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

A portfolio earns an unlevered return of 3%, below the 4% cost of borrowing. If the manager increases leverage (assets/equity) from 2 to 3, what happens to the return on equity?

Return on equity falls from 2% to 1%. When the asset return of 3% is below the 4% borrowing cost, the spread is negative, so more leverage magnifies the shortfall: 3% minus 1% is 2% at leverage 2, and 3% minus 2% is 1% at leverage 3.

  1. AIt rises from 2% to 1%
  2. BIt falls from 2% to 1%Correct
  3. CIt rises from 3% to 4%
  4. DIt remains 3% because asset return is unchanged

Explanation

ROE = r + (D/E)(r - c). At leverage 2, D/E = 1: 3% + 1 x (-1%) = 2%. At leverage 3, D/E = 2: 3% - 2% = 1%. Leverage magnifies a negative spread, so the first option's direction is wrong.

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