Financial Risk Manager Part 1

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Explanation:

Explanation

D is correct. The correlation between each pair of $U_i$ distributions is equal to $a^2$ .

Why other options are incorrect:

A is incorrect: The default probabilities are each mapped to the standard normally distributed variable $U_i$ , however, values in the extreme left tail represent default. As such, low values of $F$ or $Z_i$ correspond with a higher likelihood of default.
B is incorrect: High values of $F$ indicate a strong economy, and low values of $F$ indicate a weak economy. As such, low values of $F$ correspond with a higher likelihood of default.
C is incorrect: $F$ is a common factor and is equal for all loans in the portfolio. It does not vary based on the cyclical nature of individual companies' businesses.

Key Concepts

The Vasicek model uses the equation: $U_i = aF + \sqrt{1 - a^2} Z_i$

Where:

$U_i$ represents the asset value of firm i
$F$ is the common systematic factor
$Z_i$ is the idiosyncratic factor
$a$ is the factor loading that determines the correlation between firms

The correlation between any two firms' asset values is $a^2$ , making the coefficient $a$ directly related to the default correlations in the portfolio.

Explanation:

Explanation

D is correct. The correlation between each pair of $U_i$ distributions is equal to $a^2$ .

Why other options are incorrect:

A is incorrect: The default probabilities are each mapped to the standard normally distributed variable $U_i$ , however, values in the extreme left tail represent default. As such, low values of $F$ or $Z_i$ correspond with a higher likelihood of default.
B is incorrect: High values of $F$ indicate a strong economy, and low values of $F$ indicate a weak economy. As such, low values of $F$ correspond with a higher likelihood of default.
C is incorrect: $F$ is a common factor and is equal for all loans in the portfolio. It does not vary based on the cyclical nature of individual companies' businesses.

Key Concepts

The Vasicek model uses the equation: $U_i = aF + \sqrt{1 - a^2} Z_i$

Where:

$U_i$ represents the asset value of firm i
$F$ is the common systematic factor
$Z_i$ is the idiosyncratic factor
$a$ is the factor loading that determines the correlation between firms

The correlation between any two firms' asset values is $a^2$ , making the coefficient $a$ directly related to the default correlations in the portfolio.

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Question 38

A junior analyst at a banking supervisory agency is taking an internal training class on the Vasicek model. The analyst reviews the following equations related to the model:
$U_i = aF + \sqrt{1 - a^2} Z_i$ $\text{Default rate as a function of } F = N \left( \frac{N^{-1}(PD) - aF}{\sqrt{1 - a^2}} \right)$
Which of the following statements regarding the Vasicek model is correct?

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Last updated: May 8, 2026 at 15:12

-1

The default probabilities of the individual loans in a portfolio are each mapped to the standard normal distribution $U_i$ of which values in the extreme right tail represent default.

15.4%

A low value of the factor $F$ indicates that the economy is strong, while a high value of $F$ represents economic weakness.

19.2%

For corporate borrowers, the value of the factor $F$ is higher for loans to companies with more cyclical businesses.

11.5%

The model coefficient $a$ directly relates to the correlations between the default probability distributions $U_i$ of the loans in the portfolio.

53.8%