Top-tenant share, Herfindahl index and the effective number of tenants, worked on two rent rolls with the same rent and the same expected loss, and what the difference does to the bad years.
Measure tenant concentration with three numbers: the largest tenant's share of rent, the top-five share, and the Herfindahl index, the sum of every tenant's squared share, whose inverse is the effective number of tenants. An illustrative eight-tenant building with a 40 per cent occupier scores 2,188, the equivalent of 4.6 equal tenants. It expects to lose the same 750,000 of rent as a sixteen-tenant building, but has a 10.2 per cent chance of losing more than half a year's rent, against 0.7 per cent.
Worked in full in The Real Estate Asset Manager by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An asset business plan carries a bad debt or void allowance, and that allowance is an expected value. It is the right number for the forecast. It says nothing about the shape of the outcomes around it, and that shape is what concentration changes. A lender sizing a covenant, a buyer pricing the income or an asset manager deciding which lease to fight for needs to know how bad a bad five years can be, not only what the average five years costs.
| Input | Concentrated | Granular |
|---|---|---|
| Annual rent | 5,000,000 | 5,000,000 |
| Number of tenants | 8 | 16 |
| Shares of rent, per cent | 40, 15, 10, 10, 8, 7, 5, 5 | 10, 9, 8, 8, 7, 7, 7, 6, 6, 6, 6, 5, 5, 4, 3, 3 |
| Chance each tenant fails over the five-year plan | 10% | 10% |
| Rent lost per failure, void plus incentive to re-let | 1.5 years | 1.5 years |
Failures are assumed independent. In practice they are not, which makes the concentrated roll worse, not better.
Step 1: the share measures. The largest tenant pays 40 per cent of rent, 2,000,000, in the concentrated roll and 10 per cent in the granular one. The top three pay 65 and 27 per cent; the top five 83 and 42.
Step 2: the Herfindahl index. Square each share and add the squares.
HHI = Σ si2 = 0.1600 + 0.0225 + 0.0100 + 0.0100 + 0.0064 + 0.0049 + 0.0025 + 0.0025 = 0.2188, or 2,188 on the 10,000 scale
Effective number of tenants = 1 ÷ HHI = 1 ÷ 0.2188 = 4.6
Excel: =SUMPRODUCT((Rent/SUM(Rent))^2)
The granular roll scores 0.0684, or 684, and behaves like 14.6 equal tenants. The index weights the large tenant by its square: the 40 per cent occupier alone contributes 0.1600, 73 per cent of the total.
Step 3: expected loss. Each tenant's chance of failing times the rent lost if it does, summed: 10 per cent × 1.5 years × 5,000,000 = 750,000 for both rolls, 15.0 per cent of a year's rent. Concentration does not change it.
Step 4: the spread. With independent failures the standard deviation of rent lost is the square root of p(1 − p) × HHI, times the loss per failure and the rent, which is why the index matters.
σ = √(0.10 × 0.90 × 0.2188) × 1.5 × 5,000,000 = 1,052,461
Granular: √(0.10 × 0.90 × 0.0684) × 1.5 × 5,000,000 = 588,451
Enumerating every combination of failures gives the full distribution of rent lost over the plan.
| Measure | Concentrated | Granular |
|---|---|---|
| Herfindahl (10,000 scale) | 2,188 | 684 |
| Effective tenants | 4.6 | 14.6 |
| Expected loss | 750,000 | 750,000 |
| Standard deviation | 1,052,461 | 588,451 |
| Chance of no failure at all | 43.0% | 18.5% |
| Chance of losing more than 2,500,000 | 10.2% | 0.7% |
| 95th percentile loss | 3,375,000 | 1,800,000 |
| 99th percentile loss | 4,125,000 | 2,400,000 |
The concentrated building is more often untouched, 43.0 per cent of the time against 18.5, and far more often hit hard: its chance of losing more than half a year's rent is 14.9 times higher. The largest tenant failing alone costs 3,000,000, 60 per cent of a year's rent. That asymmetry is why the same expected loss deserves a different yield, a different covenant headroom and a different amount of asset management time.
A concentration measure belongs beside WAULT in the rent roll summary, because the two interact: if the 40 per cent tenant also has the earliest break, the expiry profile and the concentration risk are the same event. See how to calculate WAULT to expiry and to first break.
| Largest tenant | New tenant | Herfindahl | Effective tenants | Chance of losing > 2,500,000 | 95th percentile |
|---|---|---|---|---|---|
| 40% | none | 2,188 | 4.6 | 10.2% | 3,375,000 |
| 30% | 10% | 1,588 | 6.3 | 6.1% | 2,625,000 |
| 20% | 20% | 1,388 | 7.2 | 4.3% | 2,250,000 |
Taking ten points of rent off the largest tenant cuts the Herfindahl by more than a quarter and the bad-tail probability by four points. The expected loss does not move at all, which is why the benefit never shows in a business plan built on averages.
Pricing concentration through the expected loss, by raising the bad debt allowance for a building with a dominant tenant. If the tenant's covenant is no weaker, the expected loss is unchanged and the adjustment is arbitrary. Price the covenant through the expected loss, as in how to price tenant default risk into a purchase, and price the concentration through the spread: the Herfindahl, the tail and what the tail does to the debt.
The asset business plan that accompanies the book, Appendix A as a working file, computes the rent roll, WAULT, the expiry profile and the concentration tests in one place: the free workbook for this case.
The sum of each tenant's share of total rent squared, often quoted on a 10,000 scale. A roll with tenants at 40, 15, 10, 10, 8, 7, 5 and 5 per cent scores 0.2188, or 2,188. Its inverse, 4.6, is the effective number of equal-sized tenants the roll behaves like, although it has eight.
Not by itself. If every tenant has the same chance of failing, expected rent lost depends only on total rent: 750,000 over five years for both illustrative rolls. Concentration widens the spread around that expectation, from a standard deviation of 588,451 to 1,052,461, which is the risk a lender or a buyer prices.
A lot, and quickly. Cutting the 40 per cent tenant to 30 per cent, with a new tenant taking the other 10, takes the Herfindahl from 2,188 to 1,588 and the chance of losing more than half a year's rent from 10.2 to 6.1 per cent. At 20 per cent it falls to 4.3.
This article is one calculation from The Real Estate Asset Manager. 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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