How much can lack of marketability affect private equity fund values?

• Author: Axel Buchner
• DOI: http://doi.org/10.1016/j.rfe.2015.10.002
• Published date: 01 January 2016
• Date: 01 January 2016

How much can lack of marketability affect private equity fund values?

Axel Buchner ⁎

Departmentof Business and Economics,University ofPassau, 94030 Passau, Germany

abstractarticle info

Articlehistory:

Received3 February 2015

Receivedin revised form 18 September2015

Accepted8 October 2015

Availableonline 20 October 2015

JEL classification:

G13

G23

G24

Keywords:

Privateequity funds

Marketability

Option-pricing

Thispaper derives an upperbound on the discountsfor lack of marketabilityof private equityfunds using option-

pricing theory.The upper bound is a function of the volatilityof the fund returns, of the (remaining)lifetime of

the fund, of two parameters governing the speed of capital drawdowns and distributions, of the volatility of

the stock market returns, an d of the return correlation between the fund and th e stock market. The model

calibration and numerica l analysis deliver several novel insights about ho w non-marketability affects the

value: (i) upper boundary discounts are increasing functionsof the return volatility of the fund, of the return

volatility of the stock market,and of the average time over which a dollar committed remains invested in the

fund; (ii) upper boundary discounts decrease non-linearly over the finite li fetime of a fund; (iii) estimated

upper boundarydiscounts at the start of an averageprivate equity fund equal$35.3 relative to $100 committed,

which corresponds to an annualupper boundary return premiumdemanded for lack of marketability of around

7%; and (iv) estimatedupper boundary discountsof venture and buyout funds arearound the same magnitude,

though, discounts of venturecapital funds are slightlyhigher.

© 2015 ElsevierInc. All rights reserved.

1. Introduction

The issue how marketability affect s the value of securities is of

fundamental importance in financ e. In general, both the theory and

the empirical evidence suggest that investors attach a lower price to

assetsthat are not frequentlytraded. In privateequity, this effect should

evenbe more pronouncedbecause stakes in privateequity fundscannot

readily be sold andinvestors are locked-in a fund investmentfor quite

long time periods, usually in the order of ten to fifteenyears. This has

dramatically been illustra ted during the financial crisis thro ugh the

failed attempts of large privateequity investors (endowments such as

Harvard, pension funds such as Calpers) to sell p arts of their private

equity portfolios at reasonable prices on the secondary privateequity

markets.For example, Harvardendowment has triedto sell a staggering

USD1.5 billion in the year 2008 in an effort to recei ve cash from its

private equity division, but fa iled to sell this stake at a reasonabl e

price. This anecdotal evidence underli nes the importance of non-

marketabilitydiscounts for private equity fund investments.However,

despite this importance, the magn itude and drivers of the discounts

are still a largelyunresolved issue in theprivate equity literature.

The main contribution of this paper is to derive a sim ple upper

bound on the value of marketabil ity of private equity funds using

option-pricingtheory. The paper adopts a framework that was initially

proposed by Longstaff (1995) to assess thevalue of marketability of a

stock investmentand extends this framework to incorporate the main

institutional features of private equity fund investments.

1

Intuitively,

the upper bound developed reflects the present value of the greatest

possible loss that an investor could experience by foregoing the right

to sell the private equity fund at any point in ti me. That is, the basic

idea adopted here is that non-marketabili ty of private equity funds

imposes an important opportunity cost on an inves tor. This can best

be explained by considering a hypot hetical investor that possesses

perfect market timing abilities but is restricted from selling the fund

over its finite legallifetime. If the marketabilityrestriction was relaxed,

the investorcould sell the fund positionwhen it most profitablefor him

to do so. Then, the principle of no-arbitrage implies that the value of

marketability to an investor with perfect market timing ability is simply

the present valueof the incremental cash flow that the investor would

receive if the marketability restriction was relaxed. Clearly, this argu-

ment holds only for an investor with perfect ma rket timing ability.

If the market timingability is imperfect, the presentvalue of the incre-

mental cash flow represents only an up per bound on the value of

marketability. The importantadvantage of this framework is, however,

that it doesnot require making allthe assumptions aboutinformational

asymmetries,investor preferences,etc. that would be requiredin a full

general equilibrium model.The framework adopted hereonly requires

the weak assumptions of a rational investor and that the principle of

Reviewof Financial Economics 28 (2016)35–45

⁎Tel.: +49 851 509 3245; fax: +49 851 509 3242.

E-mailaddresses: axel.buchner@uni-passau.de,axel.buchner@googlemail.com.

1

Koziol& Sauerbier(2007) modify theapproach of Longstaff(1995) to analyzepossible

pricediscountsof illiquid bonds.Chesney & Kempf (2012)also propose an approachto de-

terminethe value of tradabilityusing option-pricingtheory. However,their model differs

from the Longstaff(1995) approachin the sense that the incentiveto trade arises fromthe

abilityof traders to exploit a temporarypricing inefficiencyin the stock market.

http://dx.doi.org/10.1016/j.rfe.2015.10.002

1058-3300/©2015 Elsevier Inc. All rightsreserved.

Contents listsavailable at ScienceDirect

Review of Financial Economics

journal homepage: www.elsevier.com/locate/rfe