Optimal Contracting, Corporate Finance, and Valuation with Inalienable Human Capital

• DOI: http://doi.org/10.1111/jofi.12761
• Author: PATRICK BOLTON,JINQIANG YANG,NENG WANG
• Published date: 01 June 2019
• Date: 01 June 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 3 •JUNE 2019

Optimal Contracting, Corporate Finance, and

Valuation with Inalienable Human Capital

PATRICK BOLTON, NENG WANG, and JINQIANG YANG∗

ABSTRACT

A risk-averse entrepreneur with access to a profitable venture needs to raise funds

from investors. She cannot indefinitely commit her human capital to the venture,

which limits the firm’s debt capacity, distorts investment and compensation, and

constrains the entrepreneur’s risk sharing. This puts dynamic liquidity and state-

contingent risk allocation at the center of corporate financial management. The firm

balances mean-variance investment efficiency and the preservation of financial slack.

We show that in general the entrepreneur’s net worth is overexposed to idiosyncratic

risk and underexposed to systematic risk. These distortions are greater the closer the

firm is to exhausting its debt capacity.

CONSIDER A RISK-AVERSE ENTREPRENEUR WHO has access to a profitable venture

with an initial capital stock K0. This entrepreneur needs to raise start-up

funds and on occasion additional working capital from investors. In a first-best

∗Patrick Bolton and Neng Wang are from Columbia University and National Bureau of Eco-

nomic Research. Jinqiang Yang is from School of Finance, Shanghai University of Finance and

Economics (SUFE), and Shanghai Institute of International Finance and Economics. This paper

was previously circulated under the title, “A Theory of Liquidity and Risk Management Based on

the Inalienability of Risky Human Capital.” We thank Bruno Biais (Editor), the Associate Editor,

and two anonymous referees for very thoughtful and detailed comments. We also thank Hengjie Ai;

Marco Bassetto; Philip Bond; Michael Brennan; Henry Cao; Vera Chau; WeiCui; Peter DeMarzo;

Darrell Duffie; Lars Peter Hansen; Oliver Hart; Arvind Krishnamurthy; Guy Laroque; David

Matsa; Jianjun Miao; Adriano Rampini; Richard Roll; Yuliy Sannikov; Tom Sargent; Ren´

e Stulz;

Raghu Sundaram; Suresh Sundaresan; Mark Westerfield; Jeff Zwiebel; and seminar participants

at the American Finance Association meetings (Boston), Boston University,Caltech, Cheung Kong

Graduate School of Business, Chinese University of Hong Kong, Columbia University, Duke Uni-

versity, Federal Reserve Bank of Chicago, Georgia State University, Harvard University, McGill

University, Michigan State University, National University of Singapore, New York University

Stern School of Business, Northeastern University, Ohio State University, Princeton University,

Sargent SRG Group, Singapore Management University,Summer Institute of Finance Conference

(2014), Shanghai Advanced Institute of Finance, Shanghai University of Finance & Economics,

Stanford Business School, Tsinghua University, University of British Columbia, University of

Calgary, University CollegeLondon, University of Hong Kong, University of Oxford, University of

Rochester,University of South Carolina, University of Texas Dallas, University of Toronto, Univer-

sity of Washington,Washington University,St. Louis, the Wharton School, Zhejiang University, and

the workshops hosted by the China YoungFinance Scholars Society for helpful comments. Jinqiang

Yang acknowledges support from the National Natural Science Foundation of China (#71522008,

#71472117, #71772112), Innovative Research Team of Shanghai University of Finance and Eco-

nomics (#2016110241), and Fok Ying-TongEducation Foundation of China (#151086). First draft:

2012.

DOI: 10.1111/jofi.12761

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1364 The Journal of Finance R

Modigliani-Miller environment, the entrepreneur would be able to diversify

away her idiosyncratic risk, fully pledge the market value of her venture,

and raise funds from investors against a promised competitive risk-adjusted

return. However, if the entrepreneur is essential to the venture and cannot

irrevocably dedicate her human capital to the firm, the promised return

may not be credible. We show that this inalienability of the entrepreneur’s

human capital, or what is also commonly referred to as key-man risk, has

critical implications not only for the firm’s financing capacity, investment,

and compensation, but also for its liquidity and risk management policy. The

larger is a firm’s liquidity or the larger is its borrowing capacity, the greater

is its ability to retain talent by making credible compensation promises. In

addition, by managing the firm’s exposures to idiosyncratic and aggregate

risk, the firm can reduce both the cost of retaining talent and the cost of

financing.

In sum, our paper offers a new theory of corporate liquidity and risk man-

agement based on the inalienability of risky human capital. Even when there

are no capital market frictions, corporations add value by optimally managing

risk and liquidity because doing so allows them to reduce the cost of key-man

risk to investors. This rationale for corporate risk and liquidity management

is particularly relevant for technology firms where key-man risk is acute.

The main building blocks of our model are as follows. The entrepreneur

has constant relative risk-averse (CRRA) preferences and seeks to smooth

consumption. The firm’s operations are exposed to both idiosyncratic and

aggregate risk. The firm’s capital is illiquid and is exposed to stochastic

depreciation. It can be accumulated through investments that are subject to

adjustment costs. The entrepreneur faces risk with respect to both the firm’s

performance and her outside options. To retain the entrepreneur, the firm

optimally compensates her by smoothing her consumption and limiting her

risk exposure. To be able to do so, however, the firm must manage its liquidity

and risk allocation. The firm’s optimized balance sheet is composed of illiquid

capital, K, and cash or marketable securities, S, on the asset side, and equity

and a line of credit (when Sis negative), with a limit that depends on the

entrepreneur’s outside option, on the liability side.

The solution to this problem has the following key elements. The en-

trepreneur manages the firm’s risk by choosing optimal loadings on the

idiosyncratic and market risk factors. The firm’s liquidity is augmented

through retained earnings from operations and through returns from its port-

folio of marketable securities, including its hedging and insurance positions.

The scaled state variable is the firm’s liquidity-to-capital ratio s=S/K.When

liquidity is abundant (sis large), the firm is essentially unconstrained and

can choose its policies to maximize its market value (or equivalently the

entrepreneur’s net worth). The firm’s investment policy then approaches the

Hayashi (1982) risk-adjusted first-best benchmark, and its consumption and

asset allocations approach the generalized Merton (1971) consumption and

mean-variance portfolio rules. In particular, the entrepreneur is completely

insulated from idiosyncratic risk.

Optimal Contracting, Corporate Finance, and Valuation 1365

In contrast, when the firm exhausts its credit limit, its single objective is to

ensure that the entrepreneur gets at least as much as her outside option, which

is achieved by optimally preserving liquidity sand eliminating the volatility of

sat the endogenously determined debt limit s. As one would expect, preserving

liquidity requires cutting investment and consumption, engaging in asset

sales, and lowering the systematic risk exposure of the entrepreneur’s net

worth. More surprisingly, preserving financial slack also involves retaining

some exposure to idiosyncratic risk. That is, relative to the first-best, the en-

trepreneur’s net worth is overexposed to idiosyncratic risk and underexposed

to systematic risk, as this helps reduce (or even eliminate) the volatility of s.

In short, the risk management problem of the firm boils down to a compro-

mise between achieving mean-variance efficiency for the entrepreneur’s net

worth and preserving the firm’s financial slack. The latter is the dominant

consideration when liquidity sis low.

The first model to explore the corporate finance consequences of inalien-

able human capital is Hart and Moore’s (1994). They consider an optimal

financial contract between an entrepreneur and outside investors to finance

a single project with a finite horizon and no cash-flow uncertainty. Both the

entrepreneur and investors are assumed to have linear utility functions. They

argue that the inalienability of the entrepreneur’s human capital implies that

debt is an optimal financial contract.

We generalize the Hart and Moore (1994) model in several important

directions. Our first generalization is to consider an infinitely lived firm, with

ongoing investment subject to adjustment costs, and an entrepreneur with a

strictly concave utility function. While the firm’s financing constraint is always

binding in Hart and Moore (1994), in our model the financing constraint

is generically nonbinding; because it is optimal to smooth investment and

consumption, the firm does not want to run through its stock of liquidity in

one go. This naturally gives rise to a theory of liquidity management even

when there is no uncertainty. We describe this special case in Section VII.

Our second generalization is to introduce both idiosyncratic and aggregate

risk, which leads to a theory of corporate risk management that links classical

intertemporal asset pricing and portfolio choice theory with corporate liquidity

demand. Investors set the market price of risk, which the entrepreneur takes

as given in determining the firm’s optimal risk exposures and how they

should vary with the firm’s stock of liquidity. By generalizing the Hart and

Moore (1994) model to include ongoing investment, consumption smoothing,

uncertainty, and risk aversion for both the entrepreneur and investors, we are

able to show that inalienability of human capital gives rise to not only a theory

of debt capacity, but also a dynamic theory of liquidity and risk management

that is fundamentally connected to the entrepreneur’s optimal compensation.

The objective of corporate risk management in our analysis is not achieving

an optimal risk-return profile for investors, they can do that on their own, but

rather offering optimal risk-return profiles to risk-averse, underdiversified key

employees (the entrepreneur in our setting) with inalienable human capital

constraint. In our setup the firm is, in effect, both the employer and the asset