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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 ...

4

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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I can only repeat myself because your mentioned previously asked question is essentially identical: => I would say do not include non-trading days, do not include days with zero position, do not include days where the asset did not trade for whatever other reason. Here some reasons and pointers: Sharpe measures excess returns scaled by volatility. The ...

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I do not have access to the exact time-series of the MSCI world, but looking at the returns from the tracking ETF, since 2001 the average return is negative. Thus regardless of the risk-free you use you will get a negative sharpe ratio.

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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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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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The annuity expression $a_{4}^{(12)}$is written as: $$a_{4}^{(12)}= \frac{1-(1+i)^{-4}}{i^{(12)}} = \frac{i}{i^{(12)}} a_4$$ where, $i$ is the effective annual rate of interest and $i^{(12)}$ is nominal rate of interest convertible monthly, which is equal to $$i^{(12)}=12((1+i)^{1/12}-1)$$ There is no closed formula to get the interest rate, you have to ...

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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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I'm currently also using daily returns which I want to annualize. This is my approach: For every month, I calculate the simple return using the formula: (end-of-month closing price / beginning-of-month closing price) - 1. I use the Excel formula somproduct(geomean(A1:A12+1)-1) to find the monthly compounded return. Finally, I annualize the result of step 2 ...

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If you assume that your monthly returns are independent from each other, then the annualized variance of each series, and the covariance can be annualized. This assumption allows you to use V(x1+X2+...+x12) = V(x1) + V(x2) + ... + V(x12) where xi is the return for the month "i". Actually, for this to happen you only need a weaker assumption: that is that ...

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