Crossing two loans does not add a cushion. It makes one property's fall coincide with the other's before the lender loses, and that is worth exactly as much as the assets are uncorrelated.
Cross-collateralisation lets a lender use the surplus value of one property to cover a shortfall on another, so it cuts expected loss by as much as the two properties' values move independently. On two illustrative $20.0M loans, each on a $30.0M property, expected loss falls from $1,140,000 standalone to $336,000 crossed, a 70.5 per cent reduction, if the properties' values are independent. If they always move together, crossing saves nothing.
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 cross-collateralised (in US usage, cross-collateralized) loan, or a pair of loans secured on each other's property with cross-default, turns several single-asset credits into one pool. Lenders ask for it on portfolios and on sponsors with more than one loan; borrowers resist it because it traps equity and complicates sales. Both sides tend to argue in principles. The benefit is a number, and it depends almost entirely on correlation.
| Input | Value |
|---|---|
| Value of each property | $30,000,000 |
| Loan on each property | $20,000,000 (66.7% LTV) |
| Enforcement and sale costs | 10% of value |
| Value change at maturity, with probability | −40% (15%), −20% (25%), 0% (40%), +10% (20%) |
| Value change | Probability | Value, $ | Net recovery, $ | Loss, $ |
|---|---|---|---|---|
| −40% | 15% | 18,000,000 | 16,200,000 | 3,800,000 |
| −20% | 25% | 24,000,000 | 21,600,000 | 0 |
| 0% | 40% | 30,000,000 | 27,000,000 | 0 |
| +10% | 20% | 33,000,000 | 29,700,000 | 0 |
Loss = MAX(0, loan − value × (1 − costs))
Expected loss per loan = 15% × $3,800,000 = $570,000; for the two loans, $1,140,000, or 2.85% of the $40,000,000 exposure. In Excel, with value changes in A2:A5 and probabilities in B2:B5: =SUMPRODUCT(B2:B5,(20000000-30000000*(1+A2:A5)*(1-10%)>0)*(20000000-30000000*(1+A2:A5)*(1-10%)))
Crossed, the lender is owed $40,000,000 and can sell both properties. Take one outcome: property A rises 10 per cent to $33,000,000 and property B falls 40 per cent to $18,000,000. Standalone, the B loan loses $3,800,000 while A's sale leaves $9,700,000 of surplus that goes to the borrower. Crossed, the two sales net $45,900,000 against $40,000,000 owed: no loss, and $5,900,000 back to the borrower.
Across all sixteen combinations of the two properties' outcomes, assuming they are independent, only three still lose money:
| Outcome | Probability | Crossed loss, $ |
|---|---|---|
| Both fall 40% | 2.25% | 7,600,000 |
| One falls 40%, the other 20% (either order) | 7.50% | 2,200,000 |
| All other combinations | 0 | |
| Expected loss | 336,000 |
Expected loss falls from $1,140,000 to $336,000, from 2.85 to 0.84 per cent of the exposure, and the probability of any loss from 27.75 per cent to 9.75 per cent. The cushion has not changed: on the combined collateral the lender still loses once values fall 25.9 per cent, as it did on each property alone. What has changed is that one property's fall must now coincide with the other's.
Model correlation simply: in a share of outcomes the two properties land in the same state, and in the rest they are independent.
| Share of outcomes moving together | Crossed expected loss, $ | Reduction vs standalone |
|---|---|---|
| 0% | 336,000 | 70.5% |
| 25% | 537,000 | 52.9% |
| 50% | 738,000 | 35.3% |
| 75% | 939,000 | 17.6% |
| 100% | 1,140,000 | 0.0% |
Two offices in the same submarket let to similar tenants will often fall together, and crossing them buys little. An office and a logistics asset in different regions are where the structure earns its keep. The value of the cross is the diversification between the assets, not the extra property in the security package.
The same arithmetic scales to a portfolio, but the combinations do not: four assets with four states each give 256 outcomes, and a real pool needs a simulation. Draw each property's value change from a distribution with a common market factor and an asset-specific one, sum the net recoveries across the pool, and compare with the total loan in each draw. The common factor's weight plays the role of the share of outcomes moving together in the table above. Run the same draws with each loan standing alone and the difference between the two average losses is the value of the cross, in dollars, for that pool.
Treating cross-collateralisation as extra collateral and lending more against it. Crossing two 66.7 per cent loans does not make a 66.7 per cent loan safer per dollar unless the assets are imperfectly correlated, and it never changes the 25.9 per cent value fall at which the pool as a whole is under water. A lender who raises leverage because the loans are crossed may have given back the whole benefit. The other common error is on the borrower's side: forgetting that crossing works in both directions, so $3,800,000 of the $9,700,000 surplus in the example above goes to the weak loan and only $5,900,000 is paid out, and that selling one asset will require a release price, usually above its allocated loan amount.
The value distribution, costs and correlation model are illustrative. Enforceability of cross-collateral and cross-default provisions depends on the structure and jurisdiction. Not advice on any loan.
Loan structuring and portfolio credit risk are the subject of the companion page for this book. What a borrower pays to take one asset out of a crossed pool is worked in how a release price is calculated on a portfolio loan, and expected loss itself in how to calculate expected loss from PD, LGD and EAD.
Securing two or more loans on all of the borrower's properties, usually with cross-default, so that the lender can apply the surplus from one sale to the shortfall on another. In the example, a property that rises 10 per cent leaves $9,700,000 of surplus that covers a $3,800,000 loss on its neighbour, turning a loss into $5,900,000 returned to the borrower.
Only to the extent the properties' values are not perfectly correlated. With independent values, expected loss on two illustrative loans falls 70.5 per cent; if they move together half the time, 35.3 per cent; if always, 0.0 per cent. The value fall at which the pool loses money, 25.9 per cent here, does not change.
Because surplus value in one asset is trapped to support the others and a sale needs a release price. Where one property is worth $29,700,000 net and its loan is $20,000,000, the $9,700,000 of surplus would be paid out on a standalone sale; crossed, $3,800,000 of it covers the weak loan and only $5,900,000 reaches the borrower.
This article is one calculation from 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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