Combing Portfolios with Uncorrelated Premiums Generates Consistent Alpha Probability of Outperforming

(%) 75

Zero Correlation

-0.3 Correlation

70 Display 9

Highest Alpha Comes with Moderate Concentration Monte Carlo Simulation of US Manager Performance*

60 55

+0.5 Correlation

50

Alpha (%) 2

Moderate Concentration

1

2

3 4 Number of Managers

5

Assumes each manager has a 0.2 information ratio Source: AllianceBernstein

0

SQUARING THE CIRCLE

(2) Excess Concentration

(4) (6) 1

5

20

50 100 200 Number of Stocks

300

400

500

Display 10

Highest Win Rate Comes with Full Diversification Monte Carlo Simulation of US Manager Performance*

Probability of Winning (%) 80

Fully Diversified

60 40 20

65

1

5

10

20 50 100 200 300 400 Number of Stocks

500

Fortunately, it’s possible to get high alpha with consistency for the plan as a whole, if not from any one manager, by combining high alpha managers with performance streams that are negatively correlated to each other. Although combining many managers with 0.5 correlation is not very helpful, combining just two or three managers with negative 0.3 correlation helps a lot (Display 11). A simple illustration helps to explain why. Let’s say you combine an aggressive growth manager with a deep value manager and both have 50-stock portfolios benchmarked to the S&P 500 (Display 12). Each 50-stock portfolio has an average weight of 2% in each stock versus the 0.02% average for the S&P 500, and average overweights that are nine times the size of its average underweights. Assuming no portfolio overlap, the two portfolios together have 100 stocks, which lowers the ratio of overweights to underweights to four times. This direct risk reduction is very significant. Display 12

*Performance for each portfolio of a target number of stocks is based on a Monte Carlo simulation in which average statistics were calculated from 100 random samples. For each sample, yearly returns were randomly generated for each of 500 stocks for 20 years. The returns were generated from a normal distribution with a mean, standard deviation, minimum and maximum return based on actual S&P 500 constituents for each of the 20 years from 1983 to 2002. Next, yearly expected returns were randomly generated for each of 500 stocks for 20 years using the same distributions described above, such that the average cross-sectional rank correlation of returns and expected returns for each year was equal to 0.05.Yearly returns for a portfolio of a target number of stocks were generated by equally allocating capital among the target number of stocks with the highest expected returns at the beginning of each year and holding those stocks for a year (annual portfolio reconstitution incurred no transaction costs). The benchmark for comparison was a portfolio constructed using the same methodology with a portfolio size of 500. Source: Standard & Poor’s and AllianceBernstein

Finding Consistent Alpha

Two Concentrated Portfolios Can Offset Risks Portfolio

Average Security Weighting

50 Value Stocks

Average Overweight

Average Underweight

Ratio of Overto Underweights

2.0%

+1.8%

(0.2)%

9x

50 Growth Stocks

2.0

+1.8

(0.2)

9

100 Stocks

1.0

0.8

(0.2)

4

Source: AllianceBernstein

5

Furthermore, the 50 value stocks are likely to be precisely the kind of ideas that the growth manager underweights, and the 50 growth stocks are likely to be the kind of ideas that the value manager underweights. As a result, the two portfolios neatly offset each other’s risks. In practice, when you combine two portfolios with complementary styles, or two portfolios that for some other reason have complementary risk factors, the correlation of their alphas is likely to be negative 0.3, or even less.

CONCLUSION

Of course, when you find such a pair, one of the managers will tend to trail when the other is leading. Needless to say, it can be very uncomfortable to stick with—and rebalance into — the laggard. For those who cannot tolerate the discomfort, there is a simple solution: Get someone else to rebalance for you. Many plan sponsors decided after the emerging-markets crisis of the late 1990s that the best way to stick with emergingmarkets equities was to invest in EAFE-plus mandates, which package emerging-markets equities with developed-market equities. Similarly, some plan sponsors today are seeking to avoid focusing on the inconsistent alpha of their active style managers by hiring a consultant or investment manager to rebalance between them.

Opponents of active management often argue that it is hard to find skillful managers and that even if you do, when you put several together, you simply end up with a high-cost index fund. While we certainly agree that skillful managers are hard to find, our research leads us to a different conclusion: By combining managers skillfully, you significantly enhance the chance of harvesting alpha. ■

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There is, after all, a practical way to have confidence that you can harvest high alpha, without waiting for 271 years. Find managers who have reasonably high alphagenerating capacity and negatively correlated sources of alpha, and rebalance between them on a disciplined basis. Under these conditions, you can have much greater confidence in the likely performance of the group than in any one manager alone.

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About the Authors Seth J. Masters Chief Investment Officer — Style Blend Equities Seth J. Masters is Chief Investment Officer for Style Blend and Core Equity Services at Alliance. He has been with Alliance and, prior to that, Sanford C. Bernstein since 1991. Mr. Masters is the Chairman of the firm’s US and Global Style Blend Investment Policy Groups, and a member of the Bernstein Global, International and Emerging Markets Value Investment Policy Groups. He joined Bernstein as a research analyst covering banks, insurance companies and other financial firms, then became CIO for Emerging Markets Value in 1994, and assumed his current position in 2002. Before joining Bernstein, he was a senior associate at Booz, Allen & Hamilton from 1986 to 1990 and taught Economics in China from 1983 to 1985. He earned a B.A. from Princeton University and an M.Phil. in Economics from Oxford University.

Drew W. Demakis Chief Investment Officer — Structured Equities Drew W. Demakis is Chief Investment Officer for Structured Equities, the Chairman of the Risk Investment Policy Group and a member of the Core/Blend Services investment team. Previously, he served as the director of product development for Structured Equities. Mr. Demakis joined Bernstein in 1998 as a senior portfolio manager—international equities, and remains a member of the Global and International Value Investment Policy Groups. Before joining Bernstein, he was managing director and head of research at BARRA RogersCasey, an investment consulting firm, which he joined in 1988. Mr. Demakis earned a B.A. in Economics from the University of Chicago and an M.B.A. from Washington University.

Finding Consistent Alpha

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