Rethinking Risk: How Diversification Amplifies Selection Skill

PRIVATE MARKETS INSIGHTS RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL

>>Our analysis suggests that both improbably The first paper in our Rethinking Risk series demonstrated that diversified private equity portfolios yield better risk- good fund selection abilities and access to the adjusted returns than concentrated portfolios. It did not, best-performing funds are necessary for an investor however, address the potential impact of investment skill with a concentrated private equity portfolio to match upon those returns. This paper therefore looks to quantify the effect of fund selection skill on investment returns – assuming the risk-adjusted returns from a randomly selected an investor is able to access their selected funds – and diversified one. compare this effect to that of diversification.

>>Our modeling shows that, irrespective of skill level, It is well established that skillful manager selection is crucial when investing in private markets, given the wide dispersion investors have been able to materially improve of returns relative to public markets. The benefits of selection risk-adjusted portfolio returns via diversification. skill increase as the dispersion of outcomes grows. In private equity, for example, where top and bottom quartile five-year In effect, diversification has been shown to amplify annual returns commonly differ by more than 20 percentage the benefits of skill. points (pp), selection skill is clearly more valuable than among mutual funds, where the spread may be much narrower (see Chart 1).

This is the second in a series of papers sharing HarbourVest’s insights into portfolio construction and risk in the context of private markets. The first paper, entitled The Myth of Over-diversification, focused on the improved risk-adjusted returns provided by diversification.

MAY 2019 45 45 40 90 40 80 35 35 0 30 30 0

5 5 50 0 Private Markets INSIGHTS 0 40 obability Density 15 30 obability Density 15 obability Density P r P r 10 P r 0 10 5 10 5 0 0 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x DPI Multiple at Maturity DPIHowever, Multiple atthis Maturity paper shows that relying on selection skill CHART 1: Return dispersionDPI Multiple much at Maturity greater in oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture oncentrated 0pp Skill US uyout aloneoncentr createsated 10pp aSkill much US uyout riskier portfolioiversified and0pp Skill is USnot uyout a substitute oncentrprivateated 10pp equity Skill US Venturethan in publiciversified markets 10pp Skill US Venture for diversification. To match the risk-adjusted returns from a 10-year annual returns from US private equity funds diversified portfolio would require an improbably high level of and US mutual funds by performance percentile skill for those pursuing a concentrated approach. Furthermore, selection skill is best used to construct a diversified 50 90 portfolio, which produces strong risk-adjusted returns when 1st uartile compared to an equivalent concentrated portfolio (as expressed 40 nd uartile 80 3rd uartile by the Sortino Ratio, see “Better risk measures for private equity” 4th uartile 1 0 on p. 14). Assuming that an investor can utilize their talent by 30 accessing and investing with the best managers, diversification 90 0 amplifies the impact of skillful selection. 80 0 0 50 ANALYTICAL FRAMEWORK 0 40 10 50 HOW TO MEASURE AND QUANTIFY SELECTION SKILL 30 40 In his 1988 book, “A Random Walk Down Wall Street”, Princeton 0 30 obability Density obability Density 0 Professor Burton Malkiel speculated that, “A blindfolded monkey P r

P r 0 throwing darts at a newspaper’s financial pages could select a -10 10 10 portfolio that would do just as well as one carefully selected by 0 0 experts”. To test this hypothesis, the Wall Street Journal ran -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 100 stock picking contests,.5 pitting3 a group3.5 of four professional4 DPI Multiple at Maturity (“skilled”)DPI Multiple investors at Maturity against the newspaper staff, who selected -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended four stocksiversified by 10pp throwing Skill lended a dart at a iversifieddartboard. 0pp Skill lended US Equity Mutual Funds US Private Equity The professionals won 61 times, outperforming the random portfolio selection approach, but later peer-reviewed research US equity data sources: Bloomberg, MorningStar. US Equity Mutual Funds demonstrated that the professional investors did not meaningfully data 10-Year annualized total returns, filtered for Bloomberg’s primary 2 share class. Returns are simple averages, using latest publically available outperform the broader market. Indeed, assessing performance data as of April 2, 2019; US private equity data source: Burgiss. US 10 10 against the average return from the specific asset class is10 a Private Equity data 10-Year net-to-LP IRRs as of September 30, 2018. 9 9 far more meaningful method of comparison. In this case, the9 8 8 professionals only beat the Dow Jones Industrial Average in8 51 of the 100 trials. For private markets, we can perform this same type of analysis by comparing returns from a specific fund portfolio against a 5 5 control portfolio in which each asset held has an equal chance5 4 4 of being in the top- or bottom-half in terms of returns. A good4 Sortino Ratio Sortino Ratio way to imagine this is to think of each fund selection as Sortino Ratio being 3 3 3 determined by a coin flip. If the coin comes up heads, the investor buys an asset that will be a top-half performer. If it comes 1 1 up tails, they buy a bottom-half asset. Skill – in this model 1– therefore effectively means being able to consistently flip more 0 0 heads than tails by using a weighted coin. The level of skill0 is 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40 the difference between the percentage of heads flipped and the Skill (pp) Skill (pp) Skill (pp) average (50%). oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

1. 1. 1 Sortino Ratio = E[R – MAR]/DD, where E = expected; R = expected return;1. MAR = minimum acceptable return; DD = downside deviation 2 Liang, Bing (1996) The “Dartboard” Column: The Pros, the Darts, and the Market. The research also found that, after careful statistical scrutiny, the professional 1.5 1.5 selections were not materially better than the dart throwers. 1.5

1.3 1.3 1.3 RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 2

1.1 1.1 1.1

Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

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0.5 0.5 0.5 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40 Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill Private Markets INSIGHTS

For example, a 10pp skill advantage means an investor builds portfolios with a 60% chance of each investment being a top-half performer. This does not guarantee that 60% of the assets in a particular portfolio will come from the top half, only that over the long term the proportion will converge towards this level. Using this example, this investor’s expected return from such a portfolio would be equal to:

R10pp Skill = (0.6×RTop-half funds ) + (0.4×RBottom-half funds ) where R = Expected Return. For comparison, the expected market return (i.e., from a 50-50 coin-flip approach) would be:

RMarket = (0.5×RTop-half funds ) + (0.5×RBottom-half funds ) Drawing on these two formulas, we can illustrate the mathematical reason that return dispersion matters when assessing the impact of selection skill:

R10pp Skill –RMarket = 0.1× (RTop-half funds – RBottom-half funds ) What this formula shows is that not only will wise fund selection help this investor outperform the market, but that the impact of their selection skill will increase in line with the dispersion of returns between good and bad assets. An important caveat to any investment analysis is that a strategy is only as good as your ability to execute it. In private markets, selecting quality funds does not necessarily mean you can actually invest in them. The implications of this will become clear in our analysis.

SIMULATION METHODOLOGY Our analysis is based on 23 years of private equity fund performance data.3 In this case, this encompasses more than 1,400 mature funds drawn from HarbourVest’s proprietary historical dataset of investment and due diligence data, supplemented by publicly available sources.4 Using this historical return data, we performed a backtest to assess the effect of selection skill on portfolio performance.5 This backtest used Monte Carlo simulations (each run 10,000 times) to model portfolios of US venture and US buyout funds, calculating expected return outcomes and producing measures of downside risk. We modeled these funds in concentrated and diversified portfolios with different levels of selection skill, and created a blended portfolio combining the two strategies (see Chart 2 on page 5).

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 3 Private Markets INSIGHTS

These model portfolios were simulated as evenly-paced allocations over consecutive three-year periods to account for the impact of the macroeconomic environment across different cycles.7 We assumed that each fund was chosen with an equal level of skill throughout each simulation, irrespective of previous selection decisions, and that our model investor was able to access all assets selected. Our simulation produced probability density graphs highlighting the likelihood of each Distributed to Paid-In Capital (DPI) Multiple at portfolio maturity.8 We also calculated the median expected return and Sortino Ratio, as well as the Expected Shortfall at the 95th percentile level (shortened to Expected Shortfall 95%), which measures the average expected return in the worst 5% of modeled scenarios. The Sortino Ratios for the different asset classes were calculated using a minimum acceptable return (MAR) of 1.5x.

CHART 2: Buyout Venture Blended Portfolio configurations in Concentrated 3 partnerships 3 partnerships 3 buyout partnerships our backtest 3 venture partnerships

Diversified 24 partnerships 24 partnerships 24 buyout partnerships 24 venture partnerships

3 Description of the HarbourVest data set may be found below each of the subsequent charts 4 Mature funds defined as funds that have distributed more than 80% of their total value to investors 5 A backtest is a simulation of an investment strategy used to calculate the returns such a strategy would have generated if it had been employed over a specified historical time period. It is important to note that these precise investment strategies cannot be reproduced in practice and were designed to evaluate the possible effect of skill, in the absence of access constraints, on investment outcomes. 6 A Monte Carlo Simulation is a mathematical technique to account for the inherent uncertainty and risk in quantitative analysis, involving repeating a calculation potentially thousands of times to produce a probability distribution. Rather than plugging in a single figure for each part of the calculation, this method uses a range of values for each input, with the frequency of usage of each value determined according to its likelihood in its own preset probability distribution. Through this approach, a Monte Carlo Simulation can estimate the likelihood of each possible potential outcome in a given scenario, instead of just producing a single estimated expected outcome. 7 Evenly-paced refers to an even commitment each year in terms of both funds and capital. Allocation timing is assigned during HarbourVest analysis. 8 DPI Multiple = Total distributions to a fund and/or investors divided by paid-in capital

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 4 Private Markets INSIGHTS

the concentrated portfolio to match the random HARD TO BEAT diversified portfolio on the basis of Sortino Ratio. DIVERSIFICATION Furthermore, the random diversified portfolio had better downside protection than even the 10pp US VENTURE skill concentrated portfolio, with a 95% Expected Our backtest, using the performance of mature US Shortfall of 0.94, against 0.65 for the skilled venture funds with vintage years from 1995 to 2010, concentrated approach. found that a randomly-constructed (“random”) diversified portfolio had a much better risk-return Our findings support the hypothesis that profile than the simulated concentrated portfolios. diversification can significantly improve median A concentrated investor would require a high degree returns when the distribution of returns is positively of skill just to match the median and risk-adjusted skewed – as Chart 3 clearly illustrates is the case for returns from a random diversified US venture US venture.9 Positively skewed distributions include portfolio (see Chart 3). a greater probability of unusually large payouts. A diversified portfolio containing multiple positively In our model, it required roughly 10.5pp extra skill skewed assets is therefore more likely to experience for the concentrated US venture portfolio to match instances of dramatic outperformance than a the random diversified US venture portfolio’s median concentrated portfolio of comparable assets. return. Approximately 8pp skill was needed for This shifts the median return upwards.

DPI Multiple CHART 3: 45 % < = 1.0x 20.35 14.12 4.23 45 Significant skill 90 40 1.0x < % <=1.5x 35.73 33.53 41.65 40 required for 80 concentrated US 35 1.5x < % <=2.0x 21.46 24.84 32.79 35 0 venture portfolio 30 % > 2.0x 22.46 27.51 21.33 30 to match 0

5 5 diversified one Median 1.42x 1.53x 1.54x 50 Modeled return 0 0 Sortino Ratio 0.20 0.38 0.34 40 probabilities of obability Density 15 Expected Shortfall 95% 0.56x 0.65x 0.94x 30 obability Density 15 concentrated US obability Density P r P r venture portfolios 10 P r 0 10 with different levels 5 5 of skill and a 10 random diversified 0 0 0 US venture portfolio 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x DPI Multiple at Maturity DPI Multiple at Maturity DPI Multiple at Maturity oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Concentrated portfolios 3 funds over 3 years; Diversified portfolio 24 funds over 3 years; DPI Multiple calculated net of general partner fees and carry and gross of HarbourVest fees and expenses. Expected Shortfall 95% represents 50 the average expected return in the lowest 5% of modeled scenarios. The graphic and data above are based on a Monte Carlo simulation. Sortino Ratio annualized for 15 years 90 1st uartile using the square root of time rule. See Appendix for more information on the construction of this simulation. Past performance is not a reliable indicator of future results. 40 nd uartile 80 3rd uartile 4th uartile 0 30

90 0 80 0 50 9 Skewness measures the degree0 of asymmetry in a distribution. Positive skew refers to a distribution where the positive, right tail is longer than the negative, left tail. In this scenario, the mean will exceed0 the median. For an example of academic literature that supports this hypothesis, see Watson, Ray & Gordon (1986) On Quantiles of Sums, 40 10 Australian & New Zealand Journal of Statistics. 50 30 40 0

30 RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page obability Density 5 obability Density 0 P r

P r 0 -10 10 10 0 0 -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 DPI Multiple at Maturity DPI Multiple at Maturity -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity

10 10 10 9 9 9 8 8 8 5 5 5 4 4 4 Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 1 1 1 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

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Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

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US BUYOUT diversified portfolio was only about 3pp. However, Unlike venture investments, the returns from US diversification sharply improved the risk-adjusted buyout funds are nearly symmetrical. The median return and significantly reduced the downside risk return for a portfolio whose underlying assets have of the portfolio (see Chart 4). symmetrical return distributions cannot be improved The random diversified US buyout portfolio had through diversification alone. As such, our simulation a far higher Expected Shortfall (1.39x vs 1.01x) found limited median return improvement from US and Sortino Ratio (2.20 vs 0.62) than the skillfully buyout portfolio diversification, but there were still invested concentrated one. To match the dramatic improvements in measures of downside diversified portfolio’s Sortino Ratio an investor risk and risk-adjusted return. with a concentrated portfolio would require skill Specifically, our backtest sampled US buyout exceeding 30pp – implying that more than 80% funds with vintage years from 1995 to 2010 and of selected funds were top-half performers. found that the skill required for the concentrated Consistent outperformance to such a degree portfolio to match the median DPI of the random is possible, yet highly unlikely.

DPI Multiple 45 % < = 1.0x 3.50 1.86 0.00 45 40 CHART 4: 90 1.0x < % <=1.5x 26.79 20.25 8.94 40 Significant skill 80 35 required for 1.5x < % <=2.0x 46.33 47.01 85.15 35 0 30 concentrated US % > 2.0x 23.38 30.88 5.91 30 buyout portfolio 0 5 Median 1.70x 1.80x 1.73x 5 to match risk- 50 0 0 return profile of 40 Sortino Ratio 0.33 0.62 2.20 obability Density diversified one obability Density 15 30 Expected Shortfall 95% 0.92x 1.01x 1.39x 15 obability Density P r Modeled return P r 10 probabilities of P r 0 10 5 concentrated US 10 5 buyout portfolios 0 with different levels 0 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x of skill and a 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x DPI Multiple at Maturity random diversified DPI Multiple at Maturity DPI Multiple at Maturity oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US VentureUS buyout portfolio oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Concentrated portfolios 3 funds over 3 years; Diversified portfolio 24 funds over 3 years; DPI Multiple calculated net of general partner fees and carry and gross of HarbourVest fees and expenses. Expected Shortfall 95% represents 50 the average expected return in the lowest90 5% of modeled scenarios. The graphic and data above are based on a Monte Carlo simulation. Sortino Ratio annualized for 15 years 1st uartile using the square root of time rule. See Appendix for more information on the construction of this simulation. Past performance is not a reliable indicator of future results. 40 nd uartile 80 3rd uartile 4th uartile 0 30

90 0 80 0 0 50 0 40 10 50 30 40 0

30 obability Density obability Density 0 P r

P r 0 -10 10 10 0 0 -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1RETHINKING 1.5 RISK: HOW DIVERSIFICATION.5 AMPLIFIES3 SELECTION3.5 SKILL4 / page 6 DPI Multiple at Maturity DPI Multiple at Maturity -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity

10 10 10 9 9 9 8 8 8 5 5 5 4 4 4 Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 1 1 1 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

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Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

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Our data shows that diversification improved DIVERSIFICATION AMPLIFIES outcomes across all our metrics for an investor THE EFFECT OF SKILL with 10pp skill in fund selection, with the diversified An investor may nevertheless still believe that portfolio producing: they possess the requisite manager selection > A higher median DPI (1.66x vs 1.53x) skill to outperform a diversified portfolio via a concentrated approach. In this section, we address > A significantly improved Sortino Ratio this hypothesis, applying the same level of skill to (0.75 vs 0.38) the two approaches to demonstrate that superior > A better Expected Shortfall 95% (1.05x vs 0.65x) outcomes are still achieved via diversification. The improved median DPI further illustrates our US VENTURE: COMPREHENSIVE argument that diversification improves outcomes RISK-RETURN IMPROVEMENT to a greater extent when the distribution of returns Using the same modeling methodology as above, is positively skewed. Meanwhile, the improved we compared the probability density of return Expected Shortfall metric reflects what is obvious outcomes from a concentrated US venture portfolio in the chart, that diversifying a US venture portfolio with those from a diversified US venture portfolio, can help reduce the likelihood of losing capital. This but this time both were built with 10pp skill in fund much-reduced downside risk underpins the sharp selection (see Chart 5). improvement in the Sortino Ratio.

DPI Multiple 45 CHART 5: 45 % < = 1.0x 14.12 0.93 40 90 Diversified US 40 80 venture portfolio 1.0x < % <=1.5x 33.53 33.02 35 has better return 35 0 1.5x < % <=2.0x 24.84 39.21 30 profile than 30 % > 2.0x 27.51 26.84 0 concentrated 5 5 50 one given equal Median 1.53x 1.66x 0 0 40 selection skill Sortino Ratio 0.38 0.75 Modeled return obability Density 15 30 obability Density 15 Expected Shortfall 95% 0.65x 1.05x obability Density P r probabilities of P r 10 P r 0 skillfully invested 10 5 10 concentrated 5 and diversified 0 0 US venture portfolios 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x DPI Multiple at Maturity DPI Multiple at Maturity DPI Multiple at Maturity oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Concentrated portfolio 3 funds over 3 years; Diversified portfolio 24 funds over 3 years; DPI50 Multiple calculated net of general partner fees and carry and gross of HarbourVest fees and expenses. Expected Shortfall 95% represents the average expected return in the lowest 5% of modeled scenarios. The graphic and data above are based on a Monte Carlo simulation. Sortino Ratio annualized for 15 years 90 using the square root of time rule. See Appendix1st for uartile more information on the construction of this simulation. Past performance is not a reliable indicator of future results. 40 nd uartile 80 3rd uartile 4th uartile 0 30

90 0 80 0 0 50 0 40 10 50 30 40 0

30 obability Density obability Density 0 P r RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 7 P r 0 -10 10 10 0 0 -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 DPI Multiple at Maturity DPI Multiple at Maturity -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity

10 10 10 9 9 9 8 8 8 5 5 5 4 4 4 Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 1 1 1 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

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Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

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45 45 40 90 40 80 35 35 The expected return in the worst 5% 0 30 30 of modeled scenarios was substantially 0

5 5 better in the diversified model. 50 0 0 40 obability Density 15 30 obability Density 15 obability Density P r P r 10 P r 0 10 5 10 5 0 0 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x DPI Multiple at Maturity DPI Multiple at Maturity US BUYOUT: IMPROVED DOWNSIDE The improvement in the median DPI in a skilled DPI Multiple at Maturity RISK MANAGEMENT oncentrated 0pp Skill US Venture diversifiedoncentra portfolioted 10pp Skill was US Venture not economicallyiversified significant 0pp Skill US V enture oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture Comparing a diversified US buyout portfolio to a (1.82x vs 1.80x) because of the near-symmetrical concentrated one, assuming both were populated return distribution of the asset class, but downside with 10pp skill in fund selection, also highlights the risk was reduced dramatically. The expected return benefits of a diversified approach (see Chart 6). in the worst 5% of modeled scenarios, represented by the Expected Shortfall at the 95th percentile level, 50 was substantially better in the diversified model. 90 1st uartile 40 nd uartile 80 3rd uartile 4th uartile DPI Multiple 0 30 CHART 6: 90 % < = 1.0x 1.86 0.00 0 Diversified US 80 1.0x < % <=1.5x 20.25 2.24 0 buyout portfolio 0 50 has better risk- 1.5x < % <=2.0x 47.01 83.53 0 10 return profile % > 2.0x 30.88 14.23 40 than equivalent 50 Median 1.80x 1.82x 30 concentrated 40 0

Sortino Ratio 0.62 7.27 obability Density portfolio 30 obability Density 0 given equal P r P r Expected Shortfall 95% 0 1.01x 1.49x -10 selection skill 10 Modeled return 10 probabilities of skillfully 0 0 -0 invested concentrated 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 and diversified US DPI Multiple at Maturity DPI Multiple at Maturity buyout portfolios -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Concentrated portfolios 3 funds over 3 years; Diversified portfolio 24 funds over 3 years; DPI Multiple calculated net of general partner fees and carry and10 gross of HarbourVest fees and expenses. Expected Shortfall 95% represents 10 10 the average expected return in the lowest 5% of modeled scenarios. The graphic and data above are based on a Monte Carlo simulation. Sortino Ratio annualized for 15 years using the square root of time rule. See Appendix for more information on the construction of this simulation.9 Past performance is not a reliable indicator of future results. 9 9 8 8 8

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 8 5 5 5 4 4 4 Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 1 1 1 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

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0. 0. 0.

45 45 40 IMPROVED90 OUTCOMES FROM As one might expect, the return distributions 40 80 exhibit characteristics of both of the underlying 35 SAMPLE BLENDED US PORTFOLIO 35 The previous0 four simulations have dealt with strategies, but the skillfully invested diversified 30 portfolio has a significantly better risk-return profile 30 diversification0 within the US buyout and US venture 5 strategies, highlighting the risk-adjusted return than its concentrated equivalent, with improved 5 50 median return, Sortino Ratio and Expected 0 improvements from diversification, irrespective of 0 skill level. 40This final simulation demonstrates that the Shortfall metrics. obability Density 15 30 obability Density 15 obability Density

P r same benefits are available for a traditional private Furthermore, the risk-adjusted returns from the P r 10 equity portfolioP r 0 that includes multiple strategies. random diversified blended portfolio were actually 10 5 5 Our final backtest10 compares returns from better than those from a concentrated version 0 blended portfolios0 with a 70% buyout and 30% constructed with superior selection skill. The 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x venture weighting.0.5x This includes1.0x two skillfully1.5x .0x random.5x diversified 3.0xportfolio had3.5x a better Sortino 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x Ratio (2.81 vs 0.89) and a much higher Expected DPI Multiple at Maturity invested portfolios – one more diversified, oneDPI Multiple at Maturity DPI Multiple at Maturity Shortall (1.41 vs 1.12). oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture more concentratedoncentr –ated and 0pp aSkill random US uyout diversified oncentr ated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture portfolio (see Chart 7).

DPI Multiple 50 CHART 7: 90 % < = 1.0x 0.77 0.00 0.00 1st uartile Diversified blended 40 nd uartile 80 1.0x < % <=1.5x 19.64 1.33 8.83 3rd uartile portfolio has better 4th uartile return profile 1.5x < % <=2.0x 52.51 82.00 80.16 0 30 than equivalent % > 2.0x 27.08 16.67 11.01 90 concentrated 0 Median 1.76x 1.79x 1.69x 80 portfolio given 0 Sortino Ratio 0.89 14.32 2.81 0 equal edge in 50 selection skill Expected Shortfall 95% 1.12x 1.52x 1.41x 10 0 Modeled return 40 50 probabilities of skillfully 30 40 invested concentrated 0 and diversified blended 30 obability Density obability Density 0 portfolios and a P r P r 0 randomly diversified -10 10 10 blended portfolio 0 0 -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 DPI Multiple at Maturity DPI Multiple at Maturity -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Blended portfolios weighted 70% buyout, 30% venture. 10 Concentrated portfolios 6 funds over 3 years (3 buyout, 310 venture); Diversified portfolio 48 funds over 3 years (24 buyout, 24 venture); DPI Multiple calculated net of 10general partner fees and carry and gross of HarbourVest fees and expenses. Expected Shortfall 95% represents the average expected return in the lowest 5% of modeled scenarios. 9 The graphic and data above are based on a Monte Carlo simulation.9 See Appendix for more information on the construction of this simulation. Sortino Ratio annualized9 for 15 years using the square root of time rule. Past performance is not a reliable indicator of future results. 8 8 8 5 5 5 4 4 4 Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 9 1 1 1 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

Skill (pp) Skill (pp) Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

1. 1. 1.

1.5 1.5 1.5

1.3 1.3 1.3

1.1 1.1 1.1

Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

0. 0. 0.

VISUALIZING THE IMPACT OF CHART 8: Summary of selection skill necessary for a concentrated portfolio to SKILL ON RETURN OUTCOMES match a randomly-created diversified portfolio Each of our backtests has shown that outperforming a randomly constructed diversified portfolio on a risk-adjusted basis is extremely difficult with a concentrated portfolio (see Chart 8). Buyout Venture The visualizations in Chart 9 show how skill incrementally improves 30pp 8pp two key risk-return profile metrics – the Sortino Ratio and the Expected Sortino Ratio Shortfall – across the three simulated portfolio types. Aside from clearly Expected Shortfall 95% 38pp 35pp highlighting the significant additional skill required for a concentrated investor to match a diversified approach, it is worth highlighting a Median 3pp 11pp couple of points made obvious in the charts: 1. The skill required for a US buyout investor following a concentrated approach to match the diversified portfolio on either metric is significant. This speaks powerfully in favor of adopting a diversified approach to buyout investing, particularly as there is little persistence in buyout fund performance, which means bridging this skill gap is improbable.10 2. The skill required for a concentrated investor to match the Sortino Ratio for a diversified US venture portfolio is much less than for US buyout. This reflects the principle articulated earlier (see “How to measure and quantify selection skill” on p. 3) that the impact of skill will scale based on the return dispersion between good and bad assets. However, it is important to note that, in contrast to buyouts, there is proven persistence in venture manager performance from fund to fund.11 In combination with typically smaller fund sizes, this means that top-performing venture funds are usually heavily oversubscribed and very difficult to access for many investors. So while the selection skill required to match the positive effects of diversification does not seem great in theory, actually accessing the funds necessary to reliably perform at this level is incredibly difficult to do and, practically speaking, impossible at scale.

Top-performing venture funds are usually heavily oversubscribed and very difficult to access for many investors.

10 See Braun, Jenkinson & Stoff (2017) How persistent is private equity performance? Evidence from deal-level data, Journal of Financial Economics. 11 See Harris, Jenkinson, Kaplan & Stucke (2014) Has Persistence Persisted in Private Equity? Evidence from Buyout and Venture Capital Funds.

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 10 45 45 40 90 40 80 35 35 0 30 30 0

5 5 50 0 0 40 obability Density 15 30 obability Density 15 obability Density P r P r 10 P r 0 10 5 10 5 0 0 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 45 DPI Multiple at Maturity DPI Multiple at Maturity 45 DPI Multiple at Maturity 40oncentr ated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture 90 oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout 40 oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture 80 35 35 0 30 30 0

5 5 50 50 0 0 4090 1st uartile obability Density 15 30 obability Density 15 nd uartile obability Density

P r 40 P r 3rd uartile 10 P r 80 10 Private Markets INSIGHTS 0 4th uartile 5 100 305 900 0 0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 00.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 4.0x 80 0 DPI Multiple at Maturity DPI Multiple at Maturity DPI Multiple at Maturity 0 50 oncentrated 0pp Skill US Venture oncentrated 10pp Skill US Venture iversified 0pp Skill US Venture oncentrated 0pp Skill US uyout oncentrated 10pp Skill US uyout iversified 0pp Skill US uyout oncentrated 10pp Skill US Venture iversified 10pp Skill US Venture 0 40 10 50 30 40 0

30 obability Density obability Density 0 P r 50 P r 0 -10 1090 1st uartile 10 CHART 9: Measuring how increasing skill impacts portfolio risk-return measures 40 nd uartile 0 How skill affects risk-return measures for different800 concentrated and diversified portfolios -0 3rd uartile 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 4th uartile DPI Multiple at Maturity 0 DPI Multiple at Maturity 30 -30 oncentrated 10pp Skill US uyout iversified 10pp Skill US uyout oncentrated 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended US Equity Mutual Funds US Private Equity 90 0 80 SORTINO RATIO 0 0 50 0 US Buyout 40 US Venture US10 Venture/Buyout Blended 50 10 30 10 10 40 0

9 obability Density 9 9 30 obability Density 0 P r

P r 0 8 8 8 -10 10 10 0 0 -0 0.5x 1.0x 1.5x .0x .5x 3.0x 3.5x 0.5 1 1.5 .5 3 3.5 4 DPI Multiple at Maturity5 5 DPI Multiple at Maturity 5 -30 oncentrated 10pp Skill US uyout 4 iversified 10pp Skill US uyout oncentrated4 10pp Skill lended iversified 10pp Skill lended iversified 0pp Skill lended 4 US Equity Mutual Funds US Private Equity Sortino Ratio Sortino Ratio Sortino Ratio 3 3 3 1 1 1 100 100 100 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40 9 9 9 Skill (pp) Skill (pp) Skill (pp) 8 8 8 oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill 5 5 5 4 4 4

Sortino Ratio 1. Sortino Ratio 1. 1.Sortino Ratio 3 3 3 1.5 1.5 1.5 1 1 1 1.3 1.3 1.3 0 0 0 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40

1.1 Skill (pp) 1.1 Skill (pp) 1.1 Skill (pp) EXPECTEDoncentr SHORTFALLated iversified 95% (DPIiversified MULTIPLE) 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill

Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9 US Buyout US Venture US Venture/Buyout Blended 0. 0. 0.

0.51. 0.51. 0.51. 0 10 0 30 40 0 10 0 30 40 0 10 0 30 40 1.5 Skill (pp) 1.5 Skill (pp) 1.5 Skill (pp) oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill oncentrated iversified iversified 0pp Skill 1.3 1.3 1.3

1.1 1.1 1.1

Expected Shortfall 0.9 Expected Shortfall 0.9 Expected Shortfall 0.9

0. 0. 0.

HarbourVest proprietary data set; Vintage years 1995-2010; Funds with residual value <20%; Residual Value = 1- (∑ Cumulative Distributions) / Total Value; Even allocation over 3 consecutive vintage years (specific timing of allocations assigned during HarbourVest analysis). Concentrated portfolios 3 funds over 3 years; Concentrated Blended portfolios 6 funds over 3 years (3 buyout, 3 venture). Diversified portfolios 24 funds over 3 years (16 buyout, 8 venture); Diversified Blended portfolios 48 funds over 3 years (24 buyout, 24 venture); Blended portfolios weighted 70% buyout, 30% venture; DPI Multiple calculated net of general partner fees and carry and gross of HarbourVest fees and expenses. Expected Shortfall 95% represents the average expected return in the lowest 5% of modeled scenarios. The graphic and data above are based on a Monte Carlo simulation. See Appendix for more information on the construction of this simulation. Past performance is not a reliable indicator of future results.

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 11 Private Markets INSIGHTS

The inherent advantages of a diversified portfolio are difficult to overcome with a concentrated approach, even with an exceptional level of investment skill.

Fund selection skill is nevertheless an invaluable OUR FINDINGS asset when investing in private markets, enhancing IN CONTEXT returns and reducing risk. However, our simulations For those familiar with the insurance market, none highlight that the inherent advantages of a diversified of our findings should come as a surprise. Indeed, portfolio are difficult to overcome with a concentrated combining skill with broad diversification is the approach, even with an exceptional level of investment foundation of many successful business models. skill. If you are truly skilled, our analysis demonstrates that you would be better off combining that skill with Insurers derive their edge from data advantages. diversification, which will likely produce portfolios with They leverage their analytical skills and information superior risk-adjusted returns and lower downside risk. resources to price each policy in their favor. There As such, our data suggests that any investor in is always the chance that individual policies may private markets, regardless of their fund selection generate a loss, but the more skilled ‘bets’ the abilities, should consider adopting a diversified insurer makes, the lower its risk of an aggregate portfolio approach. portfolio loss becomes. Greater diversification can be achieved by underwriting policies across a variety While we would never advocate aping Malkiel’s of different markets with different characteristics. monkey by selecting funds via an entirely random The large number of policies and diversified dartboard approach, we might suggest carefully exposure produces a superior risk-adjusted return. aiming plenty of darts at the highest scoring segments on the board.

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 12 Private Markets INSIGHTS Private Markets INSIGHTS

APPENDIX BETTER RISK MEASURES FOR PRIVATE EQUITY No investor is agnostic to risk, and any practical approach to private equity portfolio construction must include an accurate appraisal of risk. Standard approaches use the standard deviation of returns to measure risk, but this relies upon the assumption of a symmetrical return distribution. This therefore penalizes upside and downside deviations equally – failing to differentiate between harmful volatility and the positive volatility that generates investor returns. The distribution of returns from private equity investments is not normal, exhibiting a significant positive skew. As such, a portfolio with a larger proportion of higher returning assets will actually tend to have a higher standard deviation and erroneously appear riskier. Furthermore, methodologies that employ standard deviation use the mean return as a target return, which means they do not necessarily reflect an investor’s return needs.

RETHINKING RISK: HOW DIVERSIFICATION AMPLIFIES SELECTION SKILL / page 13 Private Markets INSIGHTS

As such, a more appropriate measure of risk for ADDITIONAL IMPORTANT INFORMATION illiquid private equity investments is downside Model performance results are inherently limited deviation, which focuses on the volatility of returns and should not be considered a reliable indicator that fall below a defined minimum acceptable of future results. No investor received the return. This addresses the issues with using indicated model performance. Certain standard deviation, as it does not rely on the faulty assumptions have been made for modeling assumption of symmetrical return distributions purposes. No representation or warranty is made or substitute average return for the investor’s as to the reasonableness of the assumptions target return. made. Changes in the assumptions may have The Sortino Ratio is a modification of the oft-deployed a material impact on the hypothetical returns Sharpe Ratio that uses downside deviation as the presented. Different model scenarios will provide measure of risk, allowing us to compare risk- different results. adjusted returns for assets with non-symmetrical return distributions, such as private equity.12 The Monte Carlo Simulations higher the Sortino Ratio the more attractive the These model (hypothetical) portfolios are intended investment’s risk-adjusted return. Using this method for illustrative purposes only. Performance allows us to approach portfolio assessment more information for each hypothetical portfolio utilized effectively, by calculating returns in relation to the a Monte Carlo Simulation and are based on the amount of bad risk assumed rather than penalizing actual cash flows of a proprietary data set that an investment equally for negative and positive includes partnership investments made by funds performance. managed by HarbourVest, along with partnership data from external sources. The capital calls and THE SORTINO RATIO distribution data are based on historic partnership investment cash flows, but does not represent Sortino Ratio = E [R – MAR] the actual experience of any investor or fund. DD The results of the simulation are impacted by Where: an uneven representation of funds with different vintage years, sizes, managers, and strategies, R = Expected Return: the annual rate of return an and a limited pool of investment cash flow data. investment is expected to generate. The actual pace and timing of cash flows is likely MAR = Minimum Acceptable Return: the minimum to be different and will be highly dependent on the acceptable return or target against which that underlying partnerships’ commitment pace, the investment is to be assessed. types of investments made by the fund(s), market conditions, and terms of any relevant management DD = Target Downside Deviation: the calculation agreements. The results presented are based of downside risk. It is determined by first effectively entirely on the output from numerous mathematical eliminating positive returns from the calculation by simulations. The simulations are unconstrained by treating them as underperformance of zero. Then the fund size, market opportunity, and minimum you take the realized returns’ underperformance commitment amount, and do not take into account relative to the MAR and calculate their deviations. the practical aspects of raising and managing a Finally, you calculate the root-mean-square of fund. The simulated hypothetical portfolio results these figures. should be used solely as a guide and should not be relied upon to manage your investments or make –1 n 2 DD = √n*∑i=1 ((min(0,xi–MAR)) investment decisions. th where xi = i return and N = total number of returns

12 Sharpe Ratio = (Expected Return – Risk-free Rate) / Return Deviation

HarbourVest is an independent, global private markets investment specialist with more than 35 years of experience and more than $50 billion in assets under management. The Firm’s powerful global platform offers clients investment opportunities through primary fund investments, secondary investments, and direct co-investments in commingled funds or separately managed accounts. HarbourVest has more than 400 employees, including more than 100 investment professionals across Asia, Europe, and the Americas. This global team has committed more than $34 billion to newly-formed funds, completed over $19 billion in secondary purchases, and invested over $8 billion directly in operating companies. Partnering with HarbourVest, clients have access to customized solutions, longstanding relationships, actionable insights, and proven results.