Turn the benchmark into a multiple over the fund's own effective holding period, and the question of a good TVPI gets a number instead of a rule of thumb.
A TVPI is good when it beats the multiple the same money would have earned in a benchmark over the time it was actually invested: (1 + benchmark return)years. The Thornbury fund's 1.6560x had its money out for an effective 4.04 years, against which an illustrative 7.1312 per cent index would have produced 1.3210x, so it is good. The same 1.6560x held for nine years would lose to the index's 1.8588x.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Investors ask "what is a good TVPI" as if there were a single number. There is not, because a multiple has no clock. 1.66x in four years and 1.66x in nine are different investments. The fix is to convert the benchmark into a multiple over the fund's own holding period and compare like with like.
Thornbury is the illustrative foundation that runs through the book: it committed 600 to a buyout fund. All figures are fictional; the index return is illustrative.
| Year | Called | Distributed |
|---|---|---|
| 1 | 90 | 0 |
| 2 | 150 | 0 |
| 3 | 138 | 29 |
| 4 | 120 | 86 |
| 5 | 66 | 143 |
| 6 to 9 | 0 | 466 |
| 10 | 0 | 67 + 143 residual NAV |
| Total | 564 | 791 + 143 |
TVPI = (distributions + residual NAV) ÷ paid-in capital
= (791 + 143) ÷ 564 = 934 ÷ 564 = 1.6560x
It says the fund turned 564 into 934, a gain of 370. It does not say how long that took. The derivation of all three multiples is in how to calculate TVPI, DPI and RVPI.
Capital went in over five years and came back from Year 3, so no single holding period applies. The cleanest measure is the effective duration implied by the fund's own two numbers: the number of years at the IRR that turns 1 into the TVPI.
Net IRR on the dated flows = 13.2935%
Effective duration = ln(TVPI) ÷ ln(1 + IRR) = ln(1.6560) ÷ ln(1.132935) = 4.04 years
Excel: =LN(1.656)/LN(1+IRR(B2:B11))
Benchmark multiple = (1 + benchmark return)duration
= 1.0713124.04 = 1.3210x
Thornbury's 1.6560x is 0.3350 of a turn above it, or 1.2536 times the benchmark multiple.
Note what the test is underneath. Because the duration is defined from the IRR, TVPI beats (1 + benchmark)duration exactly when the IRR beats the benchmark: 13.29 against 7.13 per cent here. The conversion adds no new verdict; what it adds is the hurdle in the unit the question is asked in, a multiple, and a direct read of how much longer the same multiple could have taken.
The ratio of 1.2536 is close to the book's Kaplan-Schoar public market equivalent of 1.2554, computed by compounding every call and distribution through the index year by year. With the index held at a constant 7.1312 per cent, the same PME comes to 1.2464. The shortcut is not a replacement for a PME, but it gets the order of magnitude right from two numbers anyone can read off a quarterly report.
Solve for the holding period at which the index catches up: ln(1.6560) ÷ ln(1.071312) = 7.32 years. Had the same multiple taken longer than that, the investor would have done better in the index. Over the whole ten-year life it is only 5.17 per cent a year if all the money had been out throughout, against an index multiple of 1.9914 over ten years: the reason a multiple read without a clock flatters a long-lived fund.
The hurdle multiple depends on the benchmark and the effective duration. Read across for your benchmark, down for the fund's duration.
| Effective duration | Benchmark 5.00% | Benchmark 7.1312% | Benchmark 10.00% |
|---|---|---|---|
| 3 years | 1.16x | 1.23x | 1.33x |
| 4 years | 1.22x | 1.32x | 1.46x |
| 5 years | 1.28x | 1.41x | 1.61x |
| 6 years | 1.34x | 1.51x | 1.77x |
| 8 years | 1.48x | 1.74x | 2.14x |
| 10 years | 1.63x | 1.99x | 2.59x |
Three funds with the same 1.6560x show why the table matters. Thornbury, at 4.04 years, clears its 1.32x bar easily. A fund that called 300 and 264 in its first two years and returned 934 in Year 4 has an IRR of 21.81 per cent and an effective duration of 2.56 years; its bar is 1.1925x, and it is better still. A fund that called all 564 in Year 1 and returned 934 only in Year 10 has an IRR of 5.76 per cent and needed 1.8588x to match the index over those nine years: same TVPI, a poor result.
The comparison here is against the capital the fund used. What the investor earned on the whole 600 set aside, including the part waiting to be called, is lower: see how much of the IRR reaches the investor.
Compute the effective duration as ln(TVPI) ÷ ln(1 + IRR), raise one plus the benchmark return to that power, and compare. Thornbury's 1.6560x against 1.3210x is a good result; the same multiple held for longer than 7.32 years would not be. The cash-flow engine and public market equivalent workbooks in the free companion files for this case compute the multiples, the crossing point and the full PME from one schedule.
It depends on how long the money was invested. Against an illustrative 7.1312 per cent benchmark, 2x matches the index over about ten years of effective duration, where the hurdle is 1.99x, and beats it comfortably over five, where the hurdle is 1.41x. Compute the effective duration from the fund's TVPI and IRR before judging the multiple.
Use the fund's IRR, not the multiple alone, because the money goes in and out at different dates. If you only have the TVPI and the effective holding period, the annual rate is TVPI^(1/years) minus 1: 1.6560x over 4.04 years is 13.29 per cent, but over ten years only 5.17 per cent.
TVPI compares value with money paid in and ignores time and the market. A Kaplan-Schoar PME compounds every call and distribution through a public index, so above 1.00 the fund beat the index on the capital it used. Thornbury's TVPI is 1.6560x; its PME on the book's index path is 1.2554.
This article is one calculation from Alternative Investments. 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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