During the past two decades, the share of passively managed equity fund assets has risen. While some lament that passive investors have consigned themselves to merely average returns, the truth is that the market average has been pretty good. The market return is the baseline upon which we can judge the performance of any stock fund. In fact, most of the movement of our funds can be explained by exposure to a broad market index, otherwise known as market beta. Any return that an active portfolio manager can deliver in excess of the return from beta is alpha.
For most funds, beta is the largest source of return. The expectation for return beyond that which can be obtained cheaply through beta could justify the higher fees that active managers charge. But according to research done in the United States, from January 2011 through December 2014 beta sources provided 104% of the return to the average active U.S. equity fund. Even among funds that managed to produce non-negative alpha, beta sources contributed 89% of the return.
The traditional market beta from the capital asset pricing model (CAPM) indicates the extent to which a portfolio is exposed to the market. The portfolio return that is related to beta represents compensation for bearing market risk. But there are other betas. Many portfolio managers have found success by buying small-cap stocks, value stocks, high-quality stocks and those with strong momentum. It turns out that these characteristics of individual stocks are systematically related to the risk/return profile of an entire portfolio.
Isolating factors
By grouping stocks according to these characteristics, we can measure the return to the characteristic, or factor, itself. We can then use these factor returns to examine portfolios. Just as we can monitor our portfolios by looking at exposures to individual stocks, we can examine the exposure of our portfolios to these factors. Why these additional sources of return exist is not clear. They may be anomalies. They may represent compensation for bearing risk. Investor behaviour could also play a role in their existence and persistence. Whatever their source, there is no guarantee that these factors will persist in the future, and they may be destined to be arbitraged away.
From 1957 through 2014, the average monthly return of the broad U.S. market in excess of the risk-free rate was 0.51% (Table 1). The table also shows the average monthly excess return from several factors. These represent the returns from going long a basket of stocks that exhibit high values of each characteristic and shorting a basket of stocks with low values. In addition, we break out a recent 48-month period which we will use to examine U.S. equity funds. The data are from AQR Capital Management.
While the average return to each of these factors is positive over the longer time frame, they can be quite volatile. Small-cap stocks have beaten large caps since the tech bubble burst around 2000, but underperformed large caps from 2011 through 2014. Value stocks underperformed growth stocks during the most recent four-year period. Momentum has shown the highest average excess return since 1957, yet it turned deeply negative coming out of the financial crisis as the market began to recover. Finally, the returns of high-quality stocks have been particularly strong in the wake of the financial crisis.
Fund performance explained
Now that we have isolated some well-known factors and looked at their returns, we are able to explore fund performance using both the single-factor CAPM model and a multifactor model that includes the other factors. Table 2 shows the beta coefficients, factor returns and a return decomposition using both the single-factor and multifactor model for three funds from January 2011 through December 2014. The funds are 
Vanguard Dividend Appreciation ETF (VIG) and two U.S.-sold mutual funds: Silver-rated JPMorgan Equity Income and Gold-rated Sequoia. In each model, the average monthly return for each fund is decomposed into alpha and the product of the beta coefficient times the return to each factor.
During the four-year period, VIG had an average monthly return of 1.1%. In the CAPM model, VIG had a beta of only 0.82. We can break VIG's return down into two components, 0.93% from beta and 0.20% per month from alpha. In the multifactor model, we see that VIG had a large beta to the quality factor. VIG buys stocks that have increased dividends for 10 consecutive years--many of these stocks are high-quality. In fact, VIG had 65% of its assets in wide-moat stocks as of June 2015, among the highest of any fund. Once we account for its quality exposure, we see that VIG's alpha disappears. This is not to say that it is a bad fund, only that its returns are what we would expect given its methodology and the performance of quality during the period.
Unlike VIG, JPMorgan Equity Income is an actively managed fund. Per the CAPM model, it generated monthly alpha of 0.35% during the period in question. But like VIG, JPMorgan Equity Income also had significant positive exposure to the quality factor. Removing that exposure dropped the fund's alpha to zero. JPMorgan Equity Income holds about 100 stocks, most of which are large-cap and high-quality.
Switching from the single-factor model to the multifactor model was no help dissecting Sequoia's 1.38% monthly return. Here's where the importance of R-squared comes into play. R-squared reveals the model's explanatory power. Whereas the model could explain 96% of the variance of return for VIG and JPMorgan Equity Income, the R-squared for Sequoia was only 77%. The model's low explanatory power for Sequoia is likely a result of the fact that the fund is concentrated, with 56% of the portfolio in just 10 stocks at the start of 2011. One of these holdings, Valeant Pharmaceuticals (VRX), provided the bulk of the fund's returns. Even after applying the multifactor model, Sequoia had a monthly alpha of 0.51%. If we assume the multifactor model adequately explained all of Sequoia's risk, then the remaining alpha represents skill.
Beta everywhere
We applied the multifactor model to all passive and active mutual funds and exchange-traded funds in the U.S.-equity category group. The chart below displays the contribution to total monthly return by all multifactor betas and by alpha for all 5,318 active U.S. equity fund share classes during the 48-month time period. Each fund's total monthly return, the sum from alpha and beta sources, is a column on the x-axis and is sorted by alpha.
Sources: Morningstar, AQR Capital Management, and author's calculations.
The average monthly return of all active funds from all beta sources was 1.14%, while the alpha was negative 0.04% for a total return of 1.10%. Thus, beta sources provided on average 104% of active funds' returns during the time period. Even among funds that managed to avoid a negative alpha, where the average alpha was 0.13% per month, the beta sources contributed 1.08%, which is 89% of the returns on average. It is clear that the returns from all beta sources has provided the majority of these funds' returns.
Performance evaluation gets smarter
The multifactor model used here is by no means perfect. As the Sequoia example illustrated, the idiosyncratic risk of individual stocks is just too high for this model to be useful in assessing a concentrated portfolio. Not every quality stock will go up when the quality factor says that it should. In addition, the definition of value is simply book value/market value, so it does not take into account other ways to define value, such as with measures of earnings or cash flow. This model also assumes stable exposure to each factor, so a manager's ability to tactically time exposures is attributed to alpha.
What this approach does show is that performance evaluation is getting smarter. The tools we use to explain returns can be applied to any fund, and the outcome can inform our understanding and expectations of a manager and better gauge how he should be compensated. There is an expanding menu of low-cost ETFs and mutual funds providing exposure to these basic elements that constitute stock markets' return.
Active managers who can consistently deliver alpha should command higher fees. Active managers might seek alpha by allocating between the factors or by identifying individual security-selection opportunities. Yet, despite the attention alpha receives, beta is the most significant source of return for most funds.
