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The KMV model measures the normalized "distance from default". How is this defined?

A) (Expected Assets - Weighted Debt) / (Volatility of assets)

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B) Equity/ (Volatility of equity)

C) Probability of stock price falling below a threshold

D) Leverage x Stock Price Volatility

答案：A

解析：The distance to default is defined as (Expected Assets - weighted debt)/(Volatility of assets). It is a normalized measure of default and therefore may be used for comparing one company to another. It does not tell you the probability of default.

In order to extend this measure to a probability of default, KMV uses historical default rates to determine an expected default frequency as a function of the distance to default.

Suppose a firm has two debt issues outstanding. One is a senior debt issue that matures in three years with a principal amount of $100 million. The other is a subordinate debt issue that also matures in three years with a principal amount of $50 million. The annual interest rate is 5% and the volatility of the firm value is estimated to be 15%. If the volatility of the firm value declines in the Merton model then which of the following statements is true?

A) If the firm is experiencing financial distress (low firm value), then the value of senior debt will increase while the values of subordinate debt and equity will both decline.

B) If the firm is not experiencing financial distress (high firm value), then the value of senior debt and subordinate debt and equity will increase.

C) If the firm is experiencing financial distress (low firm value), then the value of senior debt and subordinate debt will increase while equity values will declines.

D) If the firm is not experiencing financial distress (high firm value), then the value of senior debt will increase while the values of subordinate debt and equity will both decline.扫码咨询，立享优惠

答案：A

解析：When firms with subordinate debt are experiencing financial distress (low firm values), changes in the value of subordinate will react to changes in the model parameters in the same way as equity. Since equity is valued as a call option in the Merton model, a decline in volatility will reduce the value of equity (and subordinate debt).

When firms with subordinate debt are not experiencing financial distress (high firm values), changes in the value of subordinate will react to changes in the model parameters in the same way as senior debt. Since senior debt is valued as the difference in firm value less equity valued as a call option in the Merton model, a decline in volatility will increase the value of senior debt (and subordinate debt).

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