Look-Ahead Benchmark Bias in Portfolio Performance Evaluation

Abstract

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.

Investment Strategies Used as Spectroscopy of Financial Markets Reveal New Stylized Facts

“…In other words, this would correspond to giving the traders ex-ante forecasting abilities. We thus avoid such look-ahead bias [36] by removing sells without prior buys. Second, at the end of the year 2003, if trader i holds some shares of stock s, we added a new entry by including a fictitious transaction selling all his shares.…”

“…Even worse, there is evidence showing that analysts' stock recommendation records are intentionally rewritten to a large extent [35]. Indeed, the performance of claimed successful strategies should be tested based on the method of random strategies, that are designed to remove survival and lookahead biases [36].…”

“…In each plot, the colored symbols (black 0 for all traders, red D for winners and green + for losers) correspond to strategic trading, the continuous lines (black line for all traders, red line for winners and green line for losers) correspond to random trading, and the dashed line indicates the base line of zero return (R~0). doi:10.1371/journal.pone.0024391.g003 characteristics are kept otherwise identical [36]. According to Fig.…”

Reverse Engineering Financial Markets with Majority and Minority Games Using Genetic Algorithms

“…In order to assess the statistical significance of the obtained success rates, we compare them to those of 1,000 random strategies, obtained by predicting with equal probability 1/2 the rise or decline of each next-day market price. Using random strategies has been shown to provide the most robust estimations of the statistical significance of strategies in the presence of biases and trends (Daniel et al 2009). In Table 1, we report the p value of the 3PGs for each ABM, calculated as the fraction of random strategies that perform better.…”

Strategies Used as Spectroscopy of Financial Markets Reveal New Stylized Facts

“…Even worse, there is evidence showing that analysts' stock recommendation records are intentionally rewritten to a large extent [33]. Indeed, the performance of claimed successful strategies should be tested based on the method of random strategies, that are designed to remove survival and look-ahead biases [34].…”