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The formula you came up with doesn't appear to account for the riskless asset. isn't the maximum Sharpe ratio portfolio $\boldsymbol{\omega}= \frac{\mathbf{\Sigma}^{-1}(\boldsymbol{\mu}-r_f\cdot \boldsymbol{\iota}_N)}{{\boldsymbol{\iota}_N\mathbf{\Sigma}}^{-1}(\boldsymbol{\mu}-r_f\cdot \boldsymbol{\iota}_N)}$ because the Sharpe ratio is $\frac{\boldsymbol{\...


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Link to discussion in the other thread notwithstanding, calculating Sharpe ratio using arithmetic return is more 'classic' than using geometric return. To start, Sharpe himself used arithmetic returns in ex-post calculation in his originating paper (JPM, 1964). Most texts also use arithmetic return, among them Grinold and Kahn and Christopherson, Carino, ...


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The Geometric Sharpe ratio is the geometric average of compounded excess returns divided by the standard deviation of those compounded returns. This is equivalent to the arithmetic average and standard deviation of log(1+rt). Geometric returns should be the preferred way of calculating returns over a time series. In any case, Should I use an arithmetic or ...


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