Maximizing accuracy of Value at Risk figures through new deal-level risk model for private capital funds
Proper risk measurement for private capital funds is notoriously difficult due to the challenges associated with the asset class’s inherent illiquidity. Many applied risk calculation methods are often only heuristic or rely heavily on public market assumptions. Moreover, existing risk models in the private equity literature usually operate on fund level. These methods neglect any diversification effects on the underlying deal level by design, resulting in inaccurate risk assessments for modestly sized portfolios. Accordingly, especially General Partner (GP) portfolios [or small Limited Partner (LP) portfolios] benefit from improved risk models that incorporate deal-level information. The recently published academic paper “Modeling the exit cash flows of private equity fund investments,”1, which AssetMetrix has supported, aims at closing this methodological gap.
1 Journal of Risk, Tausch, Buchner, Schlüchtermann – Modeling the exit cash flows of private equity fund investments (2022)
The academic paper, published in the peer-reviewed Journal of Risk, was written by Tausch, Buchner, and Schlüchtermann. Christian Tausch is a quantitative researcher and developer at AssetMetrix GmbH. He helped to develop the full AssetMetrix analytical model suite (including Forecasting, Risk, Benchmarking, Stress Testing, and Program Planning). Axel Buchner is a Professor of Finance at the ESCP Business School in Berlin, and he has published numerous articles on advanced private equity models. Georg Schlüchtermann is a Professor of Mathematics at the University of Applied Sciences in Munich, and he also teaches at the LMU in Munich. His research focuses on stochastic methods in finance, engineering, and information systems.
The new paper develops a deal-level model for the exit cash flows of private equity funds. The novel modeling approach jointly describes portfolio companies’ exit timing and exit performance. A proprietary dataset provided by AssetMetrix is used for empirical estimation of the model parameters. Finally, a Monte Carlo simulation example analyzes risk management applications, emphasizing the deal-level diversification effects within a single fund.
Figure 1 displays the empirical cumulative distribution function (ECDF) of the multiple on invested capital (MOIC) in the Venture Capital (VC) dataset to exemplify the high risk on deal level in the private capital universe. Concretely, more than 22% of VC deals in our dataset result in a total default, which corresponds to an exit multiple of exactly zero. We apply a so-called “two-part model” to split the MOIC distribution in a Probability of Default (PD) part and a parametric part for the positive exit multiples to account for these high default ratios. As a potential simpler alternative, traditional return distributions like the normal or lognormal distribution cannot reflect the zero-heavy nature of private capital deal multiples and thus are not suitable for risk management on deal level. Consequently, once again, the uniqueness of the private capital asset class calls for a bespoke model to ensure realistic risk results.
Figure 1: Empirical cumulative distribution function (ECDF) of exit multiple of VC deals.
The AssetMetrix analytics team incorporates the main insights from the paper in their established risk module. The same “two-part modelling” idea is applied to an extended dataset to develop a tailored deal-level risk model that can provide 95%, 99%, and 99.5% Value at Risk figures for one- and three-year horizons. The new and improved model is perfectly compatible with the existing AssetMetrix fund-level risk model and thus can also handle mixed portfolios (consisting of deals and funds on the same level). Consequently, our risk engine can provide realistic risk figures even for complex portfolio structures with several investment layers.
Our model accounts for diversification effects between funds and/or deals for multiple dimensions like vintage year, fund segment, region, industry, and currency. To better understand the risk contributions of the individual portfolio components, additional analyses like a Marginal Value at Risk attribution can be easily performed on top of the newly refined model output. Moreover, we designed the risk model to require only a minimum amount of input data to increase the robustness of the risk assessment. Finally, due to the general data scarcity in the private capital environment, the initial model calibration is accompanied by annual backtesting exercises to validate the model results constantly.
Importantly, our new model enables a look-through approach (to the underlying deal level), which regulatory frameworks like Solvency II and Basel III highly encourage. Nevertheless, we can also run the risk model on several levels in parallel (e.g. on fund-of-fund, fund, and deal level) to compare these different results and assess their suitability on this new increased data basis.
To conclude, the new deal-level risk model is especially interesting for GP portfolios that are by design only modestly diversified (as GPs usually hold more concentrated portfolios than LPs). However, LPs with a decent number of direct investments (or a young private capital program) might also benefit from the higher accuracy achieved by the new model extension.