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Luck vs. Skill: An Update!

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The active fund industry is a marketing machine; ready to pitch short term outperformance as an indication of manager skill. Investors subsequently make a large allocation to these “winners” and more often than not end up earning less than stellar performance thereafter. Nonetheless, there is a brand new set of “winners” that are highlighted and investors follow suit. Wash, rinse, repeat….all towards inferior investment performance.

Why is this case?

What many investors fail to recognize that there is a more than likely chance that any type of short term outperformance is completely due to luck. Yes, Lady Luck and her temptation to fool us all by choosing the heroes and duds of the investment industry. Fortunately for us, we can use statistics, large datasets, and an academic (not marketing) approach to discovering the truth about our 5-star money managers.

Eugene Fama and Ken French produced a paper (2009) entitled Luck Versus Skill in the Cross Section of Mutual Fund Performance where they examined the performance of 3,156 different mutual funds from 1984-2006 through the lens of their original Fama/French 3 Factor Model. As a quick reminder, their original model extends from Bill Sharpe’s original CAPM model, which exclusively looked at Beta or market risk, into further dimensions of stock returns; that is size and relative-price (value). 

What they discovered was that the entire active fund universe during that time period underperformed the market, on average, by about the fees they charge for their services. Nobel Laureate, Bill Sharpe, predicted this outcome almost 2 decades earlier in his famous paper The Arithmetic of Active Management (1991).

Did some managers outperform the market? Yes they did! But the number that did outperform the market with a high degree of certainty (t-stat>2) was less than what is expected by random chance. The best way to explain this concept is to give an analogy. If we filled Yankee Stadium (54,251 max capacity) and gave everyone a coin to flip, just by random chance a handful of individuals might get 10 heads in a row. Are they skilled coin flippers? Of course not!

The big takeaway for investors is that if you are trying to find the next best manager that can outperform the market, looking at past performance may be setting you up to be fooled by randomness.

Over the last 4 years, further research in the field of empirical finance has produced two more dimensions of expected return, which are highlighted in Fama and French’s 2014 paper A Five-Factor Asset Pricing Model. Building off of their original 3-factor model, Fama and French add profitability and investment factors. These factors helped in explaining certain anomalies that couldn’t be explained by their original model.

Dimensional Fund Advisors recently updated Fama and French’s original 2009 study of mutual fund performance by examining it under the lens of the updated 5-factor model.[1] Using a sample of 3,870 individual active mutual funds, researches looked at their performance over the 32-year period from 1984 to 2015. In aggregate, they found that the active mutual fund industry, as a whole, underperformed the Russell 3000 Index by 1.34% per year.

Similarly, they found that the original 3-factor and the new 5-factor model explained 99% of the variation in active mutual fund returns, which underperformed both models by -0.08% and -0.06% per month, respectively. This is roughly in line with the average actively managed fund expense ratio and once again Bill Sharpe’s now 25-year old prediction. The figures in parentheses represent the t-statistic of the explanatory factors on the aggregate active US equity mutual fund returns. As you can see, most of these figures are well above the level 2 threshold (95% confidence level) that is that standard in scientific research. You can interpret these t-statistics as indicating very high degrees of certainty in regards to the monthly estimates of the explanatory variables. For example, using the 5-factor regression, the estimate of 0.09 on the size factor with a 8.52 t-statistic means that we can be over 99.9% confident that the aggregate active US Equity Mutual Fund was slightly smaller in terms of market capitalization than the overall market from 1984-2015.

Also similar to Fama and French’s 2009 conclusions, the number of active managers that outperformed the 3-Factor and 5-Factor Models with a high degree of confidence (t-stat>2) was less than was is expected by random chance. The chart below shows three different distributions. First, there is a distribution that looks identical to a normal distribution. This distribution represents the potential range of the t-statistics of alpha of active US equity managers based on chance alone. In any given year, we would expect 1 out of every 40 active managers to have a t-stat greater than 2 by chance alone. On the right side of the distribution we have the potential outcomes for the extremely lucky managers and on the left side we have the potential outcomes for the extremely unlucky managers. The other 2 distributions represent the actual t-statistics of alpha for active US equity managers after they have been adjusted by the 3-Factor and 5-Factor regression models. What is very telling is the significant left of both distributions compared to the "by-chance" distribution. This means that a significant number of active US equity managers had t-statistics of alpha that were significantly less than what is expected just by random chance alone. 2.4% had alphas with a t-stat greater than 2 where we would expect 2.9 just by random chance. As in the author’s own words, “these funds do as well as would be expected by extremely lucky funds found in a zero-alpha world.”

Research has given us insight into the wide world of investing. While many fund companies are quick to highlight their own outperformance over any given time period, a large study of active management indicates that there is a more than probable chance that this outperformance is a result of luck.

In the context of an individual investor, the question you have to ask yourself is, “is it worth it to gamble with my life’s savings in order to possibly earn an above average return?” The risk is that you end up being apart of the extremely unlucky group of managers and subsequently harm your financial future.

We don’t believe the risk is worth it and there is no evidence that suggests it is in investor’s best interest to begin with. The more prudent approach would be to buy and hold a globally diversified portfolio of index funds.


[1] Meyer-Brauns, Philipp. “Mutual Fund Performance through a Five-Factor Lens.” Dimensional Fund Advisors, LP. August 2016.