Surviving Survivorship Bias

The purpose of this study is twofold: First: to introduce a new notion of survivorship bias for mutual fund data taking into account the fact that cancellation or termination of fund records may have both a positive and a negative effect on the overall evaluation of performance Second: to analyze in detail the most widely used dataset for mutual fund performance evaluation: CRSP to assess whether such a dataset possesses the properties needed for being a sound basis for performance evaluation and, in particular, for the estimation of survivorship bias effects. A third and strictly connected purpose: the statement and estimation of a survival model for survivorship bias correction, shall be pursued in a following paper. The standard statement of the problem can be simply subsumed: mutual funds with poor performance close down and are forgotten in standard databases. Hence, the use of such databases for the assessment of overall fund performance is bound to yield upward biased results. Inclusion of the deleted fund result in the database solves the problem. The implied assumption is that a full correction for the deletion of funds from the database can be accomplished simply adding to the database all the deleted funds, with no further correction. This assumption about dataset completion, only holds if we suppose that deletion of funds to be a random event. In this case, however, fund deletion shall not create any bias in the overall analysis of the industry performance even if deleted funds are not reinserted in the dataset. If, as it is likely, fund deletion depends on fund performance (so that a problem of bias may exist), the simple reintroduction of deleted data in the dataset shall not “correct” the bias. In fact the only way, in this case, for correcting the bias is to study the interaction between the NAV process and the censoring rule, or, in other words, the survival model. Any different NAV model joint to a survival model shall yield different bias evaluation and the simple trick of “completing” the dataset cannot solve such a problem. In order to understand this, it is useful to realize that, ideally, the “complete”, bias free, dataset should contain the full history of “revived” funds run from the date of their demise to the date of observation of the dataset. Since this completion is impossible, the only alternative, as said above, is to study the interplay between the NAV model and the censoring rule. In the first part of the empirical analysis, survivorship bias is estimated according to its standard definition, that is: as the difference in performance between the set of surviving mutual funds and the set of all mutual funds existed in a specific time period. After excluding from the analysis all the funds for which data are missing, 29258 equity mutual funds that existed between January 2000 and December 2011 are analyzed. The difference in performance between survived and dead funds is positive and bigger the higher is the time horizon considered. However, the number of surviving mutual funds underperforming non-surviving ones is always very high suggesting that performance is not enough to explain mutual fund survival. In the second part of the analysis, data on fund volatility, age, size, target, turnover, expenses and sensitivity to risk factors are employed as explanatory variables for survival. Survival is evaluated in 6 different points in time for a time horizon of 6 years. Size, turnover and expenses seem to matter in explaining mutual fund survival suggesting that stochastic survival models should be built considering these variables in addition to performance.