The statement of operations already holds the year's result; the denominator has to account for the capital that came in and went out, and the realised gain has to be read beside the unrealised line.
Take the net increase or decrease in net assets resulting from operations, which already includes income, fees, realised and unrealised gains and the carry accrual, and divide it by opening net assets plus capital calls and less distributions, each weighted by the time it was in the fund. On an illustrative fund with 400.0 of opening net assets, that is a loss of 5.0 on a base of 422.5: minus 1.18 per cent, in a year that reported a 26.5 realised gain.
Worked in full in How to Read a Private Fund's Financial Statements by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Private fund accounts do not print a return. They print the ingredients: a statement of operations that ends in the result for the year, and a statement of changes in net assets that adds the contributions and takes off the distributions. Putting the two together gives the fund's return for the year, and splitting it by line shows where it came from.
| Line | Amount |
|---|---|
| Opening net assets attributable to limited partners | 400.0 |
| Capital called, 31 March (in the fund for 0.75 of the year) | 60.0 |
| Distributions, 30 September (out for 0.25 of the year) | 90.0 |
| Dividend and interest income | 6.0 |
| Management fee / fund expenses / facility interest | 8.0 / 2.0 / 1.5 |
| Net realised gain, one exit | 26.5 |
| Net change in unrealised appreciation | −27.2 |
| Decrease in accrued carried interest | 1.2 |
Result from operations = income − fees and expenses + realised gain + change in unrealised − change in carry accrual
Return = result / (opening NAV + Σ call × weight − Σ distribution × weight)
The weight is the share of the year remaining after the flow. In Excel: =Result/(Opening+SUMPRODUCT(Flows,Weights)), with calls positive and distributions negative.
Step 1, the result. Income of 6.0 less 11.5 of fees, expenses and facility interest gives net investment income of minus 5.5. Add the 26.5 realised gain and the minus 27.2 change in unrealised: minus 6.2 before carry. The carry accrual falls by 1.2 as values fall, which is returned to the limited partners' column, so the result attributable to them is minus 5.0. Closing net assets are 400.0 + 60.0 − 90.0 − 5.0 = 365.0, which must tie to the balance sheet.
Step 2, the base. The 60.0 called on 31 March was at work for three quarters of the year, so it counts 45.0. The 90.0 distributed on 30 September was in the fund for three quarters and out for one, so it removes 22.5. The capital employed is 400.0 + 45.0 − 22.5 = 422.5.
Step 3, the return. Minus 5.0 over 422.5 is minus 1.18 per cent. This is the modified Dietz method, a money-weighted return for the year that approximates the period's IRR; a true time-weighted return would need a valuation on each flow date, which annual accounts do not give. For a single year with two flows it is close enough for any reading of the accounts.
| Line | Amount | Contribution |
|---|---|---|
| Income | 6.0 | 1.42% |
| Fees, expenses and facility interest | −11.5 | −2.72% |
| Net realised gain | 26.5 | 6.27% |
| Net change in unrealised | −27.2 | −6.44% |
| Change in carry accrual | 1.2 | 0.28% |
| Result from operations | −5.0 | −1.18% |
The two gain lines must be read together. The asset sold had been carried 23.0 above its cost, and that unrealised gain is reversed when the realised gain is booked. So the exit itself added 3.5, the rest of the portfolio was marked down by 4.2, and the investments as a whole made minus 0.7. A 6.27 per cent contribution from realisations is real cash, but it is not this year's performance. Before fees and carry the portfolio returned 1.25 per cent; the fee and expense load of 2.72 per cent turned that into a loss.
| Method | Base | Return |
|---|---|---|
| Time-weighted flows (modified Dietz) | 422.5 | −1.18% |
| Both flows at mid-year | 385.0 | −1.30% |
| Opening NAV only | 400.0 | −1.25% |
| Average of opening and closing NAV | 382.50 | −1.31% |
| Closing over opening NAV, minus one | −8.75% |
Any sensible base gives a figure between minus 1.18 and minus 1.35 per cent. Comparing closing with opening NAV does not: it reports a loss of 8.75 per cent because 30.0 more was distributed than called. That is cash returned, not value lost.
The markdown elsewhere drives the answer. Holding the carry accrual change at 1.2, no markdown would have left the fund at minus 0.19 per cent; a markdown of 12.0 instead of 4.2 takes it to minus 3.03 per cent, with the realised gain unchanged at 26.5.
The common mistake is to read the realised gain as the year's result: 26.5 on 400.0 of opening NAV looks like 6.62 per cent. The second is to forget the carry accrual, which rises in good years and falls in bad ones, and belongs in the limited partners' result. The exit-side journal entries behind the reversal are set out in realised vs unrealised gain on a fund exit.
Return for the year = result from operations / time-weighted capital: here minus 5.0 / 422.5 = minus 1.18 per cent. Then read realised and unrealised together, because a large realised gain and a large negative unrealised change usually describe one exit. The book's reporting pack, with every statement and its reconciliations as live formulas, is in the free workbooks for this book.
Because most of a realised gain was already recognised in earlier years as unrealised appreciation, and is reversed when the asset is sold. On the illustrative fund a 26.5 realised gain sits beside a 23.0 reversal, so the exit added only 3.5. With a 4.2 markdown elsewhere, the investments made minus 0.7 in the year.
Opening net assets plus each capital call and less each distribution, weighted by the share of the year it was in the fund: the modified Dietz method. On the illustrative fund that is 422.5. Dividing by opening NAV alone gives minus 1.25 per cent and by average NAV minus 1.31, against minus 1.18.
Only if no capital moved. On the illustrative fund closing net assets of 365.0 against 400.0 suggest a loss of 8.75 per cent, but 30.0 of the fall is simply distributions exceeding calls. The result of operations was a loss of 5.0, which on the capital employed is minus 1.18 per cent.
Case 1 of Appendix C of How to Read a Private Fund's Financial Statements is the exit that looks like a write-down; the free companion workbook decomposes it. 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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