One open-account export order, priced with and without a policy: the premium, the uncovered tenth, the break-even default probability and the tail the expected loss hides.
Trade credit insurance is worth its premium when the expected loss it removes is larger than the premium. On a 4,200,000 export order on 90-day open account, a 0.62 per cent premium costs 26,040 and, with 90 per cent cover, removes 30,975 of the 34,416 expected loss: a net gain of 4,935. The policy breaks even at a buyer default probability of 3.45 per cent a year; below that it is dear on expected values, though it may still be worth buying for the tail.
Worked in full in Trade Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The question is usually asked as "how much does credit insurance cost?" and answered with the premium rate. The premium is only one side. The other is the loss the policy takes off your hands, which depends on the buyer's risk, on how long you carry it, and on the share the policy leaves with you.
| Input | Value |
|---|---|
| Contract value | 4,200,000 |
| Operating margin before finance (7.3%) | 306,600 |
| Cost of goods sold (81.5%) | 3,423,000 |
| Exporter's cost of funds, actual/360 | 8.4% |
| Production / transit / buyer credit, days | 70 / 26 / 90 |
| Buyer one-year default probability | 4.1% |
| Loss given default, unsecured trade claim | 62% |
| Premium, share of the invoice | 0.62% |
| Share of a loss the policy pays | 90% |
=0.9*B2*(1-(1-B7)^(116/365))*B8-B2*B9The same order, with the financing of the cost over 186 days to cash (148,558.20) included on both sides:
| Line | Uninsured | Insured |
|---|---|---|
| Financing on cost | 148,558.20 | 148,558.20 |
| Premium | 0.00 | 26,040.00 |
| Expected loss borne | 34,416.21 | 3,441.62 |
| Total cost | 182,974.41 | 178,039.82 |
| Margin after finance | 123,625.59 | 128,560.18 |
Set the loss removed equal to the premium and solve for the buyer's annual default probability p:
Against the 4.1 per cent the case assumes, the policy is bought below its actuarial price: the insurer is pricing this buyer as safer than the exporter's own credit view. Every unit of premium removes 1.19 units of expected loss.
| Buyer PD a year | Expected loss | Removed | Net value | Margin, uninsured | Margin, insured |
|---|---|---|---|---|---|
| 1.00% | 8,304 | 7,474 | -18,566 | 149,738 | 131,171 |
| 2.00% | 16,666 | 14,999 | -11,041 | 141,376 | 130,335 |
| 3.45% | 28,933 | 26,040 | 0 | 129,108 | 129,108 |
| 4.10% | 34,416 | 30,975 | 4,935 | 123,626 | 128,560 |
| 6.00% | 50,706 | 45,636 | 19,596 | 107,336 | 126,931 |
| 8.00% | 68,098 | 61,288 | 35,248 | 89,944 | 125,192 |
Read the last column. Insured, the margin barely moves across the whole range, from 131,171 to 125,192. Uninsured it falls from 149,738 to 89,944. That is what the premium buys: not a better average, but a margin that no longer depends on a probability nobody can measure precisely.
The premium rate moves the break-even directly. At 0.40 per cent the policy pays above a 2.24 per cent buyer default probability; at 0.80 per cent it needs 4.44 per cent; at 1.00 per cent, 5.53 per cent.
Expected values understate the case for cover on a single large order. One default on this order loses 4,200,000 × 62% = 2,604,000, which is 8.5 times its whole operating margin. With the policy, the retained tenth is 260,400. An exporter with a few large buyers is buying protection against that tail, and may rationally pay a premium above the break-even to get it.
Measuring the exposure from the invoice. On open account the risk starts when the goods leave, so the 26 days of transit count. Using 90 days instead, the default probability falls to 1.03 per cent, the loss removed to 24,068, and the policy appears 1,972 too dear when it is 4,935 cheap. The break-even rises to 4.43 per cent and the wrong answer comes out.
Setting the premium against the whole expected loss. 34,416 − 26,040 = 8,376 overstates the gain by 3,442, the uncovered tenth that stays with the exporter whether or not the policy is bought.
Netting the premium against the retained loss. The premium is certain; the retained loss is not. Keep them on separate lines, as the table above does, so that the total cost compares like with like across routes.
The free workbook for this case, on the Trade Finance companion page, prices open account with and without the policy alongside the other five routes to payment. The bank-side equivalent of this decision is worked in is a letter of credit confirmation fee worth paying.
Premiums are usually quoted as a percentage of insured turnover or of each invoice. At an illustrative 0.62 per cent, a 4,200,000 export invoice costs 26,040 to insure. The economic cost is the premium less the expected loss it removes: on a buyer with a 4.1 per cent annual default probability the policy removes 30,975, so its net cost is negative, a gain of 4,935.
The uninsured share, typically ten per cent, plus commercial disputes, losses after a breach of the policy conditions, and the delay of the waiting period. On a 4,200,000 order with a 62 per cent loss given default, the retained tenth of a default is still 260,400, close to the order's entire operating margin of 306,600.
Because the risk starts at shipment, not when the credit period starts running. Goods 26 days in transit on 90-day terms carry the buyer for 116 days, a 1.32 per cent default probability at 4.1 per cent a year. Measuring 90 days instead makes the same policy look 1,972 too dear when it is 4,935 cheap.
This article is one calculation from Trade Finance. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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