Sahajik Finance's loan tape has 2,000 borrowers in four internal grades with a year of default counts. Compute the default rate by grade and the expected loss at 55% loss given default, check whether the grades rank risk correctly, and suggest pricing by grade.

Default rates run A 1.0%, B 3.0%, C 2.0% and D 8.0%, and expected loss on the Rs 382.5 crore book is about Rs 4.98 crore, 1.30% of loans. Grade C is out of order, but the gap to B is only about 1.1 standard errors, so I would not re-grade on one year. Price A at 12.05%, B at 13.15%, C at 12.93% on the pooled B and C rate, and D at 15.90%.

Divide defaults by borrowers in each grade, then turn default rates into money. Expected loss is exposure times the probability of defaultThe chance that a borrower fails to pay within a set period, usually one year, estimated from past default counts. times the loss given defaultThe share of the loan the lender loses if the borrower defaults, after recoveries from collateral and guarantees., and across the book it comes to about Rs 4.98 crore on Rs 382.5 crore of loans. Grade B carries the most expected loss in rupees because it is large and fairly risky; grade D carries the highest rate but the smallest book.

A rating scale is a promise that each step down is riskier than the one above, like exam grades that should predict who struggles next year. A, B and D behave; C, at 2.0%, defaults less than B at 3.0%, so on this tape the scale is out of order between B and C. If it is real, the lender is overcharging C borrowers and undercharging B borrowers, or approving the wrong mix of both.

Nine defaults is a small number. The standard error of a default rate is the square root of p times one minus p over n: about 0.64 points for B and 0.66 for C. The one-point gap is only about 1.1 standard errors, well within what chance alone produces, so one year of data cannot tell you the grades are wrong. The next steps are to pull more years and vintages, check whether C borrowers are newer loans that have not had time to default, and look at what drives the grade.

Build the rate from the same blocks for every grade: cost of funds, operating cost, capital charge, and expected loss, which is the default rate times 55%. That gives A 12.05%, B 13.15% and D 15.90%; for C, until more data arrives, use the pooled B and C default rate of 2.61%, which gives 12.93%. Pooling avoids both mistakes at once: it does not reward C for a result that may be luck, and does not punish it with B's rate.

State the limits. A single capital charge is generous to grade D, which needs more capital against the chance of a bad year, and a flat 55% severity ignores that larger A loans may be better secured. Both are the first refinements to suggest.