#fintwit hivemind when ya'll calc correlations between crypto (or any 7-days-a-week asset) returns and SPY, how do you handle the weekends? Impute a zero for SPY? Or impute NA for crypto? Or something else?
cc @GestaltU @alphaarchitect @choffstein @daniel_egan
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Replying to @jkregenstein @GestaltU and
So here's a thing that doesn't answer your question, but you can think of it as a jumping off point. Imagine you have two securities: A trades from t1 to t2, and B trades from t3 to t4. t3>t2 so the trading periods are disjoint.
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Replying to @AgustinLebron3 @jkregenstein and
Get daily returns for A: t2 -> t2' (where ' denotes next day) And daily returns for B: t3 -> t3'. Calculate corr.
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Replying to @AgustinLebron3 @jkregenstein and
This will be biased down because (assuming martingales) you're correlating A's t2 -> t3 return with B's "zero" (in expectation) return. Same for B's t2' -> t3 return with A's "zero" over the same time.
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Replying to @AgustinLebron3 @jkregenstein and
So, you can undo the bias by increasing the corr you calculate by the fraction of vol (of A and B) from t2 -> t3. How do you get this vol number, given you don't have a t3 snap for A and a t2 snap for B? Priors. :)
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Replying to @AgustinLebron3 @jkregenstein and
Even better, calculate the same-day covariance and the one-day-lagged covariance, add together, and divide by the square root of the product of one-day-variance.
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By “better” I mean that this will have lower standard error. Obviously both methods are unbiased estimators of correlation.
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