$$\begin{aligned} Sharpe\;Ratio &= \left[ Expected\;Return\;-\;Risk\;Free\;Rate\over Standard\;Deviation\;of\;Excess\;Return \right] \\\\\\\ &= \left[ Risk\;Premium\over Standard\;Deviation\;of\;Excess\;Return \right] \\\\\\\ &= \left [E(r_i)\;-\;r_f \over \sigma_i \right]\end{aligned}$$
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