Financial Risk Manager Part 2

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Explanation:

A is correct. Distance to Default (DtD) approximates the number of standard deviations to reach the default threshold; thus, the higher the DtD, the least likely to default.

DtD = \frac{\ln V_a - \ln F + \left(\mu - \frac{\sigma_a^2}{2}\right)(t)}{\sigma_a \sqrt{t}}

DtD can be simplified by reducing the forward time periods to 1 (t=1) and minimizing the drift factors $(\mu - \sigma^2/2)$ that tend to be small (assumed to equal 0) over one period to yield:

DtD \cong \frac{\ln V_a - \ln F}{\sigma_a}

Using this formula results in:
DtD for Company P = $\ln(100/60)/0.10 = 5.11$
DtD for Company Q = $\ln(150/100)/0.07 = 5.79$
DtD for Company R = $\ln(250/160)/0.08 = 5.58$
Q is least likely to default; R is in the middle; P is most likely to default.

Learning Objective Calculate distance to default and default probability using the Merton model.

Reference John C. Hull, Risk Management and Financial Institutions (Sixth Edition, John Wiley & Sons, 2023). Chapter 17. Estimating Default Probabilities.

Explanation:

A is correct. Distance to Default (DtD) approximates the number of standard deviations to reach the default threshold; thus, the higher the DtD, the least likely to default.

DtD = \frac{\ln V_a - \ln F + \left(\mu - \frac{\sigma_a^2}{2}\right)(t)}{\sigma_a \sqrt{t}}

DtD can be simplified by reducing the forward time periods to 1 (t=1) and minimizing the drift factors $(\mu - \sigma^2/2)$ that tend to be small (assumed to equal 0) over one period to yield:

DtD \cong \frac{\ln V_a - \ln F}{\sigma_a}

Learning Objective Calculate distance to default and default probability using the Merton model.

Reference John C. Hull, Risk Management and Financial Institutions (Sixth Edition, John Wiley & Sons, 2023). Chapter 17. Estimating Default Probabilities.

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Question A credit manager in the counterparty risk division of a large bank uses a simplified version of the Merton model to monitor the relative vulnerability of its largest counterparties to changes in their valuation and financial conditions. To assess the risk of default of three particular counterparties, the manager calculates the distance to default assuming a 1-year horizon (t=1). The counterparties: Company P, Company Q, and Company R, belong to the same industry, and are non-dividend-paying firms. Selected information on the companies is provided in the table below:

Company P Q R
Market value of assets (EUR million) 100 150 250
Face value of debt (EUR million) 60 100 160
Annual volatility of asset values 10.0% 7.0% 8.0%

Using the information above with the assumption that a zero-coupon bond maturing in 1 year is the only liability for each company, and the approximation formula of the distance to default, what is the correct ranking of the counterparties, from most likely to least likely to default?

Company	P	Q	R
Market value of assets (EUR million)	100	150	250
Face value of debt (EUR million)	60	100	160
Annual volatility of asset values	10.0%	7.0%	8.0%

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Last updated: July 5, 2026 at 07:29

P; R; Q

Q; P; R

Q; R; P

R; Q; P