Bootstrapping data for two variables

Question

I've been back-testing a trading system that balances a portfolio between the S&P (via SPY) and 20-year Treasury bonds (via TLT). Through data mining, I've been able to identify a trading strategy that produces a Sharpe ratio of 2.06 over a 6-year back-test.

I'm now trying to test my strategy against bootstrapped data as I'm concerned about the data mining bias that likely exists. To start, I'm calculating the daily % change of each ETF and re-sampling to reconstruct new prices to run my strategy against.

My question is should I re-sample each ETF independently of the other? Meaning, do I re-sample the distribution of SPY and then re-sample the distribution of TLT ignoring how each moved in relation to the other on a given day? Or should I force the re-sample to maintain the correlation by following the re-sampled order for each bootstrap test?

I hope this makes sense!

Thanks, Julia

Answer 1

It depends on the intended purpose of the bootstrap tests. If you are trying to get a feel for how the strategy might perform in the future I'd argue that you should attempt to maintain any correlation between the two series, the reason being that there are fundamental factors which link the two; in times of crisis there is a "flight to safety" from stocks to treasuries, which implies that stocks will decrease as treasuries increase in value. Similarly, as opportunity is perceived to be present in stocks money will rotate out of treasuries into stocks and imply the opposite relationship. Any bootstrap tests for future performance should attempt to preserve this phenomena as there is no reason to believe it will cease to exist in the near future.

However, you may also wish to posit the hypothesis that your system attempts to capture and benefit from the movements described above, and you want to test whether this is a real effect or whether you're just fooling yourself. In this case you might sample independently to get a null hypothesis distribution for the null hypothesis that your system does not exploit this phenomena, because independent sampling destroys any correlation that exists except for that which exists by chance.

If your "real" results are significantly better, in a p-value sense, than the results of your system on this null hypothesis distribution you can reject the null hypothesis and accept that your system successfully exploits a real market edge. If this is so, the first set of tests can then be used to project likely future performance(s) of the system.