Answer: Sharpe ratio

### Answer **C — Sharpe ratio** ### What Sharpe measures (and formula) Sharpe = (Rp − Rf) / σp - Rp = portfolio return, Rf = risk‑free rate, σp = standard deviation of portfolio returns. - It measures excess return per unit of *total risk* (standard deviation), so it includes both systematic and idiosyncratic volatility. ### Quick numeric example If Rp = 12%, Rf = 2%, and σp = 10%: Sharpe = (0.12 − 0.02) / 0.10 = 1.0 → one unit of excess return per unit of total volatility (a good result). ### Why the other choices are wrong - Jensen’s alpha: alpha = Rp − [Rf + βp (Rm − Rf)]. This gives an absolute abnormal return relative to CAPM, not a “per unit of total risk” ratio. - Treynor ratio: Treynor = (Rp − Rf) / βp. Denominator is beta (systematic risk) only, so it measures reward per unit of market risk — appropriate when portfolios are well diversified and idiosyncratic risk is negligible. - Sortino ratio: Sortino = (Rp − Rf) / downside deviation. It focuses only on harmful (downside) volatility, not total volatility. ### When to use each - Use Sharpe when you care about all volatility (undiversified portfolios, absolute comparisons). - Use Treynor for well‑diversified portfolios where only market risk matters. - Use Sortino when downside risk matters more than upside variability. - Use Jensen’s alpha to test manager skill vs CAPM expectations. Think critically: choose the metric that matches your risk definition—total, downside, or just systematic—because each answers a different practical question.

Author: Tanishq Prabhu