Financing a whole loan on a repo line turns a high single-digit yield into a mid-teens return on equity. The same arithmetic multiplies the losses and adds a margin call.
Back leverage turns a loan yield into a return on equity with one formula: ROE = loan yield + (loan yield − repo cost) × debt / equity. An illustrative $50.0m bridge loan yielding 8.383 per cent, financed 75 per cent on a repo line costing 6.283 per cent, earns 14.68 per cent on the fund's $12.5m of equity. The same leverage makes every point of credit loss four points of equity loss, and adds a margin call if the loan is marked down.
Worked in full in The Real Estate Debt Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A fictional debt fund originates a floating-rate whole loan on a transitional property and finances it with a repurchase facility. Both float on SOFR. All rates are illustrative.
| Input | Value |
|---|---|
| Whole loan | $50.0m |
| SOFR | 4.30% |
| Loan spread | 3.75% |
| Origination fee, spread over a 3 year expected life | 1.0% |
| Repo advance rate | 75% |
| Repo spread | 1.90% |
| Repo upfront fee, over 3 years | 0.25% |
Loan yield = SOFR + spread + fee / life = 4.30% + 3.75% + 1.0% / 3 = 8.05% + 0.333% = 8.383%
Repo cost = SOFR + repo spread + fee / life = 4.30% + 1.90% + 0.25% / 3 = 6.20% + 0.083% = 6.283%
Repo = $50.0m × 75% = $37.5m; fund equity = $12.5m; D/E = 3.0
Spreading the fees straight-line over the expected life is a simplification; an effective-interest calculation gives a slightly different figure, but the ranking does not change.
Loan income = $50.0m × 8.383% = $4.1917m
Repo interest = $37.5m × 6.283% = $2.3562m
Net income = $1.8354m; ROE = $1.8354m / $12.5m = 14.68%
Check: 8.383% + (8.383% − 6.283%) × 3.0 = 8.38% + 6.30% = 14.68%
Excel: =Yld+(Yld-Repo_cost)*Adv/(1-Adv)
The fund earns 2.10 points of carry on every dollar the repo lender provides, and there are three of those for each dollar of equity. That is the whole trick, and it is why debt fund marketing quotes levered and unlevered returns side by side.
| Advance rate | Repo +1.60% | Repo +1.90% | Repo +2.20% |
|---|---|---|---|
| 60% | 11.98 | 11.53 | 11.08 |
| 70% | 13.98 | 13.28 | 12.58 |
| 75% | 15.58 | 14.68 | 13.78 |
| 80% | 17.98 | 16.78 | 15.58 |
Leverage only helps while the repo costs less than the loan yields. The break-even repo spread here is 4.00 per cent: above it, each extra dollar of advance lowers the return. Because loan and repo both float, SOFR passes straight through to equity: ROE is 13.68 per cent at a 3.30 per cent SOFR and 15.68 per cent at 5.30 per cent, one for one, because the fund keeps the index on its own $12.5m.
Credit losses land on the fund before the repo lender. At a 75 per cent advance each point of loss on the loan is 4 points on the equity.
Unlevered yield after a 0.50% expected loss = 8.38% − 0.50% = 7.88%
Levered ROE after the same loss = 14.68% − 0.50% × 4 = 12.68%
Then there is the mark. Repo facilities let the lender revalue the collateral and demand cash to restore the advance rate. If the loan is marked at 95, its value is $47.5m, the maximum repo is $35.625m, and the fund must post a margin call of $1.875m, 15 per cent of its equity, on top of a $2.5m mark-to-market loss that is 20 per cent of the equity. The borrower has not missed a payment. This is the funding risk the unlevered return does not show, and it arrives in exactly the market in which the fund's other loans are being marked too.
Terms vary widely: some facilities are non-mark-to-market or mark only on credit events, which costs more in spread. The sensitivity worth running is the advance rate after the first adverse mark, not the advance rate on day one.
Comparing a levered debt fund's 14.68 per cent with an unlevered lender's 8.38 per cent as if they were the same risk. They are not: the levered return carries four times the credit loss, a margin call on marks, and a refinancing risk if the facility matures before the loans. The fair comparison deducts expected loss on the levered equity, prices the funding risk, and asks what capital the strategy actually needs to survive a 5 point mark. The same trade-off measured at fund level, where facility leverage on a direct lending book buys return by giving up loss capacity, is worked in how much leverage adds to a private credit fund's return; this page is the asset-level version, one loan on one repo line, with a margin call triggered by a mark on that loan. That discipline, deducting cost of funds, expected loss, operating cost and capital before ranking loans, is the argument of margin versus return on capital on a real estate loan. The securitised version of the same leverage is worked in how to calculate CRE CLO equity return.
The book's return on capital comparison, with the cost of funds, expected loss and capital lines live, is in the free workbook for this case.
Financing that a lender takes against loans it has already made, usually a repurchase facility or a loan-on-loan from a bank. On an illustrative $50.0m whole loan, a 75 per cent advance provides $37.5m, so the fund's own equity is $12.5m and its return on that equity rises from 8.38 to 14.68 per cent.
When both the loan and the repo float on the same index, the return on equity moves one for one with it, because the fund keeps the index on its own equity. In the illustrative case ROE is 13.68 per cent at a 3.30 per cent SOFR, 14.68 at 4.30 and 15.68 at 5.30.
Because the repo lender is repaid before the fund. At a 75 per cent advance, every point of loss on the loan is four points of loss on the fund's equity. An expected loss of 0.50 per cent a year cuts the unlevered yield to 7.88 per cent but the levered return by 2.00 points, from 14.68 to 12.68 per cent.
The four deductions between a loan's margin and the return the lender actually earns are worked in chapter 7 of The Real Estate Debt 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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