Riders in the Storm
This paper examines public and private asset average performance during the VIX spike quarter and in the pre- and post-volatility spike periods.
Modeling private investment cash flows is an important challenge for investors. With a cash flow model an investor can simulate possible market scenarios, cash flow shortfalls, and liquidity crises. Such an analysis can be very useful for CIOs who must make important decisions related to asset allocation and liquidity planning.
The Takahashi and Alexander’s (TA) framework to model private capital portfolio’s cash flows has stood the test of time. However, estimating its single lifetime growth parameter remains a challenge. The single paramater for growth also makes the model cash flows insensitive to short-term movements in the broad market returns. This is especially problematic in a simulation setting in which market returns are sampled many times. How might a private investment behave in different market scenarios is an important portfolio management question.
We explore a modification to the TA model in which a series of periodic growth rates are used to model distributions and valuations. In a simulation setting these growth rates can be correlated with public market returns via lagged regression of quarterly IRRs on several lags of quarterly public market returns. This makes the modified model more realistic as the model valuations and distributions become responsive to short-term market movements.
Using historical simulation on actual market data we show that the modified version of the TA model does a better job modeling actual cash flows, while retaining the spirit of the original TA model.
Comparison of Lifetime and Periodic Growth TA Models
We compare two versions of the TA model: one that uses a single lifetime growth parameter and one that uses a set of periodic growth parameters. For this comparison we fix all other TA parameters which we calibrate using pooled US buyout data across vintages 1980 through 2020. We use a bow factor of 4, lifespan of 12y, and rate of contribution 28% in the first year, 25% in the second year and 30% onwards.
To begin, we first use actual data for the two sets of growth parameters. For the lifetime growth parameter, we use the actual 12y IRR, when available, and since-inception IRR otherwise, as reported by Burgiss. For the set of periodic growth parameters, we use actual quarterly IRRs, also from Burgiss. This exercise provides an “estimation-free” comparison between the two models. In reality, the value of a cash flow model lies in its predictive power for which we would also have to predict (or, estimate) the growth parameter.
We compare these two TA model versions using 15 individual consecutive vintages from 2000 to 2014. Figure 1 shows the cumulative net cash flow, by vintage, generated by each model. A quick look at Figure 1 may tempt one to conclude that the two models are nearly the same, as the periodic and lifetime growth models’ cumulative cash flows track each other. Toward the end of 12y lifespan the periodic and lifetime models do start to drift apart as the quarterly IRRs become noisier as valuations gets smaller. However, since these noisy periodic growth estimates are applied to smaller valuations, the gap between the two models is effectively small.
We present a modified version of the TA model in which the model’s lifetime growth parameter is replaced with period-specific growth parameters – i.e., a growth parameter for each period. Periodic growth values are modeled using lagged regression. The modified TA model provides a systematic way to link private capital growth and distributions to public markets. We present computational evidence using buyout and public market data to show the usefulness of this modified TA model.