| Course | FIN-3820 Risk Management |
|---|---|
| Module | Module 5 |
| Paper type | Written assignment 5: credit risk |
| Length | About 645 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | B.S.B.A. in Finance |
| Updated | October 2026 |
Free sample paper for FIN 3820 Module 5
Pricing the Chance of Default: Credit Risk in a Community Bank's Commercial Loans
Student Name
B.S.B.A. in Finance, Thomas Edison State University
FIN-3820: Risk Management
Mentor Name
Month Day, Year
Pricing the Chance of Default: Credit Risk in a Community Bank's Commercial Loans
Problem 1: Default Probabilities From Spreads
Market prices contain information about default risk. If a five-year bond issued by a BBB-rated company yields 1.6 percentage points more than a Treasury of the same maturity, and investors expect to recover 40 percent of face value in a default, the implied average annual default intensity is approximately the spread divided by one minus the recovery rate (Hull, 2023): Stulz (1996) argues that a firm should manage risk to avoid financial distress, which for a bank means watching concentrations in its loan book.
λ ≈ 0.016 / (1 − 0.40) = 2.67 percent a year.
Over five years, that implies a cumulative default probability of about 1 − e^(−0.0267 × 5) = 12.5 percent. This risk-neutral estimate is typically far higher than default rates observed historically for BBB bonds, because spreads also compensate investors for bearing systematic default risk and for illiquidity. Historical rates are better for estimating actual losses; spread-based rates are better for pricing.
Problem 2: Expected Loss
Expected loss on a loan depends on three inputs: the probability of default (PD), the loss given default (LGD), the share lost after recoveries, and the exposure at default (EAD).
Expected loss = PD × LGD × EAD.
Taken as a whole, a 2 percent average PD and 45 percent LGD give $50 million × 0.02 × 0.45 = $450,000. Expected loss is a cost of doing business: the bank should cover it through loan pricing and its allowance for credit losses.
| Segment of the commercial book | EAD | PD | LGD | Expected loss |
|---|---|---|---|---|
| Owner-occupied commercial real estate | $20 million | 1.2% | 35% | $84,000 |
| Investor commercial real estate | $18 million | 2.5% | 45% | $202,500 |
| Small business lines and term loans | $12 million | 2.6% | 52% | $162,240 |
| Total | $50 million | | | about $448,700 |
Problem 3: Unexpected Loss and Concentration
Capital exists to absorb losses beyond expectations. Unexpected loss depends on how much defaults vary and, crucially, on how much they are correlated. If the bank's commercial borrowers were independent, defaults would average out; but most are in the same region and many depend on the same commercial property market, so a regional downturn would raise defaults together. Concentration in one region and one property type is the bank's largest credit risk, because it makes unexpected losses much larger than the expected loss figure suggests.
Problem 4: Merton's Structural Model
Merton (1974) treated a firm's equity as a call option on its assets, with the debt's face value as the strike: shareholders receive the assets' value above the debt at maturity and walk away if assets are worth less. Default occurs when asset value falls below debt. Using equity prices and volatility, the model infers the asset value and volatility and the "distance to default," the number of standard deviations asset value is above the default point. Commercial models built on this idea let banks track public borrowers' default risk daily. For a community bank's private small business borrowers, the model is harder to apply because they have no traded equity, so the bank relies more on financial statements, credit scores and collateral.
Problem 5: Mitigating Credit Risk
The bank can reduce credit risk through collateral and guarantees, which lower LGD; covenants and monitoring, which give early warning; diversification across industries and property types, which lowers correlation; loan participations, which sell part of large loans to other banks; and credit derivatives, though these are rarely practical at a bank this size. Its most important step is setting concentration limits by property type and borrower, as its risk appetite statement proposed.
Conclusion
Credit risk measurement separates what can be priced, expected loss, from what must be capitalized, unexpected loss. For a community bank, the size of unexpected loss depends less on individual borrowers than on how many of them share the same risks.
References
Hull, J. C. (2023). Risk management and financial institutions (6th ed.). Wiley.
Merton, R. C. (1974). On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29(2), 449-470. https://doi.org/10.1111/j.1540-6261.1974.tb03058.x
Stulz, R. M. (1996). Rethinking risk management. Journal of Applied Corporate Finance, 9(3), 8-25. https://doi.org/10.1111/j.1745-6622.1996.tb00295.x
FIN 3820 Module 5 instructions, in plain terms
Credit risk fills the fifth module. Expect problems on estimating default probabilities from ratings, historical data or bond spreads, computing expected loss from PD, LGD and EAD, distinguishing expected from unexpected loss and credit VaR and explaining structural models such as Merton's. The loan book here is a composite with illustrative parameters; your problems will supply their own. Expect probabilities of default from ratings or market data, expected loss calculations and a discussion of unexpected loss and capital. Many versions supply a small loan portfolio with ratings. Ratings-based default rates come from published agency studies.
Inside the FIN 3820 Module 5 example
Problem 1 infers a default intensity from a bond spread and explains why risk-neutral and historical probabilities differ. Problem 2 computes expected loss by segment in a table and in total. Problem 3 explains why correlation and concentration make unexpected loss the driver of capital. Problem 4 outlines Merton's model and its limits for private borrowers, and Problem 5 lists mitigation tools with the bank's most important step. A short conclusion separates what is priced from what is capitalized. Expected and unexpected losses are computed for the same portfolio so the difference between them is clear. A short paragraph explains how the bank should price for unexpected loss. Results are summarized by rating grade.
Where the marks sit in the FIN 3820 Module 5 rubric
Expected loss for the bank's commercial loans anchors the credit risk grade. Mentors look for correct default probability and expected loss calculations, a clear distinction between expected and unexpected loss and an accurate account of structural models. Knowing why default odds implied by bond prices exceed real-world odds, and why correlation drives losses on a loan book, marks a top answer. Answers that explain why spread-implied default probabilities exceed historical ones, and which to use for what purpose, show depth. Clear tables of each loan's inputs allow partial credit. Mentors also credit a comment on concentration in the portfolio. Credit risk answers that compute expected loss from probability of default, loss given default and exposure, and explain how correlation raises losses in a downturn, show the module's key ideas.
FIN 3820 Module 5 help: mistakes that cost marks
Credit risk answers lose points for treating spread-implied default rates as forecasts of actual defaults, for omitting LGD from expected loss and for discussing borrowers individually without considering correlation. Show the default intensity formula and its assumptions. Compute expected loss with all three inputs. Explain why concentration raises unexpected loss. Explain the Merton model simply, then say where it fails. A free first sample of your own FIN-3820 Module 5 problems is available on request. Show probability of default, exposure and loss given default for each loan before summing expected loss. Explain what capital is for: unexpected, not expected, loss. State the recovery rate assumed for each loan.
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FIN 3820 Module 5 questions, answered
Where can I find a free FIN 3820 Module 5 sample paper?
The community bank problem set above infers default probabilities from spreads, computes expected loss, explains unexpected loss and concentration and outlines Merton's model.
How do you calculate expected credit loss?
Multiply the probability of default by the loss given default and the exposure at default.
How are default probabilities estimated from bond spreads?
Approximately as the spread over the risk-free rate divided by one minus the expected recovery rate.
What is the difference between expected and unexpected loss?
Expected loss is the average loss, covered by pricing and reserves; unexpected loss is variation above it, covered by capital.
What is the Merton model?
A structural model that treats equity as a call option on a firm's assets and defines default as assets falling below debt.