Everysk's private model uses a data centric approach to observe hundreds of thousands of limited partner cashflows to/from private investments in order to calculate their return and risk characteristics. Our approach is predicated in letting the data inform the model and not the other way around. We can generate proprietary indices that better reflect the true risk of allocating to private investments.

Please reach out to sales@everysk.com if you would like to receive a free sample of our indices: VC, buyout, private debt and private real estate.

**1. Background**

Everysk can seamlessly integrate illiquid investments with a portfolio of traded securities and funds. Illiquid investments such as venture capital, buyout, private credit and private real estate have no reliable time series (like AAPL stock for example). The secondary markets for these investments are very thin and the only observable data are the cashflows from limited partners.

The lack of data is problematic because illiquid investments are prominent in the portfolios of high net worth individuals. Whereas various techniques exist to establish the performance of these private investments, such as: PME measures, IRR and TWR- trade weighted returns, no acceptable measure of their market risk exists. The "state-of-the-art" approach is to use a pooled index from a well known provider as the underlying risk factor in the covariance matrix.

The problem of using pooled indices for risk is that these indices are valued by the general partner of the fund and hired appraisers and, at times, can underestimate the true risk involved with these private investments.

Everysk takes a different approach that has 2 objectives:

- To produce more responsive, market driven indices for private investments that do not suffer from "appraisal smoothing"
- To be able to decompose our indices into a measure of return and risk that is derived from traded factors (systematic) and an orthogonal component of the true alpha of these private investments after other cross-sectional explanatory factors such as marker, size, value and illiquidity are taken into account.

We follow an approach akin to Andrew Ang's 2013 paper[1] with some proprietary modifications. In what follows we describe the approach and present some results. Our benchmarks are more realistic for risk management and our derived idiosyncratic components can be used more reliably to rank private investments.

**2. Methodology**

We use Preqin's database with capital calls and distributions from LPs into private funds. The database contains north of 330,000 reliable, realized flows that fiduciaries are required to report and that are accessible via the Freedom of Information Act (FOIA). We process the information separately for each of: venture capital, buyout, private debt and private real estate.

By analyzing this large amount of data we can derive granular information on the realized return of these 4 categories. Once we extract a reliable return stream, risk follows naturally. But deriving a return stream that explains cross-sectionally and over time the behavior of private investments is not a trivial task. Let's see why:

First, let's start with an illustrative equity investment whereby an investor puts more money into the investment over a 2 period timeframe:

$$ \displaystyle \text{V}_{t} = \frac{\text{CF}_{t+1}}{1+g_{t+1}} \ + \ \frac{\text{CF}_{t+2} +V_{t+2}}{(1+g_{t+1})(1+g_{t+2})} $$

By equating the value of the investment at time t (a historical point in time), %% \text{V}_{t} %%, to the present value of its future cashflows, %% \text{CF}_{t+\Delta t} %%, we can derive a time series of realized returns: %%g_{t+1}, g_{t+2}%%. The reason we can easily compute the realized return time series is because we control the timing of the cashflows and there is a single investment in the example. Even when we have multiple investments in a portfolio but there is proper separation of assets - such as in a real estate property fund - we can still retrieve the realized return of the portfolio using an ordinary least squares method (the only requirement is that we need more projects in the portfolio than the number of periodic realized returns being calculated).

The approach above is not applicable to private investments for 2 main reasons: a) we are not in control of the timing of cashflows, the general partner (GP) of the fund is, and; b) there is no proper separation of assets. For example: in the 2-period example above, part of the distribution %%\text{CF}_{t+2}%% could be due to a capital call that happened years ago and that decision is solely due to the GP (naturally under certain restrictions). Present-valuing the full %%\text{CF}_{t+2}%% to time %%t%% would be incorrect and would overestimate the realized performance.

Thus, for private investments, we need to infer the realized returns using a Bayesian approach. Everysk has partnered with PyMC Labs (https://www.pymc-labs.io/), a global consortium of Bayesian specialists and the inventors of the PyMC3 library (https://docs.pymc.io/) to help develop our indices.

The approach is predicated that, under the null that the realized returns are correct, the present value of capital calls must equate the present value of the distributions, both across time and across different funds. In equation format:

$$ \displaystyle \text{E} \left[\sum_{t} \text{C}_{it} (1 +g_{t})^{-1}\right] \ = \ \text{E} \left[\sum_{t} \text{D}_{it} (1 +g_{t})^{-1}\right] , \ \ \ \forall i$$

Where %%\text{C}_{it}%% is the capital call for fund %%i%% at period %%t%% and %%\text{D}_{it}%% is the distribution for the same fund at the same period. In practice the equation above (observation equation) is mapped to a log ratio:

$$ \displaystyle ln \ \frac{\text{E} \left[\sum_{t} \text{D}_{it} (1 +g_{t})^{-1}\right]}{ \text{E} \left[\sum_{t} \text{C}_{it} (1 +g_{t})^{-1}\right]} = 0$$

We further assume that the inferred realized returns, %%g_{t}%%, are comprised of a systematic component and a time-varying private equity premium, %%f_{t}%%:

$$ \displaystyle g_{t} = \alpha + \beta^{T} \text{F}_{t} + f_{t} $$

- %% \small \displaystyle \alpha %% is the average excess return of private equity to liquid factors
- %% \small \displaystyle \beta%% are the betas to a 3 factor model, described below.
- %% \small \displaystyle F%% are the factor returns
- %% \small \displaystyle f_{t} %% is the time-varying private equity idiosyncratic return with mean zero.

The 3 factors are as follows:

Factor | explanation |

Mkt-RF | Excess return of market exposure |

HML | Measures the value risk premia |

IML | Pastor and Stambaugh liquidity factor |

We eliminated SMB (size factor) from our parametrization as the illiquidity factor seems to capture a significant overlap in explanatory power. Furthermore we assume that %%f_{t}%% is not easily arbitraged away and shows persistence of returns. This is mathematically expressed as an AR(1) model:

$$ \displaystyle f_{t} = \phi f_{t-1} + \sigma_{f} \epsilon_{t} $$

The details of the Bayesian approach are beyond the scope of this article. At a high level, we infer the latent parameters of the model that are most likely to have generated the observed cashflows. This is contrary to classic approaches that would just infer point estimates of the parameters to explain the data and thus do not allow for estimation of optimistic or pessimistic interpretations of the same data. In addition, we constraint the parameters of the model using regularizing priors to reduce the risk of overfitting to idiosyncratic patterns in the data.

In what follows, we describe the inferred properties for each of: venture capital, buyout, private credit and private real estate. We use the full database of cashflows from Preqin but limit the vintages to be between 1994 and 2015.

**3. Venture Capital**

The posteriors for our Venture Capital index are:

Posterior | Mean | Standard Deviation |

Alpha | 2.43% | 2.42% |

Beta_Mkt-RF | 0.97 | 0.50 |

Beta_HML | -1.28 | 0.55 |

Beta_IML | 0.05 | 0.61 |

The excess return over liquid, tradable markets is 2.43% quarterly. The other loadings are consistent with the published literature for VC, such as a large negative loading into value.

A total return plot of our VC index versus the SP500 and Cambridge Associates VC Index is presented below:

The y-axis indicates the net cumulative return. Thus, a terminal value of 2.0 means we have 3x our initial investment. From 2007 to today, the risk return properties are:

Index | Annualized Return | Annualized volatility |

Everysk VC Index | 9.41% | 20.47% |

SP500 | 8.55% | 16.06% |

Cambridge Associates VC | 10.02% | 8.05% |

It seems that the Cambridge Associates VC Index underestimates the risk of venture capital investing with half the SP500 volatility for the period. Because our index is market driven (inferred from realized cashflows) it is less prone from any smoothing biases.

Another important characteristic of the model is that we can decompose our index in terms of contributions from systematic and idiosyncratic sources (a true time-varying VC value-add):

First let's plot the alpha to liquid markets plus the idiosyncratic portion, %%\alpha+f_{t}%%:

This is an interesting result. In aggregate, after conditioning for 3 risk premia: market, value and liquidity, it seems that VC funds have not generated alpha. Despite a large alpha to systematic factors (2.43% quarterly), the idiosyncratic part has been negative, resulting on a sideways contribution. The alpha has improved since 2018.

The systematic portion of VC index, %%\beta^{T} F%%:

which is very tight around the SP500. Similar to a post-2018 improvement in alpha, the systematic portion has also generated higher upside, which has resulted in an overall strong performance in the last 2-3 years.

**4. Buyout**

Posterior | Mean | Standard Deviation |

Alpha | 2.93% | 2.42% |

Beta_Mkt-RF | 0.27 | 0.50 |

Beta_HML | 0.13 | 0.55 |

Beta_IML | 0.19 | 0.61 |

Compared to VC, the buyout index has more alpha, less market betas and more illiquidity premium priced in. A plot of our buyout index below:

Index | Annualized Return | Annualized volatility |

Everysk Buyout Index | 15.79% | 16.53% |

SP500 | 8.55% | 16.06% |

Cambridge Associates BO | 8.43% | 10.24% |

The alpha to liquid markets plus the idiosyncratic portion, %%\alpha+f_{t}%%:

And %%\beta^{T} F%%:

Our buyout index shows a significant alpha creation and low reliance on the liquid risk premia over the period.

**5. Private Debt**

The recovered posteriors are:

Posterior | Mean | Standard Deviation |

Alpha | 2.61% | 2.04% |

Beta_Mkt-RF | 0.16 | 0.37 |

Beta_HML | -0.13 | 0.43 |

Beta_IML | -0.23 | 0.48 |

The overall total return from 2007:

Index | Annualized Return | Annualized volatility |

Everysk PD Index | 10.52% | 9.34% |

SP500 | 8.55% | 16.06% |

The alpha to liquid markets plus the idiosyncratic portion, %%\alpha+f_{t}%%:

And %%\beta^{T} F%%:

**6. Private Real Estate**

The recovered posteriors:

Posterior | Mean | Standard Deviation |

Alpha | 1.93% | 2.07% |

Beta_Mkt-RF | 0.48 | 0.41 |

Beta_HML | 0.00 | 0.50 |

Beta_IML | 0.22 | 0.57 |

The overall total return from 2007:

Index | Annualized Return | Annualized volatility |

Everysk RE Index | 4.23% | 19.17% |

SP500 | 8.55% | 16.06% |

The alpha to liquid markets plus the idiosyncratic portion, %%\alpha+f_{t}%%:

And %%\beta^{T} F%%:

**7. Conclusion**

Everysk's private model uses a data centric approach to observe hundreds of thousands of limited partner cashflows to/from private investments in order to calculate their return and risk characteristics. Our approach is predicated in letting the data inform the model and not the other way around. We can generate proprietary indices that better reflect the true risk of allocating to private investments.

Furthermore, the ability to decompose the realized returns into the true alpha versus other liquid factors is a valuable outcome of the model. Without the "help" of the market and other risk premia, the approach above enables us to rank these 4 types of investments based on the terminal value of the idiosyncratic part: in the last 12+ years, the best alpha by far is from buyout, followed by private debt, private real estate and finally venture capital (negative alpha)

Index | Everysk Buyout | Everysk Private Debt | Everysk Private Real Estate | Everysk Venture Capital |

Alpha multiple (*) | 3.75x | 2.9x | 1.3x | 0.9x |

We are incorporating these idiosyncratic orthogonal return streams, %%f_{t}%%, into our orthogonal factor model, everysk_factor_model.

The 4 indices plotted together:

Please reach out to sales@everysk.com if you would like to receive a free sample of our indices: VC, buyout, private debt and private real estate.