FRM Part I · FRM Exam Part I · Measuring Credit Risk
In a Merton model, the firm's asset value is 200 with asset volatility of 20%. The value of risky debt is 136, so equity is 64. At this point N(d1) is 0.80. Using the relationship between equity and asset volatility, what is the implied equity volatility?
Equity volatility is 50%. Using sigma_E times E equals N(d1) times sigma_V times V, we get 0.80 times 0.20 times 200 divided by 64, which is 32/64. The leverage effect of V/E magnifies asset volatility into higher equity volatility.
- A50.0%Correct
- B16.0%
- C23.5%
- D20.0%
Explanation
Equity is a call on assets, so sigma_E * E = N(d1) * sigma_V * V. Then sigma_E = 0.80 * 0.20 * 200 / 64 = 32/64 = 50%. The 16% option omits the leverage factor V/E; 23.5% wrongly divides by the debt value of 136.
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