Sharpe Ratio
Excess return per unit of total risk — (portfolio return − risk-free rate) divided by standard deviation.
The exam usually hands you a return, a risk-free rate, and a standard deviation and asks you to compute the slope of the capital allocation line — because the Sharpe ratio is the slope of any portfolio’s CAL, and the steepest CAL belongs to the optimal risky (tangency) portfolio. The classic “tell” is being given beta alongside standard deviation: that beta is a distractor steering you toward Treynor, so confirm whether the question wants total risk (use the standard deviation, pick Sharpe) before plugging in.
The trap students fall for is ranking with negative Sharpe ratios: when excess return is negative, a larger standard deviation makes the ratio look less negative, so the ordinary “higher is better” rule produces backwards, meaningless comparisons (M-squared sidesteps this — it scales the portfolio to market volatility and expresses the result as a percentage return). Don’t confuse Sharpe with the information ratio, which divides active return by tracking error against a benchmark, not excess return by total volatility. Memory hook: Sharpe = “Slope” — both start with S, and it’s literally the CAL’s slope.
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