Credit Concentration and Economic Capital for a Regional Bank
A regional Korean bank has a corporate loan portfolio of KRW 1.2 trillion across 800 borrowers. The average one-year PD is 1.8%, average LGD is 40%, and the Basel asset correlation is 0.12. The bank uses the asymptotic single-factor model to set economic capital at a 99.9% confidence level. The top 10 borrowers represent 38% of exposure, commercial real estate is 22%, and one construction chaebol accounts for 6% of exposure. The bank's internal rating migration matrix shows that 3.5% of BBB-rated borrowers migrate to BB or below each year. A proposed KRW 60 billion loan to the chaebol would be secured by a completed office building valued at KRW 55 billion, but the bank's stress test assumes a 25% CRE price decline. The credit committee asks whether the portfolio's 99.9% worst-case default rate and economic capital are adequate, and whether the new loan should be approved.
1. Using the Vasicek one-factor formula, estimate the 99.9% worst-case default rate and the portfolio's unexpected-loss capital. State any assumptions.
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ASRF worst-case default rate: PD_99.9 = N[(N^-1(PD) + sqrt(rho) N^-1(0.999)) / sqrt(1-rho)]. With PD=0.018, N^-1(0.018) is about -2.097; N^-1(0.999) is about 3.090; sqrt(0.12)=0.346; sqrt(0.88)=0.938. Numerator = -2.097 + 0.346 x 3.090 = -2.097 + 1.070 = -1.027. Divide by 0.938 = -1.095; N(-1.095) is about 0.137, or 13.7%. Expected loss = 1.2tr x 0.018 x 0.40 = KRW 8.64bn. Unexpected-loss capital = 1.2tr x 0.40 x (0.137 - 0.018) = KRW 57.1bn. If capital covers worst-case loss rather than UL only, it is 1.2tr x 0.40 x 0.137 = KRW 65.8bn. Assumptions: one-factor, infinitely granular portfolio, constant PD/LGD, no concentration, and no correlation between PD and LGD. The last assumptions are violated here.
2. Assess the concentration risks and whether the ASRF economic capital is adequate, including the top-10, CRE, and chaebol exposures.
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The ASRF capital is not adequate for this portfolio because it assumes infinite granularity. With only 800 borrowers, top-10 exposure at 38%, CRE at 22%, and one chaebol at 6% (KRW 72bn), there is material idiosyncratic concentration. A chaebol default with 40% LGD would produce about KRW 28.8bn loss, half the ASRF UL capital, from one name. The new KRW 60bn loan would raise the chaebol to KRW 132bn, about 10.5% of the enlarged portfolio, worsening single-name concentration. The CRE stress is also severe: a 25% decline cuts the KRW 55bn collateral to KRW 41.25bn, leaving a KRW 18.75bn shortfall on a KRW 60bn loan before costs, so LGD would exceed 40%. The ASRF number should be treated as a floor, with a concentration add-on and stress testing. The 3.5% migration rate also signals rating drift risk.
3. Recommend credit risk mitigation and monitoring actions for the new loan and the portfolio.
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Do not approve the loan as proposed. Either reduce the amount to a level that keeps the chaebol below a single-name limit, require a stronger guarantee or additional collateral, or structure it as syndicated/participated. Set loan-to-value based on stressed collateral value, not current value: at KRW 41.25bn stressed value, a 60% LTV supports only KRW 24.75bn. Add covenants, cross-default, and periodic revaluation; independently appraise the building. At portfolio level, set sector limits for CRE, single-name limits, and migration triggers; run stress tests with correlated defaults and LGD downturn. Monitor the chaebol's rating, cash flow, and refinancing. If the strategic relationship justifies the loan, charge a spread that compensates for the concentration capital and require credit risk mitigation such as a guarantee. Report the concentration add-on to the credit committee.