
Hey all, pretty basic question. I have a strategy that seems to work quite well, backtested with robust transaction cost model etc.
Naturally, the ask is to show that the equity curve is "provably uncorrelated" with 1. the market, 2. some existing return series.
Let's say the return series is daily NAV for 2500 trading days. Is this as simple as running a few regressions of the entire return series? Do I regress with or without tx costs and other implementation shortfall? Does it make sense to do some sort of bootstrapping?
I'm well capable of running regressions, and I know this may sound a bit trivial, but I really want to do this as properly as possible. 
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I would do at least:
 Scatter plot of daily/weekly/monthly returns  Rolling 1Y daily/weekly correlations 
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doomanx


Total Posts: 109 
Joined: Jul 2018 


I think as always, it depends what you're using it for. Yes, if you mention the word 'correlation' too loudly an army of angry Talebians might knock on your door tomorrow morning with pitchforks screeching about entropy at the top of their lungs.
Correlation is a meanaverage. It suffers from all the usual estimation issues that calculating meanaverages do. If the returns series exhibits very nonGaussian characteristics (which is likely to be some of our old friends skew, kurtosis, autocorrelation, heteroskedasticity, nonstationarity) then a meanaverage based metric might not capture what you're looking for (and the coefficient from univariate ols is proportional to correlation).
That being said the simplest way to do this is to fit ols and do a ttest with null hypothesis beta = 0 (again, keeping in mind all the usual issues with hypothesis testing). Unless your return series is reeeeealy weird, the results should be quite reasonable; it's pretty robust to departures from nonnormality, extreme nonstationarity might be a problem but can be handled by upsampling your returns to approximately match the regime shifts, say monthly/yearly. 
did you use VWAP or triplereinforced GAN execution?



Maggette


Total Posts: 1301 
Joined: Jun 2007 


As always I agree with doomax. The misuse of ttests and pvalues gave this approach a worse rep than it deserves. Simple ttest should do the trick under many circumstances.
AS an aside: the question you are probably asking is: does the strategy actually add value to an SP500 long only (or whatever benchmark)? And if you are scared that correlation of returns doesn't do the trick because of lacking of stationarity and correlation of different lags a simpel approach could be:
1) create a simple equally weighted portfolio of your strategy and the benchmark 2) simulated many runs of this with random entry and exit points to create random holding periods with sufficient length. 3) compare CAGR statistics (say average CAGR, median CAGR and IQR of CAGR) to the benchmark. 4) create random walk paths with mean and std of your strategy. Repeat 1)3) for them. These "strategies" are by construction a mixture of the benchmark and an uncorrelated strategy. Do they behave differently? You could do an KS tests on the returns of the generated portfolios and your portfolio
But this has no real mathematical justification and in almost all cases will give the same answer as the approach that doomax provided. So (in my experience) does fiddling around with cointegration. 
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gaj


Total Posts: 117 
Joined: Apr 2018 


do you only have the equity curve? if you could examine the portfolio, or better yet the input signals, that would provide a better answer. 




Thanks guys, very insightful. I am doing the Ttests and rolling correlations, glad to hear that it's not a terrible approach. @maggette, the adding value to the benchmark idea is cool and would play well.
@gaj, I do have the raw signals and portfolio, but because of exposure controls and such, the portfolio coming out is not as simple as top/bottom of signal. So I can do crosssectional stuff as well, just would not be fully representative of my portfolio construction process (though the raw signal does play the strongest role in determining the portfolio). 
"Nothing is more dangerous to the adventurous spirit within a man than a secure future." 
