Comparing Private Equity and Public Equity Returns When Building Multi-Asset Portfolios

Public equity and private equity (PE) returns each reflect the future profit-generation capabilities of operating businesses. However, the different ways in which public and private companies are valued produce a meaningful mismatch in returns. For instance, in 2015, global publicly traded equities (as measured by the MSCI ACWI) fell 4.3%, while private equity rose 6.0%, as measured by the State Street Private Equity (SSPE) index. Conversely, in 2009, public equity rose 31.5% versus 12.3% for private equity.

One can debate which valuation methodology is more representative of true economic value. For example, was Facebook, a company with $40 billion to $50 billion in revenues, really worth 20% less on July 25 than on July 24 before it announced results? Or are private companies’ appraisal-based valuations too backward looking and uncannily smooth? Regardless of where one lands in this debate, it is necessary when constructing multi-asset portfolios to equalize public and private valuation methodologies in order to make the appropriate assessments for portfolio construction.

Making Public and Private Returns Comparable

We can adjust both public equity and private equity returns to make them more comparable. The volatility and overreactions inherent in public equity returns are easier to address. By using less frequent measures of public equity returns — perhaps looking at month-end or quarter-end values rather than daily or minute-by-minute numbers — we smooth these returns.

Devising a methodology to de-smooth private equity returns is more complicated. The use of appraisals to set the values of private equity companies between market transactions (e.g., purchases or sales of companies) often produces backward-looking valuations. Valuation committees and other assessors look to historic multiples of comparable companies to determine quarterly marks and thus performance.

By developing a quantitative model that accounts for lags in PE valuations, we can make PE returns less smooth and thus more comparable to our periodic public equity returns. We will then have return series with which we can more readily calculate the statistics required for many portfolio construction processes. These include betas, alphas, correlations and common factors underlying PE performance.

By developing a quantitative model that accounts for lags in private equity (PE) valuations, we can make PE returns less smooth and thus more comparable to our periodic public equity returns.

De-smoothing Private Equity Returns

Fortunately, there is a robust body of research on this topic of de-smoothing and disaggregating returns — by Geltner [1991] and Pedersen [2014], among others — on which we have been able to build. Our work has made three substantive contributions. First, we have developed an integrated model (see Rudin [2018]) that eliminates the autocorrelation effects present in earlier formulations, thus simplifying the regression process and producing a more robust output (see Figure 1).

For those interested in the development and mechanics of this formulation, our 2018 paper provides an in-depth explanation.

Our second contribution relates to how to use this regression in the most robust way possible. One key decision is how many lags should be utilized in calculating the regression. Our model and those of others allow for an unlimited number of lags. Prior researchers have typically found that more lags produced a tighter result. Our research benefited from access to an extensive database of private equity returns, the 2800+ individual PE fund returns that underlie the SSPE index. By devising mini-programs of randomly selected, equal-weighted fund programs, we were able to conduct out-of-sample tests on the robustness of our regression formula. We found that a one-lag calculation was optimal. Two or more lags produced over-fitted results that introduced new risks.

SSPE index data also provided the basis on which we made our third contribution. We took the index’s constituent information and developed a model to determine the optimal number of private equity commitments for a portfolio. The model starts by quantifying the idiosyncratic risks that accompany a particular number of private equity commitments. Our model then balances the advantages of diversification, which enables portfolio sponsors to access the benefits of private equity while limiting idiosyncratic risk, and the costs of adding more funds to a PE program. Since the benefits of diversification and the costs of additional commitments will depend on each individual portfolio and organization, we are working with clients to apply the model to their individual situations.

The Importance of Time Frames

Another important dimension of private equity investing is time. Time frames, particularly how frequently portfolios will be assessed, are important in determining the right amount of de-smoothing. For a single-lag smoothing model, we were able to calculate the adjustment in risk as time progresses (see Figure 2) (Rudin paper [2018 B]).

For shorter time horizons, the total equity risks from a mixed public/private portfolio will be dominated by gyrations in the public component. For longer time horizons (5+ years), public and private investments will contribute similarly. For an intermediary horizon, the private equity contribution to the total equity risk grows as the time horizon increases.

Time frames, particularly how frequently portfolios will be assessed, are important in determining the right amount of de-smoothing.

What are the Implications for Portfolio Construction?

By de-smoothing private equity returns and smoothing public ones, we can create enough commonality between these return streams to make useful comparisons when constructing portfolios. We can also determine the contributions of public and private equity allocations to overall portfolio characteristics, helping portfolio managers to make appropriate trade-offs between allocations to each.

Using our de-smoothing methodology on the SSPE index with the most robust one-lag calculation, we find that SSPE had a 0.5 beta to the S&P500, with alpha of 4.6%. This result may surprise those who think of PE as levered equity and thus expected PE to have a de-smoothed beta in excess of 1. Given the tools available to private equity managers, including operational improvements, leverage, dividend recapitalizations and the timing of purchases and sales, we believe this outcome makes sense. It also makes private equity appear an attractive option for those investor portfolios that can handle the illiquidity, a dimension that de-smoothing methodology does not capture.

Our research also shows that determining how much to allocate to private equity depends not only on the rest of one’s portfolio — its risk/return characteristics, investor tolerance for illiquidity and the costs of adding PE funds — but also on the time frame for portfolio assessment. Comparing public and private equity returns over a given time frame can help investors build a multi-asset portfolio with a mixture of public and private equity allocations that are best suited to their objectives, risk appetite and diversification requirements. 


Geltner, D. “Smoothing in Appraisal-Based Returns.” The Journal of Real Estate Finance and Economics, Vol. 4, No. 3 (1991), pp. 327­–45.

Pedersen, Niels, Sébastien Page, and Fei He. “Asset Allocation: Risk Models for Alternative Investments.” Financial Analysts Journal, Vol. 70, No. 3 (May/June 2014), pp. 34–45.

Rudin, Alexander, Jason Mao, Nan R. Zhang, Anne-Marie Fink. “Fitting Private Equity into the Total Portfolio Framework” (Research paper, Rudin 2018).

Rudin, Alexander “Risk of Illiquid Assets and Investor Time Horizon” (Research paper, Rudin 2018 B, in progress).


Alpha: A gauge of risk-adjusted outperformance that measures the excess return of a fund relative to the return of a benchmark.

Beta: A measure of an investment’s sensitivity to market movements.

MSCI All Country World Index (ACWI): An index designed to track large and mid-cap equities across 23 Developed Market and 24 Emerging Market countries.

S&P500® Index: A market-value-weighted index of 500 stocks that reflects the performance of a large-cap universe made up of companies selected by economists.

State Street Private Equity Index: An index developed by State Street in partnership with leading academics and large asset owners. It is comprised of more than 2,800 funds representing about $2.7 trillion of capital commitments. The Index has generated quarterly results since Q3 2004 and is published approximately 100 days after quarter-end.

The private equity dataset includes Buyouts (Mega, Large, Mid-Size, Small), Venture Capital (Early, Balanced and Late Stage) and Private Debt (Distressed, Mezzanine, Special Lendings).


The views expressed in this material are the views of Alexander Rudin and Anne-Marie Fink through the period ended August 3, 2018 and are subject to change based on market and other conditions. This document contains certain statements that may be deemed forward-looking statements. Please note that any such statements are not guarantees of any future performance and actual results or developments may differ materially from those projected.

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