In finance, survivorship bias, also known as "survivor bias", refers to the tendency for mutual funds or hedge funds that have produced poor performance or low asset accumulations to be either liquidated or merged out of existence. In the case of long term global asset returns, survivorship bias comes into play with the extinction of whole markets due to war and or revolution. The result is an overestimation of past returns, as these poor returning funds/national markets are dropped from the data base. 
Mutual fund survivorship bias
A Gruber, Elton, Blake study  of survivorship bias in U.S. mutual funds examines the period between 1976-1993. The paper has a section devoted to a review of prior studies (along with their methodology problems). Here are the numbers:
Brown & Goetzmann  : examining raw returns fund data from 1976-1988 found overestimation bias of 20 and 80 basis points, depending on the weighing scheme. Malkiel (1994) using unadjusted raw data found overestimation bias of 150 basis points.
Gruber, Elton, Blake: Modelers attempting to determine bias measure performance either by considering the common stock investing policy at the beginning of the period or by considering the common stock investing policy throughout the period. The study authors report both approaches. The authors prefer a risk-adjusted three index method (passive benchmarks for large cap stocks, small cap stocks, bonds and bills) over all other measuring methods, such as single index (S&P 500 index), or raw returns. The following table, reproduced from the paper, shows survivorship bias results according to various methodologies for the 1976-1993 period. Panel A looks at results assuming investment ends at the point the fund disappears from the data record via merger or policy change. Panel B shows a "follow the money" method, assuming the the investment continues to be held in the new merged fund after the disappearing fund has been merged. GE&B also mention their 1993 paper  on survivorship bias in bond funds. Using similar risk-adjusted three index factor methodology the authors report 27 basis points of overestimated return due to survivorship bias.
Additional findings from Grubar, Elton, Blake:
- Disappearing funds are mostly small funds.
- The funds into which the disappearing funds are merged tend to have higher expense ratios. The expense ratio tends not to decline after the merger.
- The funds into which the disappearing funds are merged tend to have better past performance records. Performance tends to drop after the merger.
|Panel A. Through month of merger or policy change||Common stock at beginning||Common stock throughout|
|Raw Return minus S&P||0.3908||-0.4190|
|Panel B. Follow the money approach||Common stock at beginning||Common stock throughout|
|Raw Return minus S&P||0.7301||0.5982|
Carhart, Carpenter, Lynch, and Musto (2000)  provide a comprehensive study of mutual fund survivorship issues using a mutual fund data set (Carhart 1997) and using a four-factor analysis of fund returns. The authors found, that in the sample, funds disappear primarily because of multi-year poor performance. They found that survivor bias in average performance tends to increase with the length of the sample period (although they caution that it is possible to construct counterexamples). In the sample, they found survivor bias of 17 basis points per annum for one year samples, increasing to larger than one percent per annum for samples longer than fifteen years.
Morningstar mutual funds
A Savant Capital Management Zero Alpha Group study  examining Morningstar mutual fund returns data for the 1995 - 2004 period finds that dropping defunct funds from the Morningstar database boosted reported returns on average by 1.3% per annum over the ten year period. The study applied returns to the closest fitting index to each asset class. For U.S equity returns the benchmark indexes were S&P indexes. For developed market international stocks the market benchmarks were MSCI indexes. Emerging markets stocks were benchmarked to the S&P/IFCI Emerging Markets index. The following table records the study findings of survivorship bias in the Morningstar data, showing the annualized return adjustment needed to provide bias-free returns.
The following table reports the study findings of survivorship bias for Morningstar bond mutual fund returns data over the 1995- 2004 period.
|Asset Class||Index||Survivorship bias|
|US Treasury Long||Lehman Brothers Long Treasury||-0.70%|
|US Treasury Intermediate||Lehman Brothers Intermediate Treasury||-0.20%|
|US Treasury Short||Lehman Brothers 1 -3 Year Government||-0.20%|
|Muni National Long||Lehman Brothers Municipal 15 Year||-0.20%|
|Muni National Intermediate||Lehman Brothers Municipal 7 Year||-0.20%|
|Muni National Short||Lehman Brothers Municipal 3 Year||-0.10%|
In 2007, Morningstar revised it's methodology to remove the effects of survivorship bias on mutual funds.
Hedge fund survivorship bias
Kat and Guarov  report the following conclusions regarding hedge fund attrition and survivorship bias for the period 1994-2001 using data from the Tremont Tass database of hedge fund returns, which start in 1994. This period includes major market events such as the Long Term Management collapse, the Russian default, and the early 2000-2001 stock market drop.
- Attrition: Hedge funds exhibit a high level of attrition; and the attrition grows over time. Hedge fund fund of funds exhibit lower levels of attrition, but they too show growing rates of attrition over time.
- Factors behind attrition: The main factors behind hedge fund attrition are lack of size and lack of performance. There are no identifiable causes for the increasing attrition over time. The authors suggest that an increasingly aggressive attitude among both old and new hedge fund managers alike might be the cause.
- Survivorship bias over mean returns: Concentrating on survivors will overestimate returns by approximately 2.0% per annum. However small and leveraged funds have bias between 4%-5% per annum. Fund of funds bias is lower, 0.63% per annum.
- Survivorship bias in higher moments: Ignoring dead funds can result in underestimating hedge fund standard deviation and kurtosis, while overestimating skewness and inflating the mean. Without adjusting for survivorship bias, investors are thus likely to substantially overestimate the benefits of hedge funds.
Ibbotson and Chen  examine hedge fund returns data (using the Tremont Tass database) for the period 1995 -2006 which reports an equal weighted net of fees hedge fund return of 16.45%. The authors find a survivorship bias of 2.74% per annum over the period. Including "backfill bias"  the overstatement of returns increases to 5.68% per annum.
Xu, Liu, and Loviscek  review hedge fund results from the CISDM (Center for International Securities & Derivative Markets) database from January of 1994 to March of 2009, a period which includes the 2008 financial crisis. The authors found a large increase in hedge fund attrition, rising to 31% in 2009. For the 2008 -2009 financial crisis period, the authors find survivorship bias to be somewhat lower than historical experience, measuring between 1.32% and 1.68%. However, the authors contend that the lack of reporting data for the last few months of a dissolving fund's existence understates the bias. They estimate actual bias between 1.68% and 6.48% for the crisis period. They report fund of funds survivorship bias of 3.8% for the crisis period.
Current reporting of fund attrition and survivorship bias
S&P reports current mutual fund attrition rates in both their regular series of S&P Index vs. Active (SPIVA) reports and in their periodic reports on fund performance persistance. The reports provide attrition over three year and five year periods. SPIVA also uses the CRSP (The Center for Research in Security Prices) Survivor-Basis Free Mutual Fund Database as the basis for comparing fund returns to index returns.
The CRSP Mutual Fund Database was developed in three stages. The database, with data beginning December 1961 through December 1995, was developed by Mark M. Carhart for his 1995 dissertation,“Survivor Bias and Persistence in Mutual Fund Performance.” Funding for this project was provided by Eugene F. Fama and the Center for Research in Security Prices. The Center for Research in Security Prices continued Mr. Carhart’s work after his graduation. Historical data in the database were collected and verified from numerous printed sources. Beginning December 2007, current and historical data back to August 1998 are provided electronically by Lipper and Thomson Reuters 
- definition, investopedia
- Elton, Edwin J., Gruber, Martin J. and Blake, Christopher R., Survivorship Bias and Mutual Fund Performance (March 1995). NYU Working Paper No. FIN-94-027. Available at SSRN: http://ssrn.com/abstract=1299448
- The paper is not available on-line. Goetzmann, William, Attrition and Mutual Fund Performance (with S.J. Brown), Journal of Finance, Vol. 49, No. 3, 1055-1056, 1994
- The paper in not available online. Malkiel, Burton G. G., Returns from Investing in Equity Mutual Funds 1971-1991. JOURNAL OF FINANCE, Vol 50 No 2, June 1995.
- The paper is not available online. Christopher R. Blake, Edwin J. Elton and Martin J. Gruber, The Performance of Bond Mutual Funds, The Journal of Business Vol. 66, No. 3 (Jul., 1993), pp. 371-403
- Carhart, Mark M., Carpenter, Jennifer N., Lynch , Anthony W. and Musto, David K., Mutual Fund Survivorship (September 12, 2000). Available at SSRN: http://ssrn.com/abstract=238713 or doi:10.2139/ssrn.238713
- Study: Hidden Bias in Morningstar Data ' Systematically and Significantly' Overstates Managed Mutual Fund Performance
- How Much? - Survivorship Bias at Morningstar, forum discussion, direct link to post.
- Kat, Harry M. and Amin, Gaurav S., Welcome to the Dark Side: Hedge Fund Attrition and Survivorship Bias over the Period 1994-2001 (December 11, 2001). Cass Business School Research Paper. Available at SSRN: http://ssrn.com/abstract=293828 or doi:10.2139/ssrn.293828
- Ibbotson, Roger G. and Chen, Peng, The A,B,Cs of Hedge Funds: Alphas, Betas, and Costs (September 2006). Yale ICF Working Paper No. 06-10. Available at SSRN: http://ssrn.com/abstract=733264
- also known as "instant history bias", investopedia defines it as follows:
Refer also to Posthuma, Nolke and Van der Sluis, Pieter Jelle, A Reality Check on Hedge Funds Returns (July 8, 2003). Available at SSRN: http://ssrn.com/abstract=438840 or doi:10.2139/ssrn.438840, for a study on hedge fund backfill bias.
An inaccuracy in the appearance of investment fund returns that occurs when only new, successful funds report their numbers while new, unsuccessful funds close and their poor returns aren't factored into an investment manager's or investment type's overall performance record.
Instant history bias, which especially occurs in hedge funds, is also called "backfill bias" because hedge fund managers may choose [to] not report fund performance to a database from the fund's inception, but instead choose to "backfill" the database later when they have established a track record of success with a fund. From Definition, investopedia
- Xu, Xiaoqing Eleanor, Liu, Jiong and Loviscek, Anthony, Hedge Fund Attrition, Survivorship Bias, and Performance: Perspectives from the Global Financial Crisis (February 12, 2010). Available at SSRN: http://ssrn.com/abstract=1572116
- The CRSP Survivor Bias-Free Mutual Fund Guide
- Published Mutual Fund Returns Not Always What They Appear, investopedia article
- The CRSP Survivor-Bias-Free US Mutual Fund Database
- The CRSP Survivor Bias-Free Mutual Fund Guide
- S&P SPIVA reports Periodic reports include survivorship-bias free returns comparisons (using CRSP Survivor Bias-Free US Mutual Fund Datatbase) as well as survivorship percentages over one, three, and five year periods.
- How Much? - Survivorship Bias at Morningstar, forum discussion