  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.
