1. Private Equity Indices Based on Secondary Market Transactions
Brian Boyer
Brigham Young University
Taylor Nadauld
Keith Vorkink
Michael Weisbach
Ohio State
2nd Annual Private Markets Research Conference
July, 2018

2. Secondary Market Transactions
We obtain a dataset on secondary market transactions in private equity
We build buyout and venture capital indices, similar to other asset classes
Basic unit of measurement: return from buying a portfolio of private equity funds one quarter, and selling next quarter
Account for sample selection in set of transactions by building a hedonic model (Heckman )
Account for measurement error in estimating performance parameters
Scholes and Williams (1979), Blume and Stambaugh (1983)
Applications:
Measure Performance
Determine optimal portfolio allocation
Estimate market-to-book ratios over the business cycle

3. How Applicable?
Private markets are much less liquid than public markets.
Limited partners often hold position until the fund liquidates
Never intend to transact in secondary markets
These market features are not unique to private equity
Corporate bond markets
Much less liquid than stock markets.
Many bond holders intend to hold the bond to maturity.
Investors still look to bond indices based on secondary markets to gauge value.
When rates go up, we still believe the holder of the bond “lost money” even though the bond wasn’t sold.
Our intent is to build similar indices for private equity.

4. Liquidity Average discount of about 10% among the transactions we use
Discounts observed in other assets that make up indices
Example banks stocks during the financial crisis
Liquidity should not impact expected returns unless a liquidity premium exists.
Arguably easier to investigate liquidity risk premia and influence of liquidity on other moments of the return process if we can first measure the actual return process itself.
Before we can understand the elements behind returns (liquidity, transaction costs, risk-premia) we first need to observe the return.

5. Measuring Performance: Other Approaches
Cross sectional regressions using IRRs
The IRR is not a return, is not unique, and may not exist.
Irregular intervals can be problematic (Axelson, Sorenson, and Stromberg (2014)).
Hedonic Indices using venture financing events
The valuation is the value at which you can get in, but not at which you can get out.
Implied valuations can be misleading (Gornall and Strebulaev (2018))
Listed fund of funds (e.g., Blackrock and KK&R )
Hold other assets
Tack on an extra layer of fees

6. Methodology
𝑃 𝑖,𝑡 = price of a $10 million commitment to fund 𝑖 at time 𝑡.
𝐷 𝑖,𝑡 = distributions between 𝑡−1 and 𝑡.
𝐶 𝑖,𝑡 = calls between 𝑡−1 and 𝑡
log return:
Return on a “price weighted index”
Given a set of weights, can generalize methodology to other weighting schemes
𝑟 𝑡 = log 𝑖 𝑃 𝑖,𝑡 + 𝐷 𝑖,𝑡 − 𝐶 𝑖,𝑡 − log 𝑖 𝑃 𝑖,𝑡−1
𝑟 𝑡 = log 𝑃 𝑡 + 𝐷 𝑡 − 𝐶 𝑡 − log 𝑃 𝑡−1 ,

7. Methodology Two methods to observe average price
𝑟 𝑡 = log 𝑃 𝑡 + 𝐷 𝑡 − 𝐶 𝑡 − log 𝑃 𝑡−1 ,
Two methods to observe average price
Naïve index: Simple average return of all observed prices.
We don’t observe prices for all funds.
If funds transact with i.i.d. probability, our measured returns are influenced by i.i.d. measurement error
Hedonic Index: Use regression model to infer missing prices.
Heckman (1979) sample selection model to jointly model selection and price.
Our inferred prices are again, influenced by i.i.d. measurement error.
Measurement error
i.i.d. measurement error: Blume and Stambaugh (1983).
Non-synchronous trading: Scholes and Williams (1979), Lo and MacKinley (1990)
We use the proper bias adjustments to account for such measurement error when estimating performace parameters: beta, alpha, volatility

8. Heckman Model 𝜋 𝑖,𝑡 = 𝑃 𝑖,𝑡 /𝑁𝐴 𝑉 𝑖,𝑡 𝑥 𝑖,𝑡 = fund characteristic
Observed
OLS
True
𝑥 𝑖,𝑡
Heckman (1979)

9. Heckman (1979) model price equation selection equation
𝜋 𝑖,𝑡 = 𝑃 𝑖,𝑡 /𝑁𝐴 𝑉 𝑖,𝑡 for funds with observed prices
𝑦 𝑖,𝑡 ∗ = latent continuous variable that determines selection that is associated with observable
characteristics. Fund 𝑖 is selected to transact if 𝑦 𝑖,𝑡 ∗ >0.
𝑦 𝑖,𝑡 observed for all funds since we observe which funds transact.
𝜖 𝑖,𝑡 and 𝑣 𝑖,𝑡 are correlated if there exists omitted variables correlated with both selection and transaction

10. Identification
The Heckman model is parametrically identified under the assumption that 𝜖 𝑖,𝑡 and 𝑣 𝑖,𝑡 are jointly normal.
Semi-parametrically identification requires an exclusion restriction
A variable correlated with selection that is uncorrelated with price.
Heckman (1990), Andrews and Schafgans (1998)
Our exclusion restriction: Fraction of limited partners that are pension funds

11. Explanatory Variables

12. Summary Statistics: Buyout

13. Summary Statistics: Venture

14. Selection Equation

15. Pricing Equation

16. Buyout Indices:

17. Buyout Indices: Excluding Crisis

18. Buyout Index Invest $1 in PE beginning of Jan 2006
Secondary Markets
Invest $1 in PE beginning of Jan 2006
Collect distributions, contributions.
Sell position at end of Q1
Invest all capital in PE end of Q1
etc
Not the value of same funds over time
Value of an investment
100% of capital is invested all the time
Distributions are immediately reinvested
Buyout Index
NAV Index
Public Equities

19. Venture Indices:

20. Venture Indices: Excluding Crisis

21. Venture Index Invest $1 in PE beginning of Jan 2006
Secondary Markets
Invest $1 in PE beginning of Jan 2006
Collect distributions, contributions.
Sell position at end of Q1
Invest all capital in PE end of Q1
etc
Not the value of same funds over time
Value of an investment
100% of capital is invested all the time
Distributions are immediately reinvested
NAV Index
Public Equities
Venture Index

22. Burgiss Index

23. Efficient Frontier

24. Market Value of Private Equity
Combine market returns with cash flow data to assign market values to funds.
Estimate market-to-book ratios (book=NAV)
Let 𝑟 𝑡 denote the estimated return for a given fund
𝑉 𝑡 =𝑁𝐴 𝑉 𝑡
𝑉 𝑡+1 = 𝑉 𝑟 𝑡+1 + 𝐶 𝑡+1 − 𝐷 𝑡+1
𝑉 𝑡+2 = 𝑉 𝑟 𝑡+2 + 𝐶 𝑡+2 − 𝐷 𝑡+2 …
𝑉 𝑇 = 𝑉 𝑇−1 1+ 𝑟 𝑇−1 + 𝐶 𝑡+𝑇 − 𝐷 𝑡+𝑇
𝑉 𝑠 = 𝑉 𝑠−1 𝑉 𝑠 + 𝐷 𝑆 − 𝐶 𝑠 𝑉 𝑠−1 + 𝐶 𝑆 − 𝐷 𝑆 = 𝑉 𝑠−1

25. Market Value of Private Equity
For 𝑡= last quarter of 4th year since vintage year we set 𝑉 𝑡 =𝑁𝐴 𝑉 𝑡
Iterate on future years to find values at later times.
At the end of each quarter for a given vintage compute “vintage market-to-book ratio"
𝑖 𝑀𝑎𝑟𝑘𝑒𝑡 𝑡 𝑖 𝑁𝐴 𝑉 𝑡
using market values and NAVs for all funds within the given vintage.

26. Market Value of Private Equity
Market to Book Ratios of Buyout Funds