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FRM Part II · FRM Exam Part II · Fundamentals of Credit Risk

In a Merton model, a firm has asset value of 120 million, zero-coupon debt with face value of 100 million due in one year, a risk-free rate of 5% (continuously compounded), and asset volatility of 25%. Holding other inputs constant, the firm's asset volatility rises to 35%. What is the effect on the equity value and the market value of the debt?

Equity value rises and debt value falls. Equity is a call option on firm assets, so higher asset volatility raises its value. Because asset value is fixed and equals equity plus debt, the debt value must decline by the same amount, transferring value from creditors to shareholders.

  1. AEquity value rises and debt value fallsCorrect
  2. BEquity value falls and debt value rises
  3. CBoth equity value and debt value rise
  4. DBoth equity value and debt value fall

Explanation

Equity is a call option on assets, and call value increases with volatility. Since equity plus debt equals asset value (unchanged), debt value must fall by the same amount. Shareholders gain from higher risk at the expense of debtholders.

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