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2010 FRM exam question 8


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The capital structure of HighGear Corp consist of two parts. one 5 yea bond with FV of $100M and the rest is equity. The current MV of the firm assets is $130 and the expected rate of change of the firm's value is 25%. The volatility is 30%. The firm's risk management division estimates the distance to default using Merton model:

[(FVB/MVa)-(m-0.5*sigma square)]*T/ (sigma * square rout of T]

Given the distance default, the estimated risk neutral default prob is?

4. 30.56%
Hi David. isn't the PD formula = [ln (V/D)+(m-0.5*sigma square)*T]/signa* square rout of T

[ln(130/100)+(.25-.5*.30'2)*5]/.30*5square rout??

The question's answer is 2.74% and I get a different answer.

Will you please help me clarify what formula we need to use?


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Sara,

This question 27 from the L2 Sample exam is discussed here @ http://www.bionicturtle.com/forum/t...risk-neutral-default-probability-credit.2158/
You are correct: the formula given is incorrect, it should be either:
  • The more typical b/c it resembles BSM d2: [LN(130/100) + (.25 - 2.5*.30^2)*5]/(.30*5) = 1.29 and PD = N(-1.29) = NORM.S.DIST(-1.29, TRUE) = 2.749%, or
  • As they meant to show: [LN(100/130) - (.25 - 2.5*.30^2)*5]/(.30*5) = -1.29 and PD = N(-1.29) = NORM.S.DIST(-1.29, TRUE) = 2.749%; equivalent because these are standardized (log) returns such that the implied distribution is symmetrically normal. I hope that helps!