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I think this is a no-brainer. Only log-returns make sense. The average return can only be computed by averaging the sum of individual log returns. Taking the average of standard (relative) returns does not give you an average of the individual returns. Consider a simple case where the value of an investment alternates between 100 and 50 an odd number of ...

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In most of the literature on the information content of various volatility estimator the relevant question is whether a particular estimator can predict (is correlated) with future realized volatility. Hence, the testing regression would be $$RV(t,T) = \alpha + \beta VOL(t) + \epsilon(t)$$ where RV(t,T) is an estimate of the realized volatility from t to ...

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Here it is: "Rebonato, R., Jackel, P. The most general methodology to create a valid correlation matrix for risk management and option pricing purposes." Recall: a covariance matrix will be the same as a correlation matrix if scale is removed. I used this method for ensuring positive definite correlations matrices.

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