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whether you do annual return as a geometric mean of monthly returns or as an arithmetic mean of returns - you are not going to have returns going too far off from each other.

however std dev of returns (denominator) would change.

I think that is the point of this entire statement.

-- need to be consistent in the period used.
-- do not try to forecast a bigger period's std. dev from a smaller period's. (once you did that - you would have a lower std. deviation on the bigger period).
-- and then use that new lower std. deviation in the sharpe ratio - your sharpe ratio would be overstated.

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