The look-through gross-up, the return on capital and the marginal cost to an insurer, worked on one illustrative levered property fund at loan to values from 0 to 60 per cent.
Looked through, a leveraged real estate fund is charged the 25 per cent property shock on the gross value of the buildings, not on the insurer's equity, so the charge as a share of what the insurer owns is 25 per cent divided by one minus the loan to value. On an illustrative €150.0 million commitment to a fund geared at 40 per cent, the fund holds €250.0 million of property and the charge is €62.5 million, 41.67 per cent of the equity. Leverage lifts the target return from 6.80 to 8.33 per cent but cuts the return on capital from 27.20 to 20.00 per cent.
Worked in full in Insurance Capital for Asset Managers by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Under the look-through approach, the insurer applies the standard formula to the fund's underlying assets as if it held them directly. The property sub-module's scenario is an instantaneous 25 per cent fall in the value of real estate, and the loss it produces falls on the holder of the equity: the fund's debt is still owed in full. A 25 per cent fall on 250.0 of buildings is a loss of 62.5 to the insurer's 150.0, whatever the fund's own accounts say about the equity.
The case is the levered property fund, one of the three cases in the companion files of Insurance Capital for Asset Managers, set against the book's unlevered real estate fund and its fictional insurer, Calder Life. All figures are illustrative, in euro millions.
| Input | Value |
|---|---|
| Equity committed by the insurer | 150.0 |
| Loan to value inside the fund | 40% |
| Property shock, on gross value | 25% |
| Return on the property, unlevered | 6.80% |
| All-in cost of the fund's debt (assumed) | 4.50% |
Step 1: gross up the equity to the property it controls.
Gross property = equity / (1 − LTV) = 150.0 / 0.60 = 250.0; debt = 100.0
Step 2: apply the shock to the gross value.
Charge = 25% × 250.0 = 62.5, or 62.5 / 150.0 = 41.67% of the equity
Equity after the shock: 150.0 − 62.5 = 87.5
Excel: =Shock*Equity/(1-LTV)
Step 3: the income and the two returns.
Income to the equity = 250.0 × 6.80% − 100.0 × 4.50% = 17.0 − 4.5 = 12.5
Return on equity, the figure the fund quotes: 12.5 / 150.0 = 8.33%
Return on capital: 12.5 / 62.5 = 20.00%, against 10.2 / 37.5 = 27.20% unlevered
Return on capital reduces to (property return − cost of debt × LTV) / 25%. Any positive cost of debt lowers it, because borrowing adds income at 4.50 per cent but adds charge at the full 25 per cent of what it buys.
The standalone figures overstate the cost, since property is diversified against the insurer's other risks. Priced at the margin against Calder Life's existing market risk of 911.25, aggregated with the Annex IV correlations, both funds cost less, but the gap does not close: the levered fund costs 1.68 times the unlevered one at the margin, slightly more than the 1.67 times standalone, because each added euro of property charge diversifies a little less than the one before.
| Measure | Unlevered | Levered, 40% LTV |
|---|---|---|
| Property held | 150.0 | 250.0 |
| Standalone charge | 37.5 | 62.5 |
| Marginal capital at Calder Life | 26.7 | 44.9 |
| Return on equity | 6.80% | 8.33% |
| Return on standalone capital | 27.20% | 20.00% |
| Return on marginal capital | 38.18% | 27.82% |
The levered fund costs 18.21 more capital at the margin for 2.3 of extra income. To tie the unlevered fund on return on capital it would need to earn 11.33 per cent on the equity, which means the buildings themselves returning 8.60 per cent, not 6.80.
| LTV | Property | Charge | Charge / equity | Return on equity | Return on capital | Marginal capital |
|---|---|---|---|---|---|---|
| 0% | 150.0 | 37.5 | 25.0% | 6.80% | 27.20% | 26.7 |
| 20% | 187.5 | 46.9 | 31.2% | 7.38% | 23.60% | 33.5 |
| 30% | 214.3 | 53.6 | 35.7% | 7.79% | 21.80% | 38.4 |
| 40% | 250.0 | 62.5 | 41.7% | 8.33% | 20.00% | 44.9 |
| 50% | 300.0 | 75.0 | 50.0% | 9.10% | 18.20% | 54.2 |
| 60% | 375.0 | 93.8 | 62.5% | 10.25% | 16.40% | 68.1 |
Two thresholds stand out. Above a 20.7 per cent loan to value the fund's return on capital falls below the book's private equity fund, 23.47 per cent; above 48.5 per cent it falls below the listed equity fund, 18.46. And from about 49.0 per cent the looked-through charge exceeds the 49 per cent type 2 equity charge, 73.5, that the same holding would attract if it could not be looked through at all, the fallback priced in what a missing look-through pack costs.
If the fund's debt is fixed-rate, it also enters the interest rate sub-module through the look-through. Like the book's case, this calculation leaves that aside; it does not change the property charge.
The common mistake is to apply 25 per cent to the net asset value. On this fund that gives 37.5 instead of 62.5 and makes the levered fund look strictly better than the unlevered one: same charge, higher return. The second mistake, on the manager's side, is to market the 8.33 per cent target to an insurer. For a buyer charged on gross value, fund-level leverage raises the quoted return and lowers what the insurer earns on its capital. The case, its rankings and the marginal cost are live in the free companion files, and the marginal method itself is worked in how to calculate the marginal SCR of an investment.
Under look-through it is applied to the underlying property, so to gross value: the 25 per cent fall in the buildings is a loss to the equity holder while the fund's debt is still owed. On a EUR 150.0 million holding in a fund at 40 per cent LTV that is 25 per cent of 250.0 million, 62.5 million, rather than 37.5 million on the net asset value.
Not when the property is charged on gross value. Return on capital becomes the property return less the debt cost times the LTV, divided by 25 per cent. With a 6.80 per cent property return and 4.50 per cent debt, it falls from 27.20 per cent unlevered to 20.00 per cent at 40 per cent LTV and 16.40 per cent at 60, while the quoted return on equity rises from 6.80 to 10.25.
When 25 per cent divided by one minus the LTV exceeds 49 per cent, which happens from about 49.0 per cent LTV, before any symmetric adjustment. On EUR 150.0 million at 50 per cent LTV the looked-through charge is 75.0 million against 73.5 million as type 2 equity. Where look-through data exist, the insurer still has to use them.
This article is one calculation from Insurance Capital for Asset Managers. 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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