Blog Posts — July 27, 2022

Building a better private market factor risk model

by Bill Morokoff, PhD and Samer Nakhla

As part of the recently announced partnership between CEPRES and Qontigo, we are developing a suite of factor risk models that provide broad coverage of the private market space in Axioma RiskTM, Qontigo’s enterprise risk management platform. The models allow us to systematically decompose the risk of private asset returns into public market factor risk exposures and private asset latent factors for portfolio risk analysis across both public and private assets. In this blog, we provide an overview of the Axioma North America Buyout Factor Risk Model (NA Buyout Model) – from model methodology to fund performance results derived from the model.

As these results show in Figures 1 and 2 below, the long-term performance of buyout funds from 1997 through 2021 was spectacular, with a compounded annual growth rate of over 19% for this period.  Over the last decade, this has led to a significant increase in private equity assets under management, driven primarily by demand from asset owners in pension plans, endowments and sovereign wealth funds seeking diversification and higher yields compared to public market assets. For investors that can manage illiquidity, private assets have become an attractive option with increasing asset allocation.  While the turmoil in public equity markets in the first half of 2022 may have led to some decrease in funding for private assets, investment is still running ahead of the five-year average1. Understanding the connection between the risks of the public and private markets has become more important than ever.

The CEPRES-Qontigo approach for the Axioma Private Market Factor Risk Models

Modeling the risk of private assets in a multi-asset class portfolio is notoriously difficult due to the lack of observable, market-traded returns from which volatilities and correlations with other risk factors can be estimated. A standard approach is to estimate fund returns from quarterly net asset value (NAV) assessments provided by fund managers. As fund NAVs are manager-reported rather than derived from traded markets, they are well known to be overly stable from quarter to quarter; therefore, to get a more realistic picture of risk, it is necessary to artificially re-introduce the hidden volatility through a method called de-smoothing. This process requires a somewhat arbitrary component that limits the accuracy of subsequent risk analysis.

For Axioma Private Market Factor Risk Models, we instead choose to work with verified fund cash flow data corresponding to fund investments and distributions. CEPRES has been collecting this verified data directly from GPs for over 20 years and has historical coverage of almost 11,000 funds, representing more 105,000 PE-backed assets and more than 1 million proprietary cash flows. Following a methodology described in Ang et al.2, we use the cash flows for funds in an estimation universe for a specified private asset category to imply monthly returns as discount factors. For example, for North America buyout funds, we use a model estimation universe of over 600 funds going back to 1997 to derive the historical monthly private equity returns. The private fund returns are then regressed as a time series on a curated set of public market factor returns to estimate beta exposures and a latent private asset factor residual. 

The actual methodology is significantly more complex, as the fund cash flows admit a probability distribution of monthly returns with nonlinear dependence on the public factor returns. Solving for the public factor betas consistent with the return distribution requires a Bayesian approach employing a Markov Chain Monte Carlo simulation. Great care must be taken in factor selection to ensure the factors are statistically significant in explaining the private asset returns and to maintain stability of the beta exposures over subsets of the estimation universe.  

The Axioma North America Buyout Factor Risk Model: Factor selection and insight

For the NA Buyout Model, we use five public market factors. The first four are taken from the Axioma North America Fundamental Equity Factor Risk Model – Medium Horizon (AXNA4). These consist of the market intercept factor and the Value, Size and Momentum style factors. The AXNA4 returns are estimated through a daily cross-sectional regression on an estimation universe of publicly trade US and Canadian listed equities. The style factor returns are estimated in excess of the market intercept return to minimize collinearity. The fifth public factor is derived from the Axioma Credit Spread Curve for USD All-Sector BBB3 bonds as the residual spread return after regression on the market intercept factor return. All these factors are highly statistically significant in the sense that the absolute value of each factor’s t-statistic is greater than 2 in over 80% of the Monte Carlo simulation sample runs with the market intercept factor’s t-statistic being greater than 2 in 100% of the samples.

The significance of the market intercept factor, which acts as a broad market cap-weighted measure of the public market performance, is intuitive in explaining private equity fund performance. Numerous other public market equity style factors were evaluated. Some, such as Market Beta and Volatility, were found to be too correlated with the market intercept in the time series to provide a distinct, significant signal to explain private fund returns. Others, such as Profitability, did not have strong regression coefficients that were clearly statistically different from zero. Given that buyout funds often focus on undervalued, consistently improving companies which tend to be smaller compared to the overall public market universe, it is not surprising that Value, Momentum and Size proved to be important factors in the model. The final factor, the residual credit spread return relative to the market intercept factor, reflects the relative demand for debt vs. equity which has been discussed in the finance literature3 as a source of private equity performance.

Figure 1 shows the cumulative NA Buyout Model implied returns as estimated by this methodology from January 1997 through September 2021, with the cumulative return of the S&P 500, including dividends, plotted for comparison. Clearly, the buyout funds show exceptional performance over this period, with a compound annual growth rate of 19.3% compared with 9.4% for the S&P 500.

Figure 1. Cumulative returns of Axioma North America Buyout Factor Risk Model vs. S&P 500 public market returns from January 1997 through September 2021

Source: S&P, CEPRES, Qontigo.

The extraordinary performance comes at the cost of higher return volatility. Figure 2 plots the annualized trailing volatility, based on a rolling three-year period, for the North America Buyout funds on a monthly basis compared with the S&P 500 volatility over the same period.  However, the higher returns more than compensate for the additional volatility.

Figure 2. Annualized volatility of the monthly returns, based on a 3-year rolling window, for North America Buyout funds and the S&P 500

Source: S&P, CEPRES, Qontigo.

The combination of CEPRES’s extensive private asset data with Qontigo’s leading public market factors delivers unique insight into the risk of private capital funds and provides an integrated risk analytics solution for portfolios containing both public and private investments.

To learn more about the Axioma North America Buyout Factor Risk Model and new partnership with CEPRES, contact us.


1 Goldman Sachs Insights. July 13, 2022.  Can private markets resist the bear market in stocks?

2 Ang, A., Chen, B., Goetzmann, W. N., & Phalippou, L. (2018). Estimating private equity returns from limited partner cash flows. The Journal of Finance, 73(4).

3 Kaplan, Steven N., and Per Johan Strӧmberg, 2009, Leveraged buyouts and private equity, Journal of Economic Perspectives 23, 121–146.