FRM Part II · FRM Exam Part II · Liquidity and Leverage
A hedge fund has equity of $100 million and total assets of $400 million. The assets earn 6% for the year and borrowing costs 3% on the $300 million of debt. What is the return on equity, ignoring fees and taxes?
The return on equity is 15%. Assets of $400 million earn $24 million, interest on $300 million of debt costs $9 million, leaving $15 million profit on $100 million of equity, which equals 15%.
- A12.0%
- B15.0%Correct
- C9.0%
- D21.0%
Explanation
Asset income = 400 x 6% = 24. Interest = 300 x 3% = 9. Net = 15 on equity of 100, so ROE = 15%. Using the formula: 6% + (3 x (6% - 3%)) = 15%. Option 12% results from using leverage of 2 instead of 3 on the spread; 21% ignores the cost of funding on the equity multiple incorrectly (4 x 6% - 3%).
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