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Merton model valuation

evelyn.peng

Active Member
Hi,
I have a practice question (non-BT) related to the use of Merton's debt valuation model.

An investor has a large position of bonds issued by XYZ Limited. He has hedged these bonds with equity using Merton’s debt valuation model. Suppose the value takes an unprecedented tumble, but the value of equity remains stable: the investor would make a loss.
Consider the following statements:
I. A liquidity crisis, similar to the one experienced in 2008, increased the liquidity component of credit spreads
II. Risk-free rate of interest fell
III. Risk-free rate of interest increased
IV. Volatility fell
V. Volatility increased


Which of the statements above would explain why the investor’s hedge strategy failed?
A. I and V
B. II and IV
C. I, II, and IV
D. III and V ----- Correct answer according to the answer key


My solution:

the investor is long debt, and short equity.
Equity = call option
Debt value = Face Value of Debt - Put on the Asset
if risk free rate increase, it would slightly increase the value of the call/equity. It would decrease the value of the Debt.
If the volatility increased, it would increase the value of the call/equity, and increase the value of the put option, so decrease the value of the debt.

Conversely if risk free rate decreased, it would slightly decrease the value of the call/equity. It would increase the value of the Debt - which contradicts case facts.
Same thing for the volatility decrease, it would decrease the value of the call/equity, and decrease the value of the put option, and increase the value of the debt - again contracting case facts.

Statement #I doesn't factor into anything.
So the only logical answer is III and V. However, I feel like the wording of the question is flawed. The hedge did not fail per se, as the equity and debt valuation were somewhat offsetting each other. Just wondered if anyone else have any thoughts on this question?
 
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