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Truly, the only difference in your definitions is between ex-post and ex-ante. It’s worth noting that the Sharpe ratio is the slope of your SML. This plots expected return for a unit of volatility (risk). Ex-ante means a prediction. You predict what will happen. Your prediction for the risk free asset in this 2 variable universe MUST have zero volatility, ...


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As you correctly pointed out, all these formulae are kind of related and try to capture the same notion. The Sharpe ratio is a measure which relates (excess) return and risk (measured by volatility) and hence, gives a metric to compare different assets (may be stocks, indices, portfolios, etc). Obviously, agents prefer a high Sharpe ratio. The standard ...


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