The Correlation Assumption in a Concentrated Portfolio
A specialty lender holds a $1.2 billion portfolio of loans to independent hotels in three coastal resort markets. Historically, defaults in the portfolio were treated as largely independent because the borrowers are unrelated family businesses with no common ownership. The risk team's economic-capital model assumes a pairwise default correlation of 0.08, calibrated on twelve years of data that included no major demand shock. A new analyst observes that all three markets depend on the same airline routes, the same seasonal weather window, and the same two online travel platforms, and that the twelve-year window contained no period when all three markets were simultaneously stressed. She proposes raising the correlation assumption to 0.30. The head of credit argues this would cut the lending capacity of the business by a third and that the historical data do not support such a change. The chief risk officer must decide what to recommend to the asset-liability committee, which sets the capital buffer.
1. Evaluate the disagreement. Whose reasoning is stronger, and what does the twelve-year calibration window tell you about the reliability of the 0.08 estimate?
Read the worked answer
The analyst's reasoning is stronger, and the key issue is not which number is right but what the historical estimate can actually support.
A correlation estimated on a window with no simultaneous stress is estimated precisely where it matters least. Correlation is not a stable parameter: in normal times, defaults are driven by idiosyncratic borrower factors and measured correlation is low; in a systemic demand shock, a common factor dominates and realized correlation rises toward one. The 0.08 figure therefore describes the benign regime and is close to uninformative about the tail. The twelve-year window is not a sample of the relevant states of the world; it is a sample that excludes them.
The head of credit's argument inverts the burden of proof. The absence of a joint stress in the window is not evidence that joint stress is unlikely; with three markets sharing airline routes, a seasonal window, and two distribution platforms, the common factors are identifiable and structural. The borrowers being unrelated family businesses addresses idiosyncratic correlation, not common-factor correlation. Unrelated owners can still default together when the same airline cuts the route.
The capacity argument is real but is a consequence, not a refutation. If a third of lending capacity depends on assuming 0.08, the business model is levered to a correlation assumption that the data cannot defend, and that is exactly what the committee needs to know. The CRO should not frame this as a choice between 0.08 and 0.30 as if both were equally evidenced. The defensible position is that 0.08 is unsupported for capital purposes, that 0.30 is a judgement anchored in the identified common factors rather than a fitted estimate, and that the committee should adopt a stressed correlation for capital while tracking the fitted value for monitoring.
2. Recommend how the CRO should present the choice to the asset-liability committee, including what sensitivity analysis would make the decision well informed.
Read the worked answer
The CRO should present the decision as a choice under uncertainty with quantified consequences, not as a technical dispute between two staff members.
Frame the question correctly. The committee is not choosing the true correlation; it is choosing the assumption used to size a buffer against a tail event. That framing makes clear why the benign-period estimate is the wrong input for a capital buffer even if it is the right input for pricing in normal conditions.
Show the sensitivity surface. Present economic capital and the resulting buffer across a range of correlations, for example 0.08, 0.15, 0.30, and 0.50, holding everything else constant. The committee should see the shape of the curve, not two endpoints. If capital is highly sensitive between 0.15 and 0.30, the choice of point estimate matters more than the debate suggests and warrants conservatism.
Stress the common factors directly. Rather than arguing about the correlation parameter, run a scenario in which one airline route is cut and one travel platform changes its commission structure in the same season. Show expected losses and capital consumption under that scenario. This is more persuasive to a committee than an abstract parameter, because it makes the common factor concrete.
Separate the decisions. Recommend a stressed correlation for capital adequacy and retain the fitted value for performance monitoring and pricing, with a documented rationale for the difference. This avoids pretending one number serves both purposes.
Be explicit about the cost. State the reduction in lending capacity and the alternatives: hold the buffer and accept lower volume, reduce concentration by entering a market with different common factors, or transfer risk through participation or insurance. The committee should choose among these with the capital consequence of each in front of it.
Record the judgement. Minute that the historical estimate was not relied on for capital because the window contained no joint stress, and that the stressed assumption is a deliberate conservatism. That minute protects the committee if the tail event occurs.