Look-Ahead Benchmark Bias in Portfolio Performance Evaluation
  Performance of investment managers are evaluated in comparison with benchmarks, such as financial indices. Due to the operational constraint that most professional databases do not track the change of constitution of benchmark portfolios, standard tests of performance suffer from the "look-ahead benchmark bias," when they use the assets constituting the benchmarks of reference at the end of the testing period, rather than at the beginning of the period. Here, we report that the "look-ahead benchmark bias" can exhibit a surprisingly large amplitude for portfolios of common stocks (up to 8% annum for the S&P500 taken as the benchmark) -- while most studies have emphasized related survival biases in performance of mutual and hedge funds for which the biases can be expected to be even larger. We use the CRSP database from 1926 to 2006 and analyze the running top 500 US capitalizations to demonstrate that this bias can account for a gross overestimation of performance metrics such as the Sharpe ratio as well as an underestimation of risk, as measured for instance by peak-to-valley drawdowns. We demonstrate the presence of a significant bias in the estimation of the survival and look-ahead biases studied in the literature. A general methodology to test the properties of investment strategies is advanced in terms of random strategies with similar investment constraints. 
Gilles Daniel, Didier Sornette and Peter Wohrmann