This is the final post in my three-part series on performance measurement for private market funds and the difficulties of using the internal rate of return (IRR) measure as equivalent to a rate of return on investments. In Part I, I discussed the rise of global assets under management (AUM) in private market funds and how this trend may have been driven by a perception of superior returns compared to traditional investments. As I illustrated, a root cause for this belief is the generalized use of IRR to infer rates of return, which is problematic.
In Part II, I discussed in more detail how IRR works and why it should not be misconstrued as an equivalent measure to infer investment rates of return. In this post, I will review existing corrective measures for IRR, which present their own challenges, and propose a fix: NAV-to-NAV IRR.
Existing IRR Corrections
The most common correction is the modified IRR (see Phalippou 2008 for a comprehensive discussion).[1] For example, Franzoni et al. (2012) use MIRR to study the determinants of the return of individual LBO investments.[2] With an MIRR, you need to choose a financing and re-investment rate. Both rates can be set to 8%, the usual hurdle rate, or to a stock market index. If intermediary cash flows are not large and the investment is held for a relatively short period of time, MIRR is fine. Thus, in a context like that of Franzoni et al. (2012), using MIRR is natural and results are insensitive to the exact reinvestment rate assumption. However, in some of the cases I reviewed previously, the holding period is long. The longest one was the 48-year track record of KKR. Over such a long period, MIRR converges to whichever reinvestment rate has been chosen, which is unappealing.
MIRR is just like a net present value (NPV) calculation. You need to choose discount rates, which is effectively the same as choosing financing and reinvestment rates. With IRR, you do not need to choose the discount rate. Just like any derivative of NPV, such as the Kaplan-Schoar Public Market Equivalent, the only conclusion that can be drawn is on relative performance. That is, if one uses an MIRR, NPV or PME, all that can be concluded is whether the benchmark has been beaten or not, but not the magnitude (alpha). We do not know how large any under- or over-performance is.
In the above example, what we calculated was an MIRR because we assumed a financing rate and a reinvestment rate and computed the rate of return ror.
Proposing a Simple, Albeit Imperfect, Fix: NAV-to-NAV IRR
My analysis so far in this series (see Part I and Part II) shows that the issue comes from early cash flows, which are high either by design (survivorship bias) or by active manipulation (exit winners quickly, use of subscription credit lines). Intuitively, a solution is a measure that takes out these early cash flows.
One option is then to require any private capital firm to report its past five-, 10-, 15-, and 20-year returns (aggregated at the level of a strategy, the whole firm, and by funds); and to forbid any use of since inception IRR. Thus, any fund or firm that is less than five years old cannot display an IRR, only a multiple. The IRR would be reported as non-meaningful.
The measure just described is called an NAV-to-NAV IRR because it takes the aggregate NAV at the beginning of the time period, treat it as an investment, record all the intermediary cash flows that occurred, treat the aggregate NAV at the end of the time period as a final distribution, and then compute the IRR on the time-series.[3] Alternative names include “horizon pooled return,” perhaps to avoid the word IRR. This measure is quite common in presentations of aggregate private capital performance.
NAV-to-NAV IRRs would be a major improvement. In a previous post, we saw that when KKR publishes a “past twenty years” IRR, their figure is around 12%. A 12% IRR is realistic because the reinvestment assumption is realistic. That 12% also squares up with its multiple. According to Preqin data, KKR’s net of fees multiple is about 1.6, which is what an investment earning 12% per annum would generate after four years, and four years is the average holding period of private equity investments.
Similarly, when Yale stopped reporting its since inception IRR, and switched to past 20 years IRR, its performance was 11.5% — a far cry from the 30% that led to the endowment being hailed an Investment Model. CalPERS, which did not experience abnormally high cash flows early on in its private equity investment program, also has a since-inception IRR of 11%. Thus, Yale and CalPERS have had similar returns in private capital. The past 20-, 15-, 10-, and five-years horizon IRRs would probably show this picture explicitly and more accurately.
Exhibit 11 shows the horizon IRRs reported by Cambridge Associates. The first two rows could be what is mandated, except for the short-term figures. A one-quarter, or even past three-years return in private markets is not meaningful because it is mostly based on the NAVs. Reported returns for private equity (only funds classified as leveraged buy-out and growth) are 18%, 16%, 16%, 15%, and 13% at 5-, 10-, 15-, 20- and 25-years horizon. These figures are reasonable.
The limits of NAV-to-NAV IRRs
The proposed solution effectively boils down to cutting the initial years. As the window moves every year, the measure cannot be gamed because the early cash flows one year no longer are the early cash flows two or three years down the line. There are two main drawbacks, however.
The first drawback is that some data is thrown away. If a fund did well between 1995 and 1999, this will not be recognized in the 2024 report because we include up to 25 years. However, these far-away results may not be relevant to judge a track record. A related issue is that if the track record for which an IRR is calculated is less than 25 years, then the first milestone should be ignored, otherwise the first NAV-to-NAV IRR is the since-inception IRR. If a track record starts in 2002, we should display the past 20, 15, 10, and five years. The past-25-year number is the since- inception IRR. Similarly, no IRR for a track record of fewer than five years would be displayed.
The second drawback is more serious and subtle. In a nutshell, if NAV is conservative, both the starting NAV and final NAV are too low. In most cases, the time value of money (cost of capital) is such that the upward bias due to the conservativeness of the initial NAV is larger than the downward bias due to the conservativeness of the final NAV. As the initial investment (i.e., initial NAV) is too low and is not fully compensated for by the final NAV bias (final NAV is also too low), the overall performance is too high.
Let us consider a simple illustrative example. Assume that at the end of each year, all the private equity funds together make 100 investments of $1 million each and hold them each for five years. They all achieve a multiple of 2, meaning that they have a geometric average return of about 15%. This pattern repeats each year and after a while, we reach a so-called steady state. Each year end, there are always 500 unexited investments (100 investments have one year to go, 100 have two years to go, etc.) Each year, the net cash flows to investors is $100 million ($200 of capital distributions from the liquidating batch, minus the $100 million of investments).
Table 6 shows the aggregate cash flows and NAVs as written by the data provider who wants to compute the “past-ten-years returns.” Each column (except the first one) corresponds to a series with a different assumption regarding the computation of NAVs. In column 2, NAVs are market values. In the steady state, each year-end the market value is the present value of receiving $200 million next year, then $200 million in two years’ time … then $200 million in five years’ time. Using a 15% discount rate, the present value of these future cash flows is $673 million. At the end of 2010, the sum of NAVs is therefore $673 million, to which we need to add the $100 million of investments and $200 million of capital distribution. The net cash flow at the end of 2010 is $773 million. Using these cash flows, the IRR is 15%, which is correct.
In column 3, NAVs are set at cost. It means that at the end of each year, the reported NAV is $500 million. The data that goes into the return computation in this case is shown in the third column of Table 6. The IRR is now exactly 20%, i.e. a 5% per annum of the true performance. This is substantial and probably a counter-intuitive result. Being conservative exaggerates performance.
Column 4 shows that if NAV is 50% of market value (hence $335 million each year) performance jumps to 30%, or twice the true return. Column 4 shows that if NAV is set to twice the cost (the gross return), performance decreases to 10%.
A practical implication is that with FAS 157, recent NAVs may be closer to market values while old NAVs are closer to cost, implying a significant upward bias in horizon IRRs.
Table 6: A simplified private equity economy
| Date | NAV marked-to-market | NAV valuation at cost | NAV half of market value | NAV twice cost |
| 31-Dec-00 | -673 | -500 | -335 | -1000 |
| 31-Dec-01 | 100 | 100 | 100 | 100 |
| 31-Dec-02 | 100 | 100 | 100 | 100 |
| 31-Dec-03 | 100 | 100 | 100 | 100 |
| 31-Dec-04 | 100 | 100 | 100 | 100 |
| 31-Dec-05 | 100 | 100 | 100 | 100 |
| 31-Dec-06 | 100 | 100 | 100 | 100 |
| 31-Dec-07 | 100 | 100 | 100 | 100 |
| 31-Dec-08 | 100 | 100 | 100 | 100 |
| 31-Dec-09 | 100 | 100 | 100 | 100 |
| 31-Dec-10 | 773 | 600 | 435 | 1100 |
| IRR | 15% | 20% | 30% | 10% |
Benchmarking Issues
The past five-, 10-, 15-, and 20- year IRRs need to be compared to a public equity benchmark. One issue is whether the benchmark returns should be the geometric ones or the arithmetic ones. In practice, most people opt to compute an IRR equivalent of a public equity benchmark. For example, Cambridge Associates calls it an mPME. In Exhibit 11, we see that their mPME using Russell 3000 is 15%, 11.5%, 14.5%, 10%, and 9% (past five, 10, 15, 20, 25).
Table 7 shows the arithmetic average return for the US large-cap benchmark that is most often used in academia (Fama-French benchmarks), and we observe that they follow a similar pattern, but the academic benchmark is about 2% above the mPME at each horizon. The mPME of the Russell 2000, which is supposed to capture small- and mid-cap stock returns is 10%, 7%, 12.5%, 8.5%, 8.5%. This one is about 3% below the Fama-French benchmarks. Exhibit 12 shows a similar computation by another industry player. They report 11% return, again a figure much more in line with public equity and more sensible than those reviewed above.
Part of the discrepancy between the public equity returns in Table 7 and the mPME is due to the difference between arithmetic and geometric return. IRR, and thus mPME, is expected to be closer to a geometric return. Another issue, which is seldom acknowledged, but significant, is that not all stock indices have the same returns, even when they aim to capture the same market (e.g. large cap US stocks). As a result, it is possible to strategically choose the stock index with the lowest performance.
MSCI and Russell indices, for example, are often those with the lowest returns. This may explain their long-lasting popularity as benchmarks. As mentioned above, in academia, the Fama-French benchmarks are used. The hundreds of papers evaluating the performance of actively managed mutual funds, hedge funds and other asset classes have nearly all used Fama-French benchmarks.
Finally, it is important to establish some rules regarding the public market that is chosen as a comparison. For example, in Exhibit 12 below, the return that pension funds obtained in private equity is compared to what they obtained in public equity and the spread is large: 11% versus 7%. Note in passing that the return obtained by private equity investor on average is once again around 11%, and thus far away from the figures shown in Exhibits 1-9, which I first referenced in Part I of this series. The issue here is that the pension fund public equity portfolio is much less exposed to the US market than the private equity one. Over the last 20 years, European stocks had poor returns. This alone explains most of the spread.
Similarly, private equity investments in certain industries are taken out of the private equity indices (e.g., commodities, real estate, oil and gas). However, these sectors are kept in the public equity benchmarks that are used. Coincidentally perhaps, these sectors have much lower returns than the average (over the last 10 and 20 years). Moreover, this reclassification seems to have been made ex post.
Key Takeaways
The rise of private capital and private investments (together private markets) has been obvious over the past two decades, in terms of global AUM. One major issue that explains this trend is the reliance on IRR to present the performance of private market funds.
- IRR should not be misconstrued as equivalent to a rate of return.
- IRR is a discount rate used to make the NPV of an investment equal to zero. It is based on the assumption that the rate of return at which all intermediary cash flows (distributions) are reinvested is equal to the IRR.
- Because IRR is driven by early distributions, fund managers can strategically manipulate IRR.
- The most common correction for IRR is modified IRR, which uses pre-determined levels for a financing and reinvestment rates to compute the overall rate of return.
- The issue remains with early cash flows, which can distort the resulting rate of return.
- One solution is to require private capital firms to report a set series of past returns and to forbid the use of since-inception IRRs. This alternative measure is called an NAV-to-NAV IRR. It considers the aggregate NAV at the beginning of the time period, treats it as an investment, records all the intermediary cash flows that occurred, treat the aggregate NAV at the end of the time period as a final distribution, and then compute the IRR on the time-series. The main idea with this solution is to remove the distorting effect from considering the initial years of a fund’s life.
- An obvious drawback from this method is that portions of the data series are dismissed.
- Another drawback is that the resulting rate of return depends on the quality (whether optimistic or conservative) of the evaluation made for the starting NAV and final NAV.
[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1111796
[2] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1517044
[3] Note that if all investments are exited then you do not need the final NAV, but this is never the case at the firm level, rarely the case at the fund level (most investments are exited by year 10 but some investments are kept until year 15-20), and more common at the investment level.
This is the final post in my three-part series on performance measurement for private market funds and the difficulties of using the internal rate of return (IRR) measure as equivalent to a rate of return on investments. In Part I, I discussed the rise of global assets under management (AUM) in private market funds and how this trend may have been driven by a perception of superior returns compared to traditional investments. As I illustrated, a root cause for this belief is the generalized use of IRR to infer rates of return, which is problematic.
In Part II, I discussed in more detail how IRR works and why it should not be misconstrued as an equivalent measure to infer investment rates of return. In this post, I will review existing corrective measures for IRR, which present their own challenges, and propose a fix: NAV-to-NAV IRR.
Existing IRR Corrections
The most common correction is the modified IRR (see Phalippou 2008 for a comprehensive discussion).[1] For example, Franzoni et al. (2012) use MIRR to study the determinants of the return of individual LBO investments.[2] With an MIRR, you need to choose a financing and re-investment rate. Both rates can be set to 8%, the usual hurdle rate, or to a stock market index. If intermediary cash flows are not large and the investment is held for a relatively short period of time, MIRR is fine. Thus, in a context like that of Franzoni et al. (2012), using MIRR is natural and results are insensitive to the exact reinvestment rate assumption. However, in some of the cases I reviewed previously, the holding period is long. The longest one was the 48-year track record of KKR. Over such a long period, MIRR converges to whichever reinvestment rate has been chosen, which is unappealing.
MIRR is just like a net present value (NPV) calculation. You need to choose discount rates, which is effectively the same as choosing financing and reinvestment rates. With IRR, you do not need to choose the discount rate. Just like any derivative of NPV, such as the Kaplan-Schoar Public Market Equivalent, the only conclusion that can be drawn is on relative performance. That is, if one uses an MIRR, NPV or PME, all that can be concluded is whether the benchmark has been beaten or not, but not the magnitude (alpha). We do not know how large any under- or over-performance is.
In the above example, what we calculated was an MIRR because we assumed a financing rate and a reinvestment rate and computed the rate of return ror.
Proposing a Simple, Albeit Imperfect, Fix: NAV-to-NAV IRR
My analysis so far in this series (see Part I and Part II) shows that the issue comes from early cash flows, which are high either by design (survivorship bias) or by active manipulation (exit winners quickly, use of subscription credit lines). Intuitively, a solution is a measure that takes out these early cash flows.
One option is then to require any private capital firm to report its past five-, 10-, 15-, and 20-year returns (aggregated at the level of a strategy, the whole firm, and by funds); and to forbid any use of since inception IRR. Thus, any fund or firm that is less than five years old cannot display an IRR, only a multiple. The IRR would be reported as non-meaningful.
The measure just described is called an NAV-to-NAV IRR because it takes the aggregate NAV at the beginning of the time period, treat it as an investment, record all the intermediary cash flows that occurred, treat the aggregate NAV at the end of the time period as a final distribution, and then compute the IRR on the time-series.[3] Alternative names include “horizon pooled return,” perhaps to avoid the word IRR. This measure is quite common in presentations of aggregate private capital performance.
NAV-to-NAV IRRs would be a major improvement. In a previous post, we saw that when KKR publishes a “past twenty years” IRR, their figure is around 12%. A 12% IRR is realistic because the reinvestment assumption is realistic. That 12% also squares up with its multiple. According to Preqin data, KKR’s net of fees multiple is about 1.6, which is what an investment earning 12% per annum would generate after four years, and four years is the average holding period of private equity investments.
Similarly, when Yale stopped reporting its since inception IRR, and switched to past 20 years IRR, its performance was 11.5% — a far cry from the 30% that led to the endowment being hailed an Investment Model. CalPERS, which did not experience abnormally high cash flows early on in its private equity investment program, also has a since-inception IRR of 11%. Thus, Yale and CalPERS have had similar returns in private capital. The past 20-, 15-, 10-, and five-years horizon IRRs would probably show this picture explicitly and more accurately.
Exhibit 11 shows the horizon IRRs reported by Cambridge Associates. The first two rows could be what is mandated, except for the short-term figures. A one-quarter, or even past three-years return in private markets is not meaningful because it is mostly based on the NAVs. Reported returns for private equity (only funds classified as leveraged buy-out and growth) are 18%, 16%, 16%, 15%, and 13% at 5-, 10-, 15-, 20- and 25-years horizon. These figures are reasonable.
The limits of NAV-to-NAV IRRs
The proposed solution effectively boils down to cutting the initial years. As the window moves every year, the measure cannot be gamed because the early cash flows one year no longer are the early cash flows two or three years down the line. There are two main drawbacks, however.
The first drawback is that some data is thrown away. If a fund did well between 1995 and 1999, this will not be recognized in the 2024 report because we include up to 25 years. However, these far-away results may not be relevant to judge a track record. A related issue is that if the track record for which an IRR is calculated is less than 25 years, then the first milestone should be ignored, otherwise the first NAV-to-NAV IRR is the since-inception IRR. If a track record starts in 2002, we should display the past 20, 15, 10, and five years. The past-25-year number is the since- inception IRR. Similarly, no IRR for a track record of fewer than five years would be displayed.
The second drawback is more serious and subtle. In a nutshell, if NAV is conservative, both the starting NAV and final NAV are too low. In most cases, the time value of money (cost of capital) is such that the upward bias due to the conservativeness of the initial NAV is larger than the downward bias due to the conservativeness of the final NAV. As the initial investment (i.e., initial NAV) is too low and is not fully compensated for by the final NAV bias (final NAV is also too low), the overall performance is too high.
Let us consider a simple illustrative example. Assume that at the end of each year, all the private equity funds together make 100 investments of $1 million each and hold them each for five years. They all achieve a multiple of 2, meaning that they have a geometric average return of about 15%. This pattern repeats each year and after a while, we reach a so-called steady state. Each year end, there are always 500 unexited investments (100 investments have one year to go, 100 have two years to go, etc.) Each year, the net cash flows to investors is $100 million ($200 of capital distributions from the liquidating batch, minus the $100 million of investments).
Table 6 shows the aggregate cash flows and NAVs as written by the data provider who wants to compute the “past-ten-years returns.” Each column (except the first one) corresponds to a series with a different assumption regarding the computation of NAVs. In column 2, NAVs are market values. In the steady state, each year-end the market value is the present value of receiving $200 million next year, then $200 million in two years’ time … then $200 million in five years’ time. Using a 15% discount rate, the present value of these future cash flows is $673 million. At the end of 2010, the sum of NAVs is therefore $673 million, to which we need to add the $100 million of investments and $200 million of capital distribution. The net cash flow at the end of 2010 is $773 million. Using these cash flows, the IRR is 15%, which is correct.
In column 3, NAVs are set at cost. It means that at the end of each year, the reported NAV is $500 million. The data that goes into the return computation in this case is shown in the third column of Table 6. The IRR is now exactly 20%, i.e. a 5% per annum of the true performance. This is substantial and probably a counter-intuitive result. Being conservative exaggerates performance.
Column 4 shows that if NAV is 50% of market value (hence $335 million each year) performance jumps to 30%, or twice the true return. Column 4 shows that if NAV is set to twice the cost (the gross return), performance decreases to 10%.
A practical implication is that with FAS 157, recent NAVs may be closer to market values while old NAVs are closer to cost, implying a significant upward bias in horizon IRRs.
Table 6: A simplified private equity economy
| Date | NAV marked-to-market | NAV valuation at cost | NAV half of market value | NAV twice cost |
| 31-Dec-00 | -673 | -500 | -335 | -1000 |
| 31-Dec-01 | 100 | 100 | 100 | 100 |
| 31-Dec-02 | 100 | 100 | 100 | 100 |
| 31-Dec-03 | 100 | 100 | 100 | 100 |
| 31-Dec-04 | 100 | 100 | 100 | 100 |
| 31-Dec-05 | 100 | 100 | 100 | 100 |
| 31-Dec-06 | 100 | 100 | 100 | 100 |
| 31-Dec-07 | 100 | 100 | 100 | 100 |
| 31-Dec-08 | 100 | 100 | 100 | 100 |
| 31-Dec-09 | 100 | 100 | 100 | 100 |
| 31-Dec-10 | 773 | 600 | 435 | 1100 |
| IRR | 15% | 20% | 30% | 10% |
Benchmarking Issues
The past five-, 10-, 15-, and 20- year IRRs need to be compared to a public equity benchmark. One issue is whether the benchmark returns should be the geometric ones or the arithmetic ones. In practice, most people opt to compute an IRR equivalent of a public equity benchmark. For example, Cambridge Associates calls it an mPME. In Exhibit 11, we see that their mPME using Russell 3000 is 15%, 11.5%, 14.5%, 10%, and 9% (past five, 10, 15, 20, 25).
Table 7 shows the arithmetic average return for the US large-cap benchmark that is most often used in academia (Fama-French benchmarks), and we observe that they follow a similar pattern, but the academic benchmark is about 2% above the mPME at each horizon. The mPME of the Russell 2000, which is supposed to capture small- and mid-cap stock returns is 10%, 7%, 12.5%, 8.5%, 8.5%. This one is about 3% below the Fama-French benchmarks. Exhibit 12 shows a similar computation by another industry player. They report 11% return, again a figure much more in line with public equity and more sensible than those reviewed above.
Part of the discrepancy between the public equity returns in Table 7 and the mPME is due to the difference between arithmetic and geometric return. IRR, and thus mPME, is expected to be closer to a geometric return. Another issue, which is seldom acknowledged, but significant, is that not all stock indices have the same returns, even when they aim to capture the same market (e.g. large cap US stocks). As a result, it is possible to strategically choose the stock index with the lowest performance.
MSCI and Russell indices, for example, are often those with the lowest returns. This may explain their long-lasting popularity as benchmarks. As mentioned above, in academia, the Fama-French benchmarks are used. The hundreds of papers evaluating the performance of actively managed mutual funds, hedge funds and other asset classes have nearly all used Fama-French benchmarks.
Finally, it is important to establish some rules regarding the public market that is chosen as a comparison. For example, in Exhibit 12 below, the return that pension funds obtained in private equity is compared to what they obtained in public equity and the spread is large: 11% versus 7%. Note in passing that the return obtained by private equity investor on average is once again around 11%, and thus far away from the figures shown in Exhibits 1-9, which I first referenced in Part I of this series. The issue here is that the pension fund public equity portfolio is much less exposed to the US market than the private equity one. Over the last 20 years, European stocks had poor returns. This alone explains most of the spread.
Similarly, private equity investments in certain industries are taken out of the private equity indices (e.g., commodities, real estate, oil and gas). However, these sectors are kept in the public equity benchmarks that are used. Coincidentally perhaps, these sectors have much lower returns than the average (over the last 10 and 20 years). Moreover, this reclassification seems to have been made ex post.
Key Takeaways
The rise of private capital and private investments (together private markets) has been obvious over the past two decades, in terms of global AUM. One major issue that explains this trend is the reliance on IRR to present the performance of private market funds.
- IRR should not be misconstrued as equivalent to a rate of return.
- IRR is a discount rate used to make the NPV of an investment equal to zero. It is based on the assumption that the rate of return at which all intermediary cash flows (distributions) are reinvested is equal to the IRR.
- Because IRR is driven by early distributions, fund managers can strategically manipulate IRR.
- The most common correction for IRR is modified IRR, which uses pre-determined levels for a financing and reinvestment rates to compute the overall rate of return.
- The issue remains with early cash flows, which can distort the resulting rate of return.
- One solution is to require private capital firms to report a set series of past returns and to forbid the use of since-inception IRRs. This alternative measure is called an NAV-to-NAV IRR. It considers the aggregate NAV at the beginning of the time period, treats it as an investment, records all the intermediary cash flows that occurred, treat the aggregate NAV at the end of the time period as a final distribution, and then compute the IRR on the time-series. The main idea with this solution is to remove the distorting effect from considering the initial years of a fund’s life.
- An obvious drawback from this method is that portions of the data series are dismissed.
- Another drawback is that the resulting rate of return depends on the quality (whether optimistic or conservative) of the evaluation made for the starting NAV and final NAV.
[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1111796
[2] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1517044
[3] Note that if all investments are exited then you do not need the final NAV, but this is never the case at the firm level, rarely the case at the fund level (most investments are exited by year 10 but some investments are kept until year 15-20), and more common at the investment level.
