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The correct answer has some intuition though it doesn't generalize to continuous time very easily: Think about the paper below like this: $Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)$ The generalization is slightly hard because the dynamics of $\mu$ and $\sigma^2$ could be dependent for arbitrary returns. You can use a GMM estimator to derive the asymptotic ...

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There are sufficiently different ways to calculate the Sharpe ratio that the best advice I can give is to do whatever your boss wants. Also, if it is for a paper or research document, just make clear you document your method. My approach is usually to calculate the highest frequency Sharpe ratio I can based on the data. The higher frequency choice is to get ...

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The answer is that it depends. In addition to the Lo paper above, there are a number of excellent references that go into depth about annualizing or time scaling non-i.i.d. returns, one of which is Roger Kauffman, "Long-Term Risk Management", 2005 which can be found at http://www.rogerkaufmann.ch/all-Budapest.pdf. There are some well known cases where the ...

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In your question you do not provide any reference. I believe that we are in front of two possibilities: annualized linear returns and Compound Annual Growth Rate (CAGR). If compounding is not mentioned, I would assume annualized linear returns. $n$-years Annualized linear returns $n$ = number of years $n * r_A = r_*$, where $r_*$ is the return over the ...

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Here is an example calculation according to the formula by William F. Sharpe, 1994. The OP's method of annualising the variance (as used below), is also specified by the Committee of European Securities Regulators in this document, page 5, box 1. For this example, taking 24 months of returns of risk-free proxy (US 4-week T-bills) and an example stock, (and ...

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