Risk-Adjusted Yield on a Four-Product Branch Portfolio
A semi-urban branch reports the following outstanding portfolio at 31 March, all figures in rupees crore, with the stated yields and gross NPAs: group loans to women's self-help groups - outstanding 480, yield 21.0%, GNPA 2.5%; individual small-business loans - outstanding 320, yield 16.5%, GNPA 4.0%; gold loans - outstanding 260, yield 11.0%, GNPA 0.8%; housing loans - outstanding 140, yield 9.0%, GNPA 1.5%. Total outstanding is 1,200 crore. The branch's credit policy assumes a loss given default of 60% for all four products, and the branch head measures product performance by net (risk-adjusted) yield rather than headline yield. The branch has committed to growing the book to 1,500 crore over the next two years, and in the last two years it grew 20% in year one and only 4.17% in year two. Two proposals are on the table: shift 100 crore of the housing book into gold loans, or keep the mix unchanged and grow proportionately.
1. Compute the portfolio's weighted average yield and its weighted average net (risk-adjusted) yield. Show the weighting logic.
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Compute each product's credit cost as GNPA x LGD (0.60), then net yield as yield minus credit cost.
| Product | Outstanding | Yield | Credit cost | Net yield |
|---|---|---|---|---|
| Group loans | 480 | 21.00% | 1.50% | 19.50% |
| Small business | 320 | 16.50% | 2.40% | 14.10% |
| Gold loans | 260 | 11.00% | 0.48% | 10.52% |
| Housing | 140 | 9.00% | 0.90% | 8.10% |
Weighted yield = (480x21 + 320x16.5 + 260x11 + 140x9) / 1,200 = (10,080 + 5,280 + 2,860 + 1,260) / 1,200 = 19,480 / 1,200 = 16.23%.
Weighted net yield = (480x19.50 + 320x14.10 + 260x10.52 + 140x8.10) / 1,200 = (9,360 + 4,512 + 2,735.2 + 1,134) / 1,200 = 17,741.2 / 1,200 = 14.78%.
The 1.45 percentage-point gap between the two is the portfolio's annual credit cost - roughly 17.4 crore on a 1,200 crore book. Using simple averages of the four yields (14.4%) would be wrong because the products are of unequal size; the correct weight is outstanding balance, and the correct denominator is the same 1,200 crore throughout.
2. Evaluate the proposal to move 100 crore from housing to gold loans. Quantify the annual effect on net interest income and state two reasons the arithmetic alone should not decide the question.
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Arithmetic. Housing net yield is 8.10%; gold is 10.52%. Moving 100 crore lifts net yield by 2.42 percentage points on that 100 crore: 100 x 0.0242 = 2.42 crore of additional annual net interest income, with the total book unchanged at 1,200 crore.
Note the headline interest income effect is larger - (11.0 - 9.0) = 2.0 points, i.e. 2.00 crore - because moving into gold also raises credit cost (0.48 - 0.90 = -0.42, i.e. a 0.42 crore offset). Quoting 2.00 crore overstates the gain by 0.42 crore.
Why the number is not the decision.
- Capacity, not preference: gold loans are demand-driven and self-liquidating; the branch cannot conjure 100 crore of pledged-gold demand. Booking to fill a spreadsheet invites LTV and valuation shortcuts.
- Concentration and liquidity: a 360 crore gold book (30% of the portfolio) creates price and purity risk on the collateral and a repayment cliff if gold prices fall, even though the GNPA ratio looks flattering.
- Mandate: housing carries priority-sector and long-tenor funding benefits that a product-level yield table ignores entirely.
Recommendation: test whether gold demand exists before modelling the switch, and treat the 2.42 crore as an upper bound.
3. The book must move from 1,200 crore to 1,500 crore in two years. The branch head describes growth as averaging 12.08% a year. Is that correct? Compute the right measure and explain the discrepancy.
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The claim is wrong. 12.08% is the arithmetic mean of the two year-on-year rates: year one 1,200 to 1,440 is +20.00%; year two 1,440 to 1,500 is +60/1,440 = +4.17%. Their average is (20.00 + 4.17)/2 = 12.08%.
Correct measure - CAGR: (1,500/1,200)^(1/2) - 1 = 1.25^0.5 - 1 = 1.1180 - 1 = 11.80%.
Why they differ. Growth compounds on a moving base. The 20% in year one is earned on 1,200 crore; the 4.17% in year two is earned on a much larger 1,440 crore. Averaging rates treats a 240 crore increment and a 60 crore increment as if they arose on the same base, which overweights the low-growth year and inflates the answer by 0.28 points.
Why it matters. If the branch plans next year's budget on 12.08% (1,500 x 1.1208 = 1,681 crore) rather than 11.80% (1,677 crore), the error looks trivial in one year but compounds: over five years the difference is roughly 20 crore of unfunded target. Always state the measure - CAGR, average of yearly rates, or incremental year-on-year - and never compare a CAGR from one period with an arithmetic average from another.