The loan Herfindahl turns a pool's size distribution into an effective number of equal loans, and it falls further than the loan count as a deal pays down.
The Herfindahl score of a CMBS pool is the reciprocal of the sum of each loan's squared share of the pool balance: 1 / Σ(balance / pool)². It reads as the number of equal-sized loans that would give the same concentration. An illustrative 20-loan, $1,000M conduit pool has a sum of squares of 0.05806 and a Herfindahl of 17.2: twenty loans, but diversified like 17.2 equal ones. Grouped by sponsor it falls to 12.1.
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A conduit with twenty loans is not twenty equal bets. Its largest loans carry most of the risk, and a default on one of them can reach the junior classes on its own. Presale reports and investor tapes commonly quote the loan Herfindahl beside the loan count for that reason: it weights each loan by its size, so a pool with a few large loans scores well below its count, and a single-asset single-borrower deal scores exactly 1.0.
| Loan | Balance | Share | Share squared |
|---|---|---|---|
| 1 | 95.0 | 9.50% | 0.9025% |
| 2 | 85.0 | 8.50% | 0.7225% |
| 3 | 80.0 | 8.00% | 0.6400% |
| 4 | 70.0 | 7.00% | 0.4900% |
| 5 | 65.0 | 6.50% | 0.4225% |
| 6 | 60.0 | 6.00% | 0.3600% |
| 7 | 55.0 | 5.50% | 0.3025% |
| 8 | 52.5 | 5.25% | 0.2756% |
| 9 and 10 | 50.0 each | 5.00% | 0.2500% each |
| 11 | 45.0 | 4.50% | 0.2025% |
| 12 | 42.5 | 4.25% | 0.1806% |
| 13 | 40.0 | 4.00% | 0.1600% |
| 14 | 37.5 | 3.75% | 0.1406% |
| 15 | 35.0 | 3.50% | 0.1225% |
| 16 | 32.5 | 3.25% | 0.1056% |
| 17 | 30.0 | 3.00% | 0.0900% |
| 18 | 27.5 | 2.75% | 0.0756% |
| 19 | 25.0 | 2.50% | 0.0625% |
| 20 | 22.5 | 2.25% | 0.0506% |
| Pool | 1,000.0 | 100% | 5.806% |
All balances are fictional. Loans 2, 6 and 9 share a sponsor.
1. Share of each loan = balance / pool. Loan 1: 95.0 / 1,000.0 = 9.50%.
2. Square each share: 9.50% × 9.50% = 0.9025%.
3. Add the squares: Σ = 0.05806.
4. Herfindahl = 1 / 0.05806 = 17.2 (17.22).
In Excel, with balances in B2:B21: =SUM(B2:B21)^2/SUMSQ(B2:B21). Dividing the squared total by the sum of squared balances gives the same result without a helper column.
The largest loan is 9.5 per cent of the pool, the top three 26.0 per cent and the top ten 66.2 per cent. The count overstates diversity by a factor of 1.16. That is a moderate gap: the pool has no single dominant loan, only a gentle slope from large to small.
Three loans, 2, 6 and 9, are made to the same sponsor. They are separate loans on separate properties, but a sponsor in difficulty tends to stop supporting all its assets at once. Treat the three as one exposure of $195.0M, 19.5 per cent of the pool, and recompute: the Herfindahl falls from 17.2 to 12.1. A pool review should run the score at loan, sponsor and, where relevant, property-type and metropolitan-area level; the loan figure is only the most optimistic of them.
| Pool | Loans | Balance | Largest loan | Herfindahl |
|---|---|---|---|---|
| Base | 20 | 1,000.0 | 9.5% | 17.2 |
| Five smallest replaced by one 137.5 pari passu note | 16 | 1,000.0 | 13.75% | 13.7 |
| Three largest repay at maturity | 17 | 740.0 | 9.46% | 15.5 |
| Only the eight largest remain | 8 | 562.5 | 16.9% | 7.7 |
| Twenty equal loans | 20 | 1,000.0 | 5.0% | 20.0 |
A single large pari passu note, a piece of a big loan split across several deals, takes the score from 17.2 to 13.7 even though the pool balance is unchanged. Paydown matters more. Loans rarely leave a pool in proportion: smaller loans refinance and the larger, harder ones extend or default. When only the eight largest remain, the pool is $562.5M, the largest loan is 16.9 per cent of it and the Herfindahl is 7.7. The junior classes, whose credit enhancement is worked in how credit enhancement is calculated in CMBS, then depend on a handful of properties.
The Herfindahl measures size concentration only. It says nothing about which loans are weak; read it beside the distribution of coverage and leverage in the weighted average DSCR of a CMBS pool.
A twenty-loan tape, the capital structure above it and the loss allocation, ready to run this score on, are in the free deal model for this book.
It is the number of equal-sized loans that would give the pool the same concentration. A pool of 20 loans whose balances range from $95.0M down to $22.5M scores 17.2, so it is diversified like 17.2 identical loans. Twenty equal loans would score 20.0, and a single-asset deal scores 1.0.
It is the same measure expressed differently. Competition analysis quotes the sum of squared shares on a 10,000 scale, so the illustrative pool's 0.05806 becomes an HHI of 581. CMBS reports usually quote the reciprocal, 17.2, because an effective number of loans is easier to compare with the loan count.
Because loans leave unevenly. If the twelve smallest loans repay and the eight largest stay, the pool falls to $562.5M and its Herfindahl from 17.2 to 7.7, with the largest loan at 16.9 per cent of what remains. The junior classes then depend on a handful of assets.
This article is one calculation from CMBS and CRE CLOs. 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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