FRM Part II · FRM Exam Part II · Liquidity and Leverage
A fund has equity of $100 million and borrows $150 million to hold a $250 million portfolio. The portfolio returns 6% and borrowing costs 2%. What is the return on equity?
The return on equity is 12%. The portfolio earns $15 million, interest costs $3 million, leaving $12 million on $100 million of equity. Equivalently, the unlevered 6% plus leverage of 1.5 times the 4% spread gives 12%.
- A12%
- B16%Correct
- C18%
- D10%
Explanation
Portfolio gain = 0.06 x 250 = 15.0m. Interest = 0.02 x 150 = 3.0m. Net = 12.0m on equity of 100m = 12%. Check: ROE = 6% + 1.5 x (6%-2%) = 12%. The 16% option wrongly omits nothing useful: it is not derived from the correct net gain; 18% ignores interest costs on borrowing.
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