A secondary sale shrinks the private book and, through the discount, the whole portfolio. The formula, the cost, and why selling to the top of the band halves it.
Solve for the sale that makes the remaining NAV equal the target share of a portfolio that has itself shrunk by the discount: S = (NAV − target × total) ÷ (1 − target × discount). On an illustrative 1,000 portfolio holding 190 of private equity, getting from 19 to 15 per cent at a 15 per cent discount means selling 40.92 of NAV, not 40, and the discount costs 6.14, or 61 basis points of the whole portfolio. Selling only to a 17 per cent band ceiling halves both.
Worked in full in The Private Markets Limited Partner by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Overallocations usually arrive through the denominator: public assets fall, private marks lag, and the private share jumps through the policy ceiling without a single new commitment. The secondary market is the only tool that cuts NAV quickly. Before an investment committee approves a sale, it should know how much has to go, what the discount costs, and whether a smaller sale would do.
| Input | Value |
|---|---|
| Total portfolio | 1,000 |
| Private equity NAV | 190 |
| Current allocation | 19% |
| Policy target / band ceiling | 15% / 17% |
| Secondary discount to NAV | 15% |
| Unfunded commitment per unit of NAV sold | 0.30 |
The naive sale is 190 − 15% × 1,000 = 40. It ignores that the LP receives 85 per cent of what it sells, so the whole portfolio loses 15 per cent of the sale. Sell 40 and the portfolio becomes 994.0 and the allocation 15.09 per cent: close, but still over target, and the gap widens with the discount.
(NAV − S) ÷ (total − discount × S) = target
S = (NAV − target × total) ÷ (1 − target × discount)
= (190 − 150) ÷ (1 − 0.15 × 0.15) = 40 ÷ 0.9775 = 40.92
In Excel, with NAV in B1, total in B2, target in B3 and discount in B4: =(B1-B3*B2)/(1-B3*B4).
| Line | Value |
|---|---|
| NAV sold | 40.92 |
| Cash proceeds | 34.78 |
| Loss against reported NAV | 6.14 |
| Remaining private equity NAV | 149.08 |
| New total portfolio | 993.86 |
| New allocation | 15.00% |
The loss is 61 basis points of the total portfolio and 3.23 per cent of the private equity book. The interests sold also take their unfunded commitments with them: at 0.30 of unfunded per unit of NAV, 12.28 of future calls leave the programme, which matters as much as the NAV for the liquidity plan.
Most policies set a range around the target. Selling back to the ceiling rather than the midpoint is the same formula with 17 per cent in place of 15:
S = (190 − 170) ÷ (1 − 0.17 × 0.15) = 20 ÷ 0.9745 = 20.52
Proceeds 17.44, loss 3.08, or 31 basis points: half the cost, for a portfolio that is back inside policy.
The rest of the gap usually closes on its own. If public assets return 8 per cent over the next year while private NAV is flat after distributions, the untouched 19 per cent allocation drifts to 17.84 per cent; at 12 per cent, to 17.32. The arithmetic of that drift is worked in how to calculate the denominator effect.
The sale also has to be the right sale. A buyer prices each interest on its own NAV, unfunded and remaining life, so the same 40.92 of NAV can be assembled from funds that trade at very different discounts. Ranking candidate interests by the cost per point of allocation removed, discount times NAV sold divided by the reduction in the allocation, is the practical way to build the sale list before going to market.
| Discount | Sell to 15% | Loss | bp of total | Sell to 17% | Loss | bp of total |
|---|---|---|---|---|---|---|
| 0% | 40.00 | 0.00 | 0 | 20.00 | 0.00 | 0 |
| 5% | 40.30 | 2.02 | 20 | 20.17 | 1.01 | 10 |
| 10% | 40.61 | 4.06 | 41 | 20.35 | 2.03 | 20 |
| 15% | 40.92 | 6.14 | 61 | 20.52 | 3.08 | 31 |
| 25% | 41.56 | 10.39 | 104 | 20.89 | 5.22 | 52 |
The discount hardly changes how much to sell: 40.00 at par, 41.56 at a 25 per cent discount. It changes what the sale costs almost linearly. The lever that halves the cost is not a better price; it is a smaller sale.
Divide the excess by one minus target times discount, then ask whether the band ceiling would do. Here 40.92 of NAV at 15 per cent costs 61 basis points; 20.52 to the ceiling costs 31, and time does the rest. The Private Markets Limited Partner treats the denominator shock and the policy response as one decision, and the free workbook for this case comes with a worked case on the same kind of breach: holding the pace, cutting the budget, or skipping vintages.
Only slightly. The discount shrinks the total portfolio as well as the private book, so the sale grows from 40.00 at par to 40.92 at a 15 per cent discount and 41.56 at 25 per cent on an illustrative 1,000 portfolio. What the discount changes is the cost: 6.14 at 15 per cent, 61 basis points of the whole portfolio.
Usually to the band ceiling. The cost is proportional to the NAV sold, so stopping at 17 per cent rather than 15 needs a sale of 20.52 instead of 40.92 and costs 3.08 instead of 6.14. Recovering public markets or distributions then do the rest of the work without a discount.
Only to the extent the NAV is a fair value. If reported marks lag a market fall, part of the discount is a correction that would have arrived anyway at the next valuation. The 61 basis points in the example are the loss against reported NAV, an upper bound on the economic cost when marks are stale.
This article is one calculation from The Private Markets Limited Partner. 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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