BANK3011 · Bank Financial Management
Credit Risk II: Loan Portfolio & Concentration Risk
Credit Risk II in BANK3011 Bank Financial Management at the University of Sydney moves from pricing a single loan to managing the whole loan book, where the real danger is concentration risk — too much exposure to one borrower, industry or region that a common shock can default all at once. Banks control it with two tools, concentration limits (a cap on exposure driven by the maximum tolerable loss and a sector's loss rate) and migration analysis (watching loans drift through a one-year rating transition matrix), and they measure the payoff from spreading risk with Modern Portfolio Theory and the Moody's KMV Portfolio Manager model. The single idea underneath everything is that a default correlation below 1 lets a bank hold the same expected return at lower risk — so the exam rewards keeping the covariance cross-terms in the portfolio-variance formula and stating that diversification fails when ρ = +1.
What this chapter covers
- 011. Concentration risk — why a loan book's real threat is correlated default, not any single borrower
- 022. Concentration limits — capping exposure at (maximum loss %) × (1 / loss rate), where loss rate = 1 − recovery
- 033. Rearranging the limit — the mirror form, maximum loss % = concentration limit × loss rate
- 044. Migration analysis — tracking loans by grade through a one-year rating transition matrix (rows sum to 1)
- 055. Modern Portfolio Theory for loans — portfolio return as the weighted average, R_p = Σ X_i·R_i
- 066. Portfolio variance — own-variance terms plus the covariance cross-terms that carry default correlation
- 077. Diversification and the minimum-risk portfolio — why ρ < 1 lowers risk and ρ = +1 removes the benefit
- 088. Moody's KMV Portfolio Manager — the three inputs R_i, σ_i and ρ_ij, and the loan efficient frontier
Two-loan portfolio: expected return, risk and the diversification benefit
- +1Weights: because the two loans are equal in size, X_A = X_B = 50,000 / 100,000 = 0.5.
- +1Portfolio return: E(R_p) = Σ X_i·R_i = 0.5(7%) + 0.5(11%) = 9%.
- +1Variance formula: σ_p² = X_A²σ_A² + X_B²σ_B² + 2·X_A·X_B·ρ·σ_A·σ_B (keep the last, covariance, term).
- +1Own-variance terms: 0.25(0.09²) + 0.25(0.15²) = 0.002025 + 0.005625 = 0.00765.
- +1Covariance cross-term: 2(0.5)(0.5)(0.25)(0.09)(0.15) = 0.0016875.
- +1Sum: σ_p² = 0.00765 + 0.0016875 = 0.0093375.
- +1Standard deviation: σ_p = √0.0093375 = 9.66%.
- +1Compare: the weighted-average σ is 0.5(9%) + 0.5(15%) = 12%, so σ_p of 9.66% < 12% — diversification has helped because ρ < 1.
Key terms
- Concentration risk
- The risk that a loan book is too exposed to one borrower, industry or region, so a single common shock defaults many loans together; it is the portfolio-level counterpart to individual credit risk.
- Concentration limit
- The largest share of capital a bank will expose to one borrower or sector: (maximum acceptable loss as % of capital) × (1 / loss rate). A higher loss rate forces a tighter limit.
- Loss rate
- The fraction of an exposure actually lost when a borrower defaults, equal to 1 − recovery rate; it is the sector-specific input that scales a concentration limit.
- Migration (transition) analysis
- Tracking loans by credit grade through a one-year rating transition matrix; if a sector downgrades faster than its historical experience, the bank curtails new lending to it.
- Default correlation (ρ)
- How strongly two borrowers tend to default together. Diversification lowers portfolio variance only when ρ < 1; at ρ = +1 the loans move in lockstep and no benefit remains.
- Minimum-risk portfolio
- The mix of loans that gives the lowest possible portfolio standard deviation for a target return — the left-most point of the achievable risk-return set.
- Moody's KMV Portfolio Manager
- A model that applies mean-variance optimisation to a loan book using three inputs per loan: expected return R_i, risk σ_i and default correlation ρ_ij with every other loan.
- Loan-volume (benchmark-deviation) model
- A partial-MPT tool that scores how far a bank's sector allocation deviates from the national or market benchmark, flagging concentration without needing a full correlation matrix.
Credit Risk II: Loan Portfolio & Concentration Risk FAQ
Can AI help me with loan portfolio and concentration risk?
Yes — ask Sia to walk through any loan portfolio and concentration risk problem or concept step by step, the way University of Sydney tests it. It explains the working — for example how to keep the covariance cross-term in a portfolio-variance calculation, or how to rearrange a concentration limit — so you learn the method rather than being handed an answer.
What is the difference between concentration limits and migration analysis?
Both control portfolio credit risk, but they work differently. A concentration limit is a hard cap: it fixes the maximum exposure to a borrower or sector as (maximum tolerable loss %) × (1 / loss rate). Migration analysis is a forward-looking monitor: it tracks how loans move between rating grades through a transition matrix and warns you to curtail a sector that is downgrading faster than its historical experience. In the exam, the tool described as forward-looking is migration analysis, because it reacts to fresh downgrade data rather than a fixed policy percentage.
Why doesn't diversification reduce risk when default correlation is 1?
Diversification works by shrinking the covariance cross-terms in the portfolio-variance formula, and those terms carry the default correlation ρ. When ρ < 1 the loans do not default in perfect step, so the combined risk falls below the weighted average of the individual risks. When ρ = +1 the cross-term is maximal and the portfolio standard deviation collapses back to the full weighted average — there is no benefit at all. That is why the marks reward stating the ρ < 1 condition explicitly whenever you claim diversification has helped.
How do I calculate the risk of a two-loan portfolio?
Use σ_p² = X_A²σ_A² + X_B²σ_B² + 2·X_A·X_B·ρ·σ_A·σ_B, then take one square root at the end. The two most common slips are forgetting to square the weights (it is X_i², not X_i) and dropping the final covariance term, which erases the entire diversification benefit. The portfolio return is simpler — just the weighted average, E(R_p) = Σ X_i·R_i. Work through the fully solved example above, then ask Sia to generate a fresh set of numbers and check your method step by step.
What three inputs does the Moody's KMV Portfolio Manager model need?
For every loan i it needs an expected return R_i = AIS_i − EDF_i·LGD_i (all-in spread minus expected loss), a risk σ_i = √[EDF_i(1 − EDF_i)] × LGD_i, and the default correlation ρ_ij with every other loan. With those, KMV traces a Markowitz-style efficient frontier of return versus risk and helps a bank rebalance toward it — same expected return, lower risk — by favouring exposures with low or negative default correlation. A common trap is confusing EDF (the probability of default) with LGD (the severity of loss), so keep those two roles straight.
Is loan portfolio and concentration risk examinable in BANK3011?
Yes. Portfolio and concentration risk is the Chapter 11 material taught in the middle of the semester, and it typically appears in the final exam as a short numerical problem — a concentration-limit calculation or a two-loan portfolio return-and-risk — plus a conceptual short-answer on why diversification needs imperfect correlation. The concentration-limit and portfolio-variance formulas are on the provided formula sheet, so the marks are in setting them up cleanly and interpreting the result. Confirm the current exam format on Canvas, as weightings can change from year to year.
Studying with AI? Sia — free AI financial modeling tutor works through BANK3011 step by step.
Exam move
Treat this topic as three linked ideas rather than a pile of formulas. First, lock down the two control tools: a concentration limit is a hard cap, (maximum loss %) × (1 / loss rate) with loss rate = 1 − recovery, and you must be able to rearrange it to maximum loss % = limit × loss rate; migration analysis is the forward-looking monitor that reacts to a sector downgrading faster than history. Second, drill the portfolio maths until the setup is automatic — the weighted-average return E(R_p) = Σ X_i·R_i, and the variance σ_p² = Σ X_i²σ_i² + covariance cross-terms — practising until you never drop the cross-term or forget to square the weights. Third, be ready to explain the intuition: diversification lowers risk only when default correlation is below 1, it drives portfolio risk toward a systematic floor it cannot cross, and it delivers nothing at ρ = +1. Rework the tutorial and end-of-chapter Saunders & Cornett problems, keep the provided formula sheet beside you so you learn where each formula lives, and during the revision week sit any past questions you can find under timed conditions. When a step will not click, ask Sia to explain it the way University of Sydney marks it, then redo a fresh version on your own.
