Performance decay when testing on bootstrap data I have a strategy that has a Sharpe ratio of 1.6 when back tested over the past 10 years.  When I run this same strategy on re-sampled data, the performance of the strategy goes down to 1.32.
Should I derive the expected return from the performance of the bootstrap results?  Does the difference in performance tell me anything else?
 A: It is great that you thought to re-sample your results, both to measure variance and check robustness. A single re-sample run does not impart a whole lot of information, but given that the re-sample run yielded a Sharpe ratio of 1.3 versus the historical Sharpe of 1.6 tells you that you should expect some variation in your system’s Sharpe ratio. Personally, I would run a bootstrap of your system’s daily returns and of its trades over a minimum of 1,000 bootstrap runs and calculate a bunch of different stats for each bootstrap run. For example, I would calculate hit ratio, max drawdown, maximum adverse excursion, and some other performance statistics along with the Sharpe ratio for every bootstrap run. The 1,000 samples will give you plenty of data to construct a distribution of the statistics to help set your expectations about the trading strategy. You can also use the samples to derive an empirical p-value for your Sharpe ratio. For example, if you observed only 100 bootstrap runs with a Sharpe ratio less than 1.0, you could infer that there is a 90% probability that the system’s true Sharpe is above 1.0 (900 bootstrap runs with a Sharpe Ratio above 1.0 / 1,000 total bootstrap runs). 
Re-sampling does not protect you from overfitting. If you crank down on the parameters of your trading system when backtesting and arrive at a model that has amazing performance, its performance is going look amazing in the vast majority of re-samples. Of course, if the system derived most of its performance from a few carefully selected trades this will show up in the bootstrap because a portion of the re-samples will not contain those cherry picked trades. However, even if your system derived its entire positive performance from one trade, that one trade is going to appear in roughly 2/3s of your re-samples if you are bootstrapping with replacement. Thus, the majority of your re-samples will be tainted by overfitting. You can mitigate this problem by sampling smaller subsets (eg sampling a year’s worth of daily returns from the entire history opposed to completely resampling the whole 10 years), thereby reducing the impact of cherry picked trades and revealing more information about the system’s variance in yearly returns. 
Finally, re-sampling does not cure the fact that the future will not look exactly like the past. You may be able to set a 95% confidence interval for your system’s Sharpe ratio by re-sampling its historical returns. Nonetheless, if a particular market environment becomes more prevalent in the future than it was in the historical data, the 95% confidence interval will not accurately reflect the range of Sharpe ratios you could expect to realize. You can partially work around this limitation by overweighting the probability of selection of portions of your system’s history when re-sampling if you believe that the overweighted portions occurred in market environments that are more likely to occur in the future. This is a very useful technique for running best and worst case market environment studies for your strategy. If you believe that the next few years will be filled with a lot of market volatility you can weight time periods like 2000-2002 and 2008-2009 more heavily than periods like 2005-2006 when you run your re-sample and this should help set your expectations for your system in high volatility periods.
Great question. 
