Swedroe: A Magical Metric That Isn’t

A recent study found a popular investment measure to be useful in predicting performance, but don’t get too excited …

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

I was recently asked to comment on an article that appears in the April 2015 issue of the American Association of Individual Investors Journal. The article is based on the paper “Mutual Fund’s R2 as Predictor of Performance,” which was published in the March 2013 issue of The Review of Financial Studies.


As you may have already guessed, the study, which covered the period from 1988 through 2012 and included about 2,500 mutual funds, examines the role of R2 in mutual fund performance. R2 is a statistical measure representing the percentage of a fund or security’s returns that can be explained by movements in a benchmark index.


R2 And Fund Performance

The study’s authors, professors Yakov Amihud and Ruslan Goyenko, proposed the following: “Fund performance can be predicted by its R2, obtained from a regression of its returns on a multi-factor benchmark model. Lower R2 indicates greater selectivity and it significantly predicts better performance.”


They continue: “This result is obtained even after controlling for fund characteristics, past performance and style.” Amihud and Goyenko go on to add: “Our results are robust to alternative factor models used as benchmarks.”


In the American Association of Individual Investors article, the authors state: “Investors can take advantage of an observed characteristic that predicts higher fund performance. As long as the fund keeps its strategy unaltered, and as long as the observed characteristic predicts good performance, investors will benefit by investing in the fund. True, in the long run, if the fund becomes very large, it may be less flexible and its advantage will be eroded.”


Amihud and Goyenko explain: “Once a fund outperforms consistently, it gains visibility, attracts a lot of cash flow and becomes too big. The bigger size has negative effect on fund performance. It is very expensive to stay active and rebalance frequently when a fund is big.” However, they note: “But this takes time; meanwhile, the fund investor can enjoy overperformance.”


In their study, the authors first sorted funds into five portfolios ranging from high to low R2 for the previous 24-month period. They then sorted each R2 portfolio into five portfolios based on their alpha for the previous month. They found that the funds in both the lowest R2 quintile and the highest alpha quintile produced a statistically significant (at the 5 percent level) alpha of about 3.5 percent a year.


The authors noted that the portfolio in the very bottom left corner of the 5-by-5 matrix was the only one of the 25 portfolios that showed statistically significant positive alpha. In other words, you need to have funds within both the lowest R2 quintile and the highest quintile alpha.



These findings led Amihud and Goyenko to conclude with the following recommendations:

  • If a fund has high R2, don’t bother buying it. Instead, buy lower-cost index funds or ETFs in the same asset class because they charge much less in terms of expense ratio.
  • Diversify among funds with both low R2 and high alpha. For example, choose to spread the total amount of money you plan to invest in this manner among, say, 10 funds with such characteristics. Investing in a portfolio of funds will increase your odds of benefiting from the advantage implied by the chosen characteristics and of outperforming the benchmark. There is too much “noise” and you leave too much to luck if you invest in one or very few funds.


Before you decide to follow such a strategy, however, you should consider seven important points.


First, as the authors themselves note, the fund chosen must keep its strategy unaltered for this approach to work. One of the problems with active funds is that investors run the risk of the manager altering styles.


Second, as the authors also noted, a fund’s advantage will be eroded once it becomes large.



Less Skill Than Methodology?
Third, it’s possible that the outcomes discovered in the study were the result not of skill but of how alpha is measured. Consider a set of value funds that are all passively managed. However, each fund uses a different metric as its measure of value. One uses price-to-book, another uses price-to-earnings and a third uses price-to-cash flow. We know that while they all provide a similar value premium, there are times when one measure performs better than another.


If you’re calculating alpha against the traditional high minus low (HmL) measure, a fund that uses price-to-cash flow will randomly generate alpha in some periods, and so will a fund that uses price-to-earnings. Thus, if an active fund is using, say, price-to-cash flow as its value metric and that “style” happens to be doing well for a period, there really isn’t any alpha.


The alpha was simply the result of the choice of the value metric used in the regression, and that’s not useful information. Active strategies use various metrics to determine if a stock is attractive, and they can randomly move in and out of favor.


Fourth, the authors define alpha as the intercept from a four-factor (beta, size, value and momentum) regression. But what looks like alpha by this definition could simply be exposure to other factors (such as profitability, quality and low beta).


These other factors have not only become well-known, but they can be accessed through low-cost and passively managed funds. We also know that some segments of the market showing “alpha” (even over long periods of time) really just reflect the limits of any model.


For instance, the smallest value stocks show alpha over the entire 88 years of market data we now have. Thus, it is possible a fund manager is generating alpha simply by fishing in the right end of the pond, and investors don’t need to pay an active manager just to do that.


Paper Vs. Real-World Returns

Fifth, it’s often a long way from paper results to real-world returns. The portfolio of mutual funds recommended by the authors has to be rebalanced every month based on the past 24 month of returns. Therefore, you would need to adjust your mutual fund holdings every single month.


Compounding the problem is that the authors themselves recommend diversifying across many funds because there’s so much noise in the data. Thus, their strategy requires a lot of work and turnover, which can lead to significant transaction costs. Unfortunately, transaction costs were not considered in the study. Even more important is that it would likely rule this strategy out for taxable accounts (regrettably, the authors don’t provide any persistence or turnover data).


Sixth, high alpha doesn’t necessarily mean high returns. Investors may get higher returns from a zero-alpha fund that has large exposure to high-return small value stocks than from a high-alpha fund that invests in a low-return sector, such as utilities.


Seventh, prudent investors know that a successful investing strategy includes risk management, and controlling risk through diversification. The low R2, high-alpha funds could, at various points in time, be concentrated among funds of a certain asset class or classes.


For example, in the late 1990s, it might have led to a huge concentration in technology stocks. At other times, it might lead to overweighting large value stocks. Investors chasing returns through this strategy will lose control over their asset allocation—by far the largest determinant of the portfolio’s return.


I’ll leave it to you to determine whether you think that there’s enough reason to consider following a strategy that involves chasing yesterday’s low R2 and high-alpha funds.

Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country. 



Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.