# Monte Carlo-style simulation analysis for private equity portfolio modeling

by Alex Billias and Jake Ledbetter

Picture this: you and a coworker are trying to decide where to get lunch. Neither of you has persuaded the other and you decide to flip a coin: heads the new salad place, tails the Korean food truck. You both consider this a fair plan, figuring that the chances of going to either place for lunch are 50/50.

In this case, it is straightforward to calculate your chances of going to either place *deterministically*. However, this problem can also be *estimated *using *Monte Carlo-style simulations*.

In a Monte Carlo simulation, you would flip a coin a large number of times, let’s say 1,000. You would record the result of each flip, and at the end, you would calculate the percentage of heads and the percentage of tails that occurred. While it is unlikely to get exactly 500 heads and 500 tails (just like in real life), this simulation exercise would *approximate* the true probability, perhaps yielding 497 heads and 503 tails. As you add more simulations (maybe 2,000, or 5,000, or 10,000), you come closer to approximating the true probability.

Of course, in the case of the coin flip, calculating the probability deterministically is easier than flipping the coin 1,000 times to simulate outcomes—and you’ll be more likely to keep your job. However, there are other probability questions that are extremely difficult (or even impossible) to answer deterministically. This is where estimating probabilities by simulation becomes very useful.

Recently, the Bella team explored the expected cash flows of a private equity (PE) portfolio. To do this, we simulated thousands of PE portfolios using historical private equity cash flow data. Each of these simulated portfolios mirrored the client’s actual portfolio and payout structure and provided one possibility for how the actual portfolio’s cash flows could look in the future. By aggregating the results of 1,000 simulations, we could answer questions like:

- What do the average simulated portfolio’s cash flows look like?
- What is the worst-case scenario in terms of performance?
- What level of distributions can we expect at the 90
^{th}percentile?

As we developed this Monte Carlo approach, we realized an analysis like this could benefit a number of organizations, such as:

- Institutional investors estimating capital availability for liability matching (i.e. pensioners, universities, etc.).
- Investment banks engaging in complex private equity transactions.
- Rating agencies determining the risk of private equity-based transactions.
- Funds-of-funds managers estimating the range of returns of their portfolios.

There are two main advantages of using Monte Carlo simulations in these contexts. First, the simulations can be constructed using historical private equity cash flow data, so the results are often more robust than predictions made using other models. By using historical data, the cash flows of the Monte Carlo simulated portfolios reflect the different market conditions that the funds in those portfolios faced at various points in PE’s history. Valuations and pricing, exit environments, and over- and under-performance are therefore all represented in the range of outcomes the simulated portfolios describe. This paints a much richer picture than other modelling methods that do not rely on historical data, such as traditional Excel models that rely on static assumptions.

The second advantage is that *thousands* of models are generated, instead of a *single* model with set assumptions. Having a large dataset of simulated models allows for any number of analyses to then be performed on the simulated data, which would produce much more nuanced insight than any single model could. Moreover, these simulations may be passed through custom-built payout structures that mirror the unique waterfalls and needs of each organization.

Given the many possible use cases for this powerful Monte Carlo approach in private markets, Bella has developed an easy-to-use online platform where clients can simulate customized PE portfolios and analyze the cash flows and valuations of these portfolios over time using their historical private equity data.

The simulation results are presented in several ways. Users may browse graphs that quickly answer question such as “What’s the average amount distributed in first year of a portfolio’s life?” For more detailed results, users also have the option of downloading the complete dataset of simulated portfolio cash flows and valuations in each period.

The Monte Carlo approach is extremely powerful, but we are just beginning to explore the full spectrum of possible use-cases for this methodology. We are excited about the prospect of giving users access to this tool and are eager to see what types of new applications we can develop based on our users’ needs. To explore how your team might use simulations like these, drop us a line at info@bella-pm.com.