For actively managed US equity mutual funds over the period from 1991 to 2020, survivorship bias overstates the median fund alpha by 0.60% per year: The median fund alpha is –0.84% per year among surviving funds compared to –1.44% per year among both surviving and non-surviving funds.
Analyzing the performance of mutual fund managers is popular among financial researchers for the many insights it provides about markets. However, the usefulness of inference from fund returns depends critically on data quality. Because non-surviving funds tend to have poorer performance than surviving funds, studies that examine only surviving strategies suffer from an upward bias in returns known as “survivorship bias.” Our research suggests that survivorship bias overstates the median fund alpha by roughly 50% compared to the survivorship bias-free median (here, alpha refers to performance after accounting for exposures to known drivers of expected returns). It also nearly doubles the proportion of funds that earn a reliably positive alpha.
IMPACT OF SURVIVORSHIP BIAS ON FUND ALPHA
Survivorship bias matters for two reasons: Funds are often liquidated or merged, and non-surviving funds tend to perform worse than surviving funds. We quantify the effects of survivorship bias using a sample of actively managed US equity mutual funds from the Morningstar Direct database (see the data appendix for the detailed sample-selection criteria). The sample period is January 1991 to June 2020.1
Exhibit 1 shows that, on average over the sample period, about 100 US equity funds were liquidated or merged each year, which is about 5% of the funds available at the beginning of any given year. Disappearances reach a high in 2009, when 275 funds were liquidated or merged, which is 11.5% of the funds in existence at the beginning of 2009. Please see the end of this document for important disclosures.
To measure performance, we estimate each fund’s alpha using the Fama/French five-factor model. This allows us to control for differences in performance due to exposures to known drivers of expected returns; namely, the market, size, value, profitability, and investment factors. Each estimate is based on a fund’s entire history of monthly returns, net of all fees and expenses, during the sample period.2
Studies of mutual fund performance should consider the full distribution of outcomes rather than individual fund results. The large number of funds in the sample (1,557 survivors and 2,545 non-survivors in total) means we are likely to observe extreme estimates—both positive and negative—by chance alone. As such, we compare the full distribution of estimates with and without survivorship bias to assess and quantify the impact of the bias on fund alpha.
Exhibit 2 shows the probability distribution of estimates for all funds as well as separately for surviving and non-surviving funds. Among survivors, the median estimate is negative: –7 basis points (bps) per month. That is, the median surviving fund underperformed relative to the five-factor model. Including non-surviving funds worsens the picture, as the median estimate among all funds is –12 bps per month. Survivorship bias thus overstates the median estimate by 5 bps per month (60 bps per year), or roughly half the magnitude of the survivorship-bias free median.3 The negative median estimate for all funds is consistent with most studies on active mutual fund performance.4
The performance distribution for non-survivors is to the left of that for survivors (the median for non-survivors is –17 bps per month) and has a more pronounced left tail. This implies that survivorship bias understates the left tail of the performance distribution. For instance, the 1st, 5th, and 10th percentiles are, respectively, –43, –29, and –23 bps per month for surviving funds but –122, –68, and –47 bps per month for all funds.
Turning to the right side of the performance distribution, survivorship bias also overstates the likelihood of a positive investment outcome. Looking only at survivors, 4.5% of funds earn a reliably positive estimate, i.e., one with a t-statistic above 2. Considering both surviving and non-surviving funds, this proportion is roughly cut in half: Just 2.4% of all funds earn an estimate that is more than two standard errors above zero, which is below the 3.2% we would expect by chance for this sample.5
WHAT CAN WE LEARN FROM THE QUANTIFICATION OF SURVIVORSHIP BIAS?
Survivorship bias overstates good performance and understates bad outcomes.
Our study highlights the importance of inference based on survivorship-bias free data. For researchers, this means using comprehensive data sets that cover the returns of both surviving and non-surviving strategies.
For investors, our results suggest that one should evaluate any given fund manager based on their full set of funds, including funds that are no longer available for investment—otherwise, a seemingly stellar track record may, in fact, be an incomplete and biased reflection of reality.
Given the noise in security returns and the volatility of premiums, however, past performance is not sufficient to evaluate a fund manager. Researchers and investors should also consider other aspects of the manager, such as their underlying investment philosophy, the robustness in their strategy design, and the efficiency in their portfolio management and trading. All these traits are important in delivering a good investment experience and helping investors achieve their goals.
1. Morningstar Direct records the date of fund liquidations and mergers starting from October 1990. Our research suggests that the database is free from survivorship bias starting from January 1991.
2. One of our sample selection criteria is that funds must have at least 12 months of returns. This introduces a slight survivorship bias but ensures that we can estimate a fund’s five-factor.
3. A rank-sum test rejects that the median estimate among survivors is the same as that among non-survivors (p = 0.00). The results are similar using means: The mean estimate is -5 bps per month among survivors but –15 bps per month among all funds and a two-sample t-test with unequal variances rejects that the mean among survivors is the same as that among non-survivors (t = 17.03).
4. See Carhart (1997), Fama and French (2010), Linnainmaa (2013), and Meyer-Brauns (2016).
5. Following the methodology of Fama and French (2010), we obtain a by-chance distribution of fund as the average of 10,000 bootstrapped simulation runs. A simulation run is a random sample (with replacement) of 354 months drawn from the 354 calendar months from January 1991 to June 2020. For each simulation run, we regress, fund by fund, benchmark-adjusted (zero-) fund returns on the five factors of Fama and French (2015), dropping funds that are in the simulation run for less than 12 months.
Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance,” Journal of Finance 52, no. 1: 57–82.
Fama, Eugene F., and Kenneth French. 2010. “Luck versus Skill in the Cross-Section of Mutual Fund Returns.” Journal of Finance 65, no. 5: 1915–1947.
Fama, Eugene F., and Kenneth French. 2015. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics 116, no. 11: 1–22.
Linnainmaa, Juhani T. 2013. “Reverse Survivorship Bias.” Journal of Finance 68, no. 3: 789–813.
Meyer-Brauns, Philipp. 2016. “Mutual Fund Performance through a Five-Factor Lens.” Dimensional Fund Advisors white paper.
The sample is actively managed, US-domiciled, USD-denominated, US-equity invested, open-end mutual funds on the Morningstar Direct database, excluding index funds and fund-of-funds. Funds are included in the sample upon first passing an assets-under-management (AUM) threshold of $5 million measured in June 2020 US dollars. To mitigate incubation bias, we exclude funds with a first monthly return within the last 5 years of the sample period. We also exclude funds with fewer than 12 months of returns during the sample period. Once a fund is included in the sample, we keep it until it is either liquidated or merged or we reach June 2020. Surviving funds are those still available at the end of June 2020.
Active management: A portfolio management approach that aims to outperform a market rate or return, or a specific benchmark, by choosing investments that deviate from the market portfolio or benchmark.
Survivorship bias: Looking only at live funds and ignoring those that have liquidated or merged.
Median: The value below which 50% of the outcomes in a sample are found. Equivalently, 50% of the outcomes are found above the median.
Alpha: The rate of return on an investment in excess of a benchmark or the return predicted by a financial model. A more positive alpha implies greater outperformance, while a more negative alpha implies greater underperformance.
Surviving fund: A fund still available at the end of the sample period (June 2020).
Liquidated fund: A fund that sells all its assets and ceases to exist altogether.
Merged fund: A fund that ceases to exist as a separate entity because it is combined with other funds.
Fama/French Five-Factor Model: A financial model describing an equity security’s expected return in excess of the return on short-term bills as a linear function of five explanatory variables or “factors.” The factors are the market’s excess return over short-term bills (the market factor), the return difference between small and large stocks (the size factor), the return difference between value and growth stocks (the value factor), the return difference between high and low profitability stocks (the profitability factor), and the return difference between low and high asset-growth stocks (the investment factor).
Small and large stocks: Small stocks are those with a relatively low market capitalization, while large stocks are those with relatively large market capitalization.
Value and growth stocks: Value stocks are those with relatively low prices relative to book value, while growth stocks are those with relatively high prices relative to book value.
Profitability: A company’s operating income before depreciation and amortization minus interest expense scaled by book equity.
Investment or asset growth: A company’s annual percentage change in total book assets.
Probability distribution: A tabulation or graphing of the frequency of different outcomes in a sample.
Percentile: The value below which a given percentage of outcomes in a sample are found. For example, the 5th percentile is the value below which 5% of the outcomes are found; equivalently, 95% of the outcomes are found above the 5th percentile.
Tails of a probability distribution: The extreme outcomes in a sample that occur with a relatively low frequency.
t-Statistic: A measure of the statistical reliability of an estimate. It is defined as the value of the estimate divided by the standard error of the estimate, where the standard error is a measure of the imprecision in the estimate. For example, a value more positive than 2 or more negative than -2 indicates that the estimate is more than two standard errors away from zero.
The information in this document is provided in good faith without any warranty and is intended for the recipient’s background information only. It does not constitute investment advice, recommendation, or an offer of any services or products for sale and is not intended to provide a sufficient basis on which to make an investment decision. It is the responsibility of any persons wishing to make a purchase to inform themselves of and observe all applicable laws and regulations. Unauthorized copying, reproducing, duplicating, or transmitting of this document are strictly prohibited. Dimensional accepts no responsibility for loss arising from the use of the information contained herein.
Eugene Fama and Ken French are members of the Board of Directors of the general partner of, and provide consulting services to, DFAL and DIL.
“Dimensional” refers to the Dimensional separate but affiliated entities generally, rather than to one particular entity. These entities are Dimensional Fund Advisors LP, Dimensional Fund Advisors Ltd., Dimensional Ireland Limited, DFA Australia Limited, Dimensional Fund Advisors Canada ULC, Dimensional Fund Advisors Pte. Ltd, Dimensional Japan Ltd., and Dimensional Hong Kong Limited. Dimensional Hong Kong Limited is licensed by the Securities and Futures Commission to conduct Type 1 (dealing in securities) regulated activities only and does not provide asset management services.
UNITED STATES: Dimensional Fund Advisors LP is an investment advisor registered with the Securities and Exchange Commission.
CANADA: These materials have been prepared by Dimensional Fund Advisors Canada ULC. Commissions, trailing commissions, management fees, and expenses all may be associated with mutual fund investments. Unless otherwise noted, any indicated total rates of return reflect the historical annual compounded total returns, including changes in share or unit value and reinvestment of all dividends or other distributions, and do not take into account sales, redemption, distribution, or optional charges or income taxes payable by any security holder that would have reduced returns. Please read the prospectus before investing. Mutual funds are not guaranteed, their values change frequently, and past performance may not be repeated.
AUSTRALIA and NEW ZEALAND: This material is issued by DFA Australia Limited (AFS License No. 238093, ABN 46 065 937 671). This material is provided for information only. No account has been taken of the objectives, financial situation or needs of any particular person. Accordingly, to the extent this material constitutes general financial product advice, investors should, before acting on the advice, consider the appropriateness of the advice, having regard to the investor’s objectives, financial situation and needs. Any opinions expressed in this material reflect our judgement at the date of publication and are subject to change.
WHERE ISSUED BY DIMENSIONAL IRELAND LIMITED OR DIMENSIONAL FUND ADVISORS LTD. Neither Dimensional Ireland Limited (DIL) nor Dimensional Fund Advisors Ltd. (DFAL), as applicable (each an “Issuing Entity,” as the context requires), give financial advice. You are responsible for deciding whether an investment is suitable for your personal circumstances, and we recommend that a financial adviser helps you with that decision.
NOTICE TO INVESTORS IN SWITZERLAND: This is an advertising document.
WHERE ISSUED BY DIMENSIONAL IRELAND LIMITED
Issued by Dimensional Ireland Limited (DIL), with registered office 10 Earlsfort Terrace, Dublin 2, D02 T380, Ireland. DIL is regulated by the Central Bank of Ireland (Registration No. C185067). Information and opinions presented in this material have been obtained or derived from sources believed by DIL to be reliable, and DIL has reasonable grounds to believe that all factual information herein is true as at the date of this document.
DIL issues information and materials in English and may also issue information and materials in certain other languages. The recipient’s continued acceptance of information and materials from DIL will constitute the recipient’s consent to be provided with such information and materials, where relevant, in more than one language.
WHERE ISSUED BY DIMENSIONAL FUND ADVISORS LTD.
Issued by Dimensional Fund Advisors Ltd. (DFAL), 20 Triton Street, Regent’s Place, London, NW1 3BF. DFAL is authorised and regulated by the Financial Conduct Authority (FCA). Information and opinions presented in this material have been obtained or derived from sources believed by DFAL to be reliable, and DFAL has reasonable grounds to believe that all factual information herein is true as at the date of this document.
DFAL issues information and materials in English and may also issue information and materials in certain other languages. The recipient’s continued acceptance of information and materials from DFAL will constitute the recipient’s consent to be provided with such information and materials, where relevant, in more than one language.
Investments involve risks. The investment return and principal value of an investment may fluctuate so that an investor’s shares, when redeemed, may be worth more or less than their original value. Past performance is not a guarantee of future results. There is no guarantee strategies will be successful.
Provided for institutional investors only. This document is deemed to be issued by Dimensional Japan Ltd., which is regulated by the Financial Services Agency of Japan and is registered as a Financial Instruments Firm conducting Investment Management Business and Investment Advisory and Agency Business. This material is solely for informational purposes only and shall not constitute an offer to sell or the solicitation to buy securities or enter into investment advisory contracts. The material in this article and any content contained herein may not be reproduced, copied, modified, transferred, disclosed, or used in any way not expressly permitted by Dimensional Japan Ltd. in writing. All expressions of opinion are subject to change without notice.
Dimensional Japan Ltd.
Director of Kanto Local Finance Bureau (FIBO) No. 2683
Membership: Japan Investment Advisers Association
FOR PROFESSIONAL INVESTORS IN HONG KONG.
This material is deemed to be issued by Dimensional Hong Kong Limited (CE No. BJE760) (“Dimensional Hong Kong”), which is licensed by the Securities and Futures Commission to conduct Type 1 (dealing in securities) regulated activities only and does not provide asset management services.
This material should only be provided to “professional investors” (as defined in the Securities and Futures Ordinance [Chapter 571 of the Laws of Hong Kong] and its subsidiary legislation) and is not for use with the public. This material is not directed to any person in any jurisdiction where (by reason of that person’s nationality, residence, or otherwise) the publication or availability of this material are prohibited or which would subject Dimensional Hong Kong (including its affiliates) or any of Dimensional Hong Kong’s products or services to any registration, licensing, or other such legal requirements within such jurisdiction or country. When provided to prospective investors, this material forms part of, and must be provided together with, applicable fund offering materials. This material must not be provided to prospective investors on a standalone basis. Before acting on any information in this materiel, you should consider whether it is suitable for your particular circumstances and, if appropriate, seek professional advice.
Unauthorized copying, reproducing, duplicating, or transmitting of this material are prohibited. This material and the distribution of this material are not intended to constitute and do not constitute an offer or an invitation to offer to the Hong Kong public to acquire, dispose of, subscribe for, or underwrite any securities, structured products, or related financial products or instruments nor investment advice thereto. Any opinions and views expressed herein are subject to change. Neither Dimensional Hong Kong nor its affiliates shall be responsible or held responsible for any content prepared by financial advisors. Financial advisors in Hong Kong shall not actively market the services of Dimensional Hong Kong or its affiliates to the Hong Kong public.
This material is deemed to be issued by Dimensional Fund Advisors Pte. Ltd., which is regulated by the Monetary Authority of Singapore and holds a capital markets services license for fund management.
This advertisement has not been reviewed by the Monetary Authority of Singapore. This information should not be considered investment advice or an offer of any security for sale. All information is given in good faith without any warranty and is not intended to provide professional, investment, or any other type of advice or recommendation and does not take into account the particular investment objectives, financial situation, or needs of individual recipients. Before acting on any information in this materiel, you should consider whether it is suitable for your particular circumstances and, if appropriate, seek professional advice. Dimensional Fund Advisors Pte. Ltd. does not accept any responsibility and cannot be held liable for any person’s use of or reliance on the information and opinions contained herein. Neither Dimensional Fund Advisors Pte. Ltd. nor its affiliates shall be responsible or held responsible for any content prepared by financial advisors.