Comparing Three Retail Loan Products on Risk-Adjusted Return
A branch is reviewing three retail loan products for the next quarter. Product X has an expected gross yield of 11.0%, a probability of default of 2.5% and an expected recovery of 40% of defaulted exposure. Product Y yields 13.0%, has a 4.0% default probability and 25% recovery. Product Z yields 9.5%, has a 1.0% default probability and 60% recovery. Operating cost is 1.2% of exposure for each product. For regulatory capital, X carries a 100% risk weight, Y 150% and Z 75%; the bank must hold capital equal to 12% of risk-weighted assets. The branch has room to grow only one product by ₹5 crore and wants the best risk-adjusted return, not just the highest yield. The credit head asks you to compare the products on expected net yield and return on regulatory capital, and to recommend one with a caveat.
1. Compute the expected net yield per ₹100 of exposure for each product.
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Use expected loss rate = probability of default × (1 − recovery). For X, expected loss = 2.5% × 60% = 1.5%. Net yield = 11.0 − 1.5 − 1.2 = 8.3%, or ₹8.30 per ₹100. For Y, expected loss = 4.0% × 75% = 3.0%. Net yield = 13.0 − 3.0 − 1.2 = 8.8%, or ₹8.80 per ₹100. For Z, expected loss = 1.0% × 40% = 0.4%. Net yield = 9.5 − 0.4 − 1.2 = 7.9%, or ₹7.90 per ₹100.
So on absolute expected net yield the ranking is Y, then X, then Z. The highest gross yield, Y, is not the same as the highest net yield after default and operating cost, but it still leads this particular comparison.
2. Compute return on regulatory capital for each product and recommend one, with a caveat.
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Capital per ₹100 = 12% × risk weight × ₹100. For X: 12% × 100% × 100 = ₹12. For Y: 12% × 150% × 100 = ₹18. For Z: 12% × 75% × 100 = ₹9. Return on regulatory capital = net yield ÷ capital. X = 8.3 ÷ 12 = 69.2%. Y = 8.8 ÷ 18 = 48.9%. Z = 7.9 ÷ 9 = 87.8%.
On capital efficiency, Z is clearly best, even though it has the lowest absolute net yield. The caveat is that lower absolute yield and lower default probability may reflect a less profitable segment; the branch must also consider collateral, concentration, origination cost and whether capital is actually the binding constraint. If capital is not binding and the branch can absorb risk, Y gives the highest net yield; if capital is scarce, Z is the rational choice.
3. If only ₹80 lakh of incremental capital is available for the ₹5 crore growth, which product or products can be supported?
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Capital required for ₹5 crore = ₹5 crore × risk weight × 12%. For X: 5 crore × 100% × 12% = ₹60 lakh. For Y: 5 crore × 150% × 12% = ₹90 lakh. For Z: 5 crore × 75% × 12% = ₹45 lakh.
With ₹80 lakh available, Y cannot be supported because it needs ₹90 lakh. X and Z are feasible individually. If the branch wants the best capital efficiency within the limit, Z is the choice; if it wants the higher absolute net yield and can fund ₹60 lakh, X is feasible but leaves less capital headroom. The branch cannot choose both X and Z at full ₹5 crore each because that would require ₹105 lakh.