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I hear many quants sating that markets change very slowly. This "fact" is even presented as a justification of statistical arbitrage, for example, by affirming that correlations remain roughly the same for long periods, and then insight given by these correlations or by a PCA applied on the correlation matrix is valid through time.

My question is : indeed, correlation matrix does not change on a daily basis, but isn't that due to an estimation bias? When the estimation is based on last 250 days for example, any new day contribution is very small and does not dramatically change the estimator, and real correlation may be much more stochastic than the stable matrix estimated.

If this is the case, how come this artificially stable correlation matrix can give profitable trading strategies relying on it?

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One easy way to cross-check that is to compute option implied correlations. Those correlations are model free and only depend on the current day option prices and they are indeed stable.

For a nice article on computing option implied correlations check Vilkov's website he has several articles discussing option implied correlations. http://www.vilkov.net/www/content/research

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  • $\begingroup$ Those implied correlation are stable just because all banks estimate correlation in the same manner and inject the same figures in the same models. We are in a circular problem with implied correlation. My question deals with correlation of actual time series of prices. $\endgroup$ – volatile Jul 27 '15 at 2:23
  • $\begingroup$ This has nothing to do with banks. These are correlations implied by the options market, in which all people can trade. There is no circularity whatsoever because this calculations are $model-free$ ! They do not depend on any model!! $\endgroup$ – phdstudent Jul 27 '15 at 8:04

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