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FRM Part II · FRM Exam Part II · Liquidity and Leverage

A portfolio with asset volatility of 8% is financed with equity of $50 million and total assets of $200 million. Assuming the cost of debt is fixed and risk-free, what is the volatility of the return on equity?

Equity return volatility is 32%. With fixed-cost debt, equity volatility scales with assets divided by equity, which is 4 here, so 4 times 8% asset volatility gives 32%. Using debt-to-equity of 3 would incorrectly give 24%.

  1. A8%
  2. B16%
  3. C24%
  4. D32%Correct

Explanation

Leverage ratio (assets/equity) = 200/50 = 4. With risk-free fixed-cost debt, equity volatility = 4 x 8% = 32%. Using 3 (debt/equity) gives 24%, a common error of using the debt-to-equity ratio instead of the asset-to-equity ratio.

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