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False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alpha

False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alpha. Laurent Barras , Olivier Scaillet and Russ Wermers. What does this paper do?.

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False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alpha

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  1. False Discoveries in Mutual Fund Performance: Measuring Luck in Estimated Alpha Laurent Barras, Olivier Scaillet and Russ Wermers

  2. What does this paper do? • This paper develops a simple technique that controls for “false discoveries”, or mutual funds that exhibit significant alphas by luck alone.

  3. Graphic Explanation Of False Discoveries

  4. The meaning of this paper • Help us set our investment goals • A portfolio construction method with the potential to beat the benchmark • Help us get an idea of the industry trend.

  5. Research Approach • Step 1: Break M active managed funds into 3 categories: 1. Unskilled (alpha<0); 2. Zero-Alpha (a=0); 3. Skilled (alpha>0) We are using as our performance measure, since it has been showed to be superior to simply alpha measure. Also, we are using the four-factor model we learned

  6. Research Approach (continued) • Step 2: Chose a significant level, and determine

  7. Research Approach (continued) • Step 3: Mix the three distributions.

  8. Problems • The centers of the three distributions • The weights used to mix the three distributions • Problems caused by sample characteristics. • What if unskilled and skilled funds are not distinguished due to sample size? • What if cross-section of actual skill levels has a complex distribution (against the simple distribution assumption we made) So we enhance our procedures to address the problems!

  9. Luck Measurement Definitions • Lucky Funds (False discoveries) • Expected Skilled Funds (Truly Skilled Funds): （3） • Expected unskilled Funds (Truly Unskilled): （4）

  10. Intuition to Determine the Weights and center locations • As we increase • Centers are

  11. Details in determine weights • False Discovery Rate (FDR) technique Facts: • Zero-alpha funds have p-values uniformly distributed over the interval [0,1] • P-values of unskilled and skilled funds are very small Based on the two facts above, we can exploit , the weights of zero-alpha funds, without knowing the weights of skilled and unskilled funds.

  12. Details in determine weights (Continued) Choose Extrapolating the rightmost four bars over the entire region between zero and one, using Where W is the number of funds in the rightmost four bars. This is Equiation（5）

  13. How to determine • Bootstrap Technique

  14. Substitute into equations, we will have a lot estimated information Similarly, we can use bootstrap technique to get the optimal r and estimate the weights of skilled and unskilled funds.

  15. Advantage of this approach • More accuracy than some other methods, supported by conducting comparison between the estimators and actual values. • The approach estimate the p-value of each fund in isolation, avoiding the complications that arise because of dependence strucuture of residuals.

  16. Empirical Results

  17. Empirical Results in English • Among 2076 funds, 75.4% are zero alpha • Only 0.6% are truly skilled, and they are not even statistically significant. • From Panel B, the majority of skilled funds are just lucky. • 24% are truly unskilled fund, and they form the majority of unskilled funds. • Unskilled funds have a relatively long life, and they tend to always underperform. How did they survive? Marketing? • Expense ratio for unskilled funds is higher.

  18. Empirical Results (Continued) • Growth funds show similar results to overall universe of funds. While growth and income funds consist of largest proportion of unskilled funds (30.7%), but have no skilled funds.

  19. Is the result consistent over the entire history? No, but even worse Skilled funds decreases from 14.4% in early 1990 to 0.6% in late 2006, while unskilled funds increases from 9.2% to 24%. Although the number of actively managed funds dramatically increases over this period, skilled managers have become exceptionally rare.

  20. Performance Consistency – Short Term result is better!

  21. Hypothetical Portfolio • The authors reform a portfolio at the beginning of every year consisting of the funds in the extreme right tail. The alpha is 1.45% for a period from 1980 to 2006! • Short term skills do exist and may lead to outperformance.

  22. Why underperform over long term? • Money flows – no arbitrage theory • Expenses have major negative impact

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