Financial Risk Manager Part 1

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.