[ 2009 FRM Sample Exam ] Quantitative Analysis Q14

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14. Firm A has equity volatility of .3 and debt to firm value (debt to capitalization) of .4. Firm B has the same debt to firm value but its asset volatility is .3. Which statement about firms A and B is true?

A. The capital of Firm A is less than the leverage of Firm B.

B. The volatility of Firm A's operations is greater than the volatility of Firm B's operations.

C. The equity of Firm B is less risky than the equity of Firm A

D. The equity of Firm A is less risky than the equity of Firm B

lalamei

 

Correct answer is Dfficeffice" />

A is incorrect because the two firms have the same capital ratio, so they have the same capital if they have the same assets.  As no mention was made of asset size, it could go either way.

B is incorrect Firm A actually has the lower asset volatility and the opposite of the sentence is true.

C is incorrect.  We know that asset volatility is smaller than equity volatility holding constant leverage, so A has the lower asset volatility.  This answer implies its asset volatility is higher.

D is correct.  See C for the explanation.

Reference: Stulz, Risk Management and Derivatives, Chapter 18