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FRM Part II · FRM Exam Part II · Portfolio Risk: Analytical Methods

A risk manager reviews a portfolio that is optimal in the mean-variance sense. Which condition must hold for every asset in the portfolio at the optimum?

At the optimum, every asset must have the same ratio of excess return to marginal contribution to risk (equivalently, excess return proportional to beta against the portfolio). If ratios differed, shifting weight toward the higher ratio asset would raise the Sharpe ratio.

  1. AEach asset has the same standalone volatility
  2. BEach asset has the same ratio of excess return to marginal contribution to riskCorrect
  3. CEach asset contributes an equal dollar amount of VaR
  4. DEach asset has a zero correlation with the portfolio

Explanation

At an optimum, the marginal gain in expected excess return per unit of marginal risk is equal across all assets, otherwise shifting weight would improve the Sharpe ratio. Equal risk contributions or equal volatilities are risk-parity features, not optimality conditions.

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