Direct Alpha worked on a nine-year fund: the compounded flows, the Excel steps, and why IRR minus the index CAGR is a different number.
Compound every cash flow, and the final NAV, to the measurement date at the public index's total return, then take the IRR of the compounded series. That IRR is Direct Alpha: the annual rate by which the fund beat the index on its own timing. On an illustrative nine-year fund with an IRR of 11.59 per cent, against an index compounding at 6.98 per cent, Direct Alpha is 4.83 per cent a year, or 4.72 per cent in its continuously compounded form. Subtracting the index CAGR from the IRR gives 4.61 points, which is a different and less meaningful number.
Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The Kaplan-Schoar PME says by how much a fund beat the index, as a ratio of future values. It does not say over how long. Direct Alpha, introduced by Gredil, Griffiths and Stucke, uses the same index-compounded cash flows and turns them into an annual rate, which is the unit an investment committee wants when it asks whether private equity earned its illiquidity premium.
| Year | Calls | Distributions | Index return | Index level | Factor to year 9 | Compounded net flow |
|---|---|---|---|---|---|---|
| 0 | 20 | 0 | 100.0 | 1.835 | −36.71 | |
| 1 | 25 | 0 | 9% | 109.0 | 1.684 | −42.09 |
| 2 | 25 | 0 | 14% | 124.3 | 1.477 | −36.92 |
| 3 | 15 | 4 | −12% | 109.3 | 1.678 | −18.46 |
| 4 | 10 | 10 | 20% | 131.2 | 1.399 | 0.00 |
| 5 | 5 | 18 | 7% | 140.4 | 1.307 | 16.99 |
| 6 | 0 | 30 | 11% | 155.8 | 1.178 | 35.33 |
| 7 | 0 | 35 | −6% | 146.5 | 1.253 | 43.85 |
| 8 | 0 | 30 | 16% | 169.9 | 1.080 | 32.40 |
| 9 | 0 | 25 | 8% | 183.5 | 1.000 | 50.00 |
| Total | 100 | 152 |
The year 9 compounded flow includes the NAV of 25.0. The fund's TVPI is 1.77x and its IRR, on the raw flows, 11.59 per cent.
Compounded flowt = (Dt − Ct) × IT ÷ It; add NAVT to the last; Direct Alpha a = IRR(compounded flows)
Year 0: −20 × 1.835 = −36.71. Year 3: (4 − 15) × 1.678 = −18.46. Year 9: (25 + 25.0) × 1.000 = 50.00.
IRR of the ten compounded flows: a = 4.83%. Continuous form: ln(1 + 4.83%) = 4.72%.
In Excel, with net flows in B2:B11 and index levels in C2:C11: put =B2*$C$11/C2 in D2, fill down, add the NAV to D11, then =IRR(D2:D11). Use XIRR with real dates on real data.
Compounding at the index removes the market's return from every flow. What is left is the fund's return in excess of the index, earned on the fund's own schedule, so its IRR is an excess return. Discounting the compounded flows at 4.83 per cent gives a net present value of zero, which is the check to build into the model.
The quick comparison takes the fund IRR, 11.59 per cent, and subtracts the index's nine-year CAGR, 6.98 per cent, for a spread of 4.61 points. That spread compares a money-weighted rate with a time-weighted one. The CAGR assumes the money was in the index for all nine years; the fund's capital was invested for much less, and the index's strong and weak years fell at different points in the fund's life. Here the spread understates Direct Alpha by 22 basis points. Ratio forms such as (1 + IRR) ÷ (1 + CAGR) − 1, at 4.31 per cent, suffer from the same mismatch.
| Shift | Index CAGR | IRR minus CAGR | Direct Alpha | KS-PME |
|---|---|---|---|---|
| −4 points | 2.96% | 8.63 | 8.95% | 1.557 |
| −2 points | 4.97% | 6.62 | 6.85% | 1.407 |
| None | 6.98% | 4.61 | 4.83% | 1.275 |
| +2 points | 8.99% | 2.60 | 2.89% | 1.158 |
| +4 points | 11.00% | 0.60 | 1.01% | 1.053 |
The gap between the spread and Direct Alpha is not a fixed correction: it differs on every row of this table, depending on how the index path lines up with the fund's flows. It matters most where outperformance is thin: at the last row the spread suggests the fund barely kept up, at 0.60 points, while Direct Alpha is 1.01 per cent, 0.41 points more. Direct Alpha and the KS-PME always agree in sign, because they are built from the same compounded flows: the PME is roughly (1 + a) raised to the fund's effective duration, here about 5.15 years.
| NAV | Fund IRR | Direct Alpha | KS-PME |
|---|---|---|---|
| 15.0 | 10.58% | 3.90% | 1.213 |
| 25.0 | 11.59% | 4.83% | 1.275 |
| 35.0 | 12.54% | 5.70% | 1.337 |
Every 10.0 of NAV moves Direct Alpha by roughly 90 basis points in this fund. For a fund still holding most of its value, Direct Alpha is a statement about the marks as much as about the manager.
Use a total return index and the actual flow dates. A price index flatters Direct Alpha by roughly the dividend yield, and year-end bucketing of flows that occurred mid-year moves the result by more than the precision it is usually quoted to.
Compound the flows at the index, take the IRR: 4.83 per cent a year here, not the 4.61 points the shortcut gives. Report it with the KS-PME, 1.275, and the share of value still in NAV. The free companion PME calculator computes Direct Alpha beside three other public market equivalents, and the Kaplan-Schoar PME worked step by step shows the ratio it is built from.
Both start from cash flows compounded at the index. The KS-PME divides the future value of distributions and NAV by that of calls, giving a ratio; Direct Alpha takes the IRR of the same compounded flows, giving an annual rate. In this example they are 1.275 and 4.83 per cent, and they always agree on whether the fund beat the index.
No. IRR minus the index CAGR compares a money-weighted rate with a time-weighted one over a period the capital was not fully invested. For this fund the spread is 4.61 points against Direct Alpha of 4.83 per cent; the gap is not a fixed correction, and where outperformance is thin it can nearly double the measured result, 0.60 against 1.01.
The natural logarithm of one plus the discrete rate, as in the original paper. A discrete Direct Alpha of 4.83 per cent is 4.72 per cent continuously compounded. State which form is reported, because the difference grows with the size of the alpha.
This article is one calculation from Private Markets Performance. 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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