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# 2010 FRM exam question 8

#### saritay

##### New Member
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?

a)2.74%
2)12.78%
3)12.79%
4. 30.56%
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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?

Best,
Sara

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
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!