Default rate, recovery and the time it takes to collect: three inputs, and the one most loss rates leave out.
A private credit loss rate is the annual default rate multiplied by the loss given default, the share of par the lender does not get back. On an illustrative $1,000M direct lending book where 2.0 per cent of par defaults each year and recoveries average 60 cents, the headline loss rate is 0.80 per cent a year. Once the 18 months it takes to collect those 60 cents are priced at the loan's own 10.50 per cent rate, the economic loss is 0.97 per cent, about a fifth higher.
Worked in full in The Private Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Loss rates in direct lending are quoted in two ways that rarely sit side by side. The first counts principal: par defaulted less cash recovered. The second counts value: what the defaulted loan is worth today against the performing loan it replaced. The difference is time. A loan that defaults stops paying interest at once, and the recovery, whether from a restructuring, a sale or a refinancing, arrives months or years later. The principal view treats 60 cents in eighteen months as 60 cents today. A fund's investors do not.
| Input | Value |
|---|---|
| Portfolio par, $ millions | 1,000 |
| Number of loans, equal size | 40 |
| Annual default rate, share of par | 2.0% |
| Recovery, share of par | 60% |
| All-in loan rate (spread plus base rate) | 10.50% |
| Years from default to recovery | 1.5 |
1. Headline loss rate: default rate × (1 − recovery) = 2.0% × 40% = 0.80% a year. On $1,000M, $20.0M of par defaults and $8.0M of principal is lost.
2. Present value of the recovery: 60 ÷ 1.1051.5 = 51.65 per 100 of par. The defaulted loan pays nothing while the workout runs, so the right discount rate is the rate the performing loan would have earned.
3. Economic loss given default: 100 − 51.65 = 48.35, of which 40 is principal and 8.35 is the cost of waiting.
4. Economic loss rate: 2.0% × 48.35% = 0.97% a year, or $9.67M on the book.
In Excel: =DefaultRate*(1-Recovery/(1+LoanRate)^Years). Set Years to zero and the formula returns the headline 0.80 per cent.
The portfolio's 10.50 per cent gross yield becomes 9.70 per cent after headline losses and 9.53 per cent after economic losses. The gap is 17 basis points a year, and the headline figure understates the real loss by 17 per cent. That is the difference between two managers who report the same default rate and the same recovery but collect at different speeds, and it is invisible in a track record that reports only cumulative principal recovered.
Concentration sits on top. In a book of 40 equal loans each position is $25.0M, so one default at 60 cents removes $10.0M of principal, 1.00 per cent of the portfolio, and $12.09M of value, 1.21 per cent, in a single event. The annual rate is an average of lumps, and a fund with 40 loans does not experience 2.0 per cent defaults smoothly: it experiences zero, one or two defaults in a given year. The way fund leverage magnifies each of those lumps for the equity is worked in how much leverage adds to a private credit fund's return.
| Default rate | 40c headline | 40c economic | 60c headline | 60c economic | 75c headline | 75c economic |
|---|---|---|---|---|---|---|
| 1.0% | 0.60 | 0.66 | 0.40 | 0.48 | 0.25 | 0.35 |
| 2.0% | 1.20 | 1.31 | 0.80 | 0.97 | 0.50 | 0.71 |
| 3.0% | 1.80 | 1.97 | 1.20 | 1.45 | 0.75 | 1.06 |
| 4.0% | 2.40 | 2.62 | 1.60 | 1.93 | 1.00 | 1.42 |
The higher the recovery, the larger the share of the loss that comes from waiting: at 75 cents the economic loss given default is 35.43 against a headline 25, so time adds 42 per cent to the loss. Senior secured lenders, whose selling point is recovery, are the ones whose loss rates are most flattered by ignoring time.
| Years to recovery | Economic LGD | Loss rate |
|---|---|---|
| 0.5 | 42.92 | 0.86% |
| 1.0 | 45.70 | 0.91% |
| 1.5 | 48.35 | 0.97% |
| 2.0 | 50.86 | 1.02% |
| 3.0 | 55.53 | 1.11% |
How many defaults the spread can absorb: divide the spread by the economic loss given default. A 5.75 per cent spread survives an 11.9 per cent annual default rate at 48.35 cents of economic loss, not the 14.4 per cent the headline 40 cents suggests. Fees and fund costs come out of the same spread, so the investor's cushion is thinner still.
Comparing a cumulative figure with an annual one. A static pool with 2.0 per cent annual defaults accumulates 9.6 per cent of defaults over five years and 3.84 per cent of principal losses. Both numbers appear in manager presentations, and a 3.84 per cent cumulative loss can sit beside a 0.80 per cent annual one without anyone saying which is which. The second error is the one this calculation corrects: a recovery reported at the price the asset was eventually sold for, with no date attached. Ask for the date of default and the date of each cash recovery, and compute the loss given default yourself. The single-loan version, probability of default times a discounted loss given default times exposure at default with an undrawn revolver, is worked in how to calculate expected loss; this page applies the same discounting to a whole book's annual loss rate and its net yield.
Loss rate = default rate × (1 − recovery ÷ (1 + loan rate)years to recovery). On this book, 2.0 per cent defaults and 60 cent recoveries cost 0.80 per cent a year on principal and 0.97 per cent in value, taking the 10.50 per cent gross yield to 9.53. The fund bridge from gross yield to net return, with losses as one of its lines, is in the free workbook for this case.
The default rate is the share of par that stops performing in a year; the loss rate is what the lender actually loses, the default rate times loss given default. With 2.0 per cent of par defaulting and 60 cents recovered, the loss rate is 0.80 per cent. A manager quoting a low default rate with weak recoveries can lose more than one with twice the defaults and strong recoveries: 1.0 per cent at 40 cents loses 0.60, 2.0 at 75 loses 0.50.
Workouts, restructurings and sales commonly take one to three years, and the loan earns nothing while they run. At a 10.50 per cent loan rate, a 60 cent recovery collected after 0.5 years costs 42.92 per 100 of par in present value terms; after 3.0 years it costs 55.53. On 2.0 per cent annual defaults that moves the loss rate from 0.86 to 1.11 per cent a year.
Divide the spread by the economic loss given default. A loan at a 5.75 per cent spread with 48.35 cents of economic loss per default can absorb an 11.9 per cent annual default rate before the spread is gone, against 14.4 per cent if the time to recovery is ignored. Fees, fund costs and leverage reduce the cushion further for the investor.
This article is one calculation from The Private Credit Investor. 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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