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FRM Part I · FRM Exam Part I · Measures of Financial Risk

A risk manager reviews four properties that a risk measure might satisfy: monotonicity, translation invariance, positive homogeneity, and subadditivity. Which statement correctly describes what subadditivity requires of a coherent risk measure?

Subadditivity requires that the risk of a combined portfolio is no greater than the sum of the stand-alone risks of its parts. This reflects diversification: merging positions should never increase measured risk beyond the simple sum of the components.

  1. AThe risk of a combined portfolio is no greater than the sum of the risks of its componentsCorrect
  2. BDoubling a position doubles its measured risk
  3. CAdding a risk-free amount of cash to a portfolio reduces its risk by exactly that amount
  4. DA portfolio with uniformly worse outcomes in every state has higher risk

Explanation

Subadditivity means rho(X+Y) <= rho(X)+rho(Y), capturing diversification. Option B describes positive homogeneity, C translation invariance, and D monotonicity.

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