Swedroe: A Magical Metric That Isn’t

May 20, 2015

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.



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