Survivorship bias

Survivorship bias, or survival bias, is the logical error of concentrating on the people or things that "survived" some process and inadvertently overlooking those that did not because of their lack of visibility. This can lead to false conclusions in several different ways. The survivors may be actual people, as in a medical study, or could be companies or research subjects or applicants for a job, or anything that must make it past some selection process to be considered further.

Survivorship bias can lead to overly optimistic beliefs because failures are ignored, such as when companies that no longer exist are excluded from analyses of financial performance. It can also lead to the false belief that the successes in a group have some special property, rather than just coincidence (Correlation proves Causation). For example, if three of the five students with the best college grades went to the same high school, that can lead one to believe that the high school must offer an excellent education. This could be true, but the question cannot be answered without looking at the grades of all the other students from that high school, not just the ones who "survived" the top-five selection process.

Survivorship bias is a type of selection bias.

In finance, survivorship bias is the tendency for failed companies to be excluded from performance studies because they no longer exist. It often causes the results of studies to skew higher because only companies which were successful enough to survive until the end of the period are included. For example, a mutual fund company's selection of funds today will include only those that are successful now. Many losing funds are closed and merged into other funds to hide poor performance. In theory, 90% of extant funds could truthfully claim to have performance in the first quartile of their peers, if the peer group includes funds that have closed.

In 1996, Elton, Gruber, and Blake showed that survivorship bias is larger in the small-fund sector than in large mutual funds (presumably because small funds have a high probability of folding). They estimate the size of the bias across the U.S. mutual fund industry as 0.9% per annum, where the bias is defined and measured as:

Additionally, in quantitative backtesting of market performance or other characteristics, survivorship bias is the use of a current index membership set rather than using the actual constituent changes over time. Consider a backtest to 1990 to find the average performance (total return) of S&P 500 members who have paid dividends within the previous year. To use the current 500 members only and create a historical equity line of the total return of the companies that met the criteria, would be adding survivorship bias to the results. S&P maintains an index of healthy companies, removing companies that no longer meet their criteria as a representative of the large-cap U.S. stock market. Companies that had healthy growth on their way to inclusion in the S&P 500, would be counted as if they were in the index during that growth period, when they were not. Instead there may have been another company in the index that was losing market capitalization and was destined for the S&P 600 Small-cap Index, that was later removed and would not be counted in the results. Using the actual membership of the index, applying entry and exit dates to gain the appropriate return during inclusion in the index, would allow for a bias-free output.

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