Equity Misvaluation and Default Options

• DOI: http://doi.org/10.1111/jofi.12748
• Author: AMIT GOYAL,ASSAF EISDORFER,ALEXEI ZHDANOV
• Published date: 01 April 2019
• Date: 01 April 2019

THE JOURNAL OF FINANCE •VOL. LXXIV, NO. 2 •APRIL 2019

Equity Misvaluation and Default Options

ASSAF EISDORFER, AMIT GOYAL, and ALEXEI ZHDANOV∗

ABSTRACT

We study whether default options are mispriced in equity values by employing a

structural equity valuation model that explicitly takes into account the value of the

option to default (or abandon the firm) and uses firm-specific inputs. We implement

our model on the entire cross section of stocks and identify both over- and underpriced

equities. An investment strategy that buys undervalued stocks and shorts overvalued

stocks generates an annual four-factor alpha of about 11% for U.S. stocks. The model’s

performance is stronger for stocks with a higher value of the default option, such as

distressed or highly volatile stocks.

ALARGE FINANCE LITERATURE ARGUES that equity securities are subject to po-

tential misvaluation by investors (see Harvey, Liu, and Zhu (2016) for a recent

survey), and that the extent of misvaluation impacts corporate decisions such

as merger and acquisition activities, stock issuance and repurchases, and in-

vestment policy. The sources of equity misvaluation are attributed primarily

to cognitive biases (see, e.g., Daniel, Hirshleifer, and Subrahmanyam (1998),

Barberis, Shleifer, and Vishny (1998), Hong and Stein (1999), and Baker and

Wurgler (2006)).

In this paper, we provide a new direction by arguing that equity misval-

uation is driven at least in part by investors’ failure to fully recognize and

adequately price the optionality of equity. It has long been recognized in the

finance literature that the equity of a firm with debt in its capital structure is

analogous to a call option written on the assets of the firm (see, e.g., Merton

(1974)). The title of the seminal paper by Black and Scholes (1973) reflects

the applicability of their model to the valuation of corporate debt and equity.

Today, nearly every corporate finance textbook (see, e.g., Brealey, Myers, and

Allen (2016)) discusses the option-based approach to valuing equity and debt.

∗Assaf Eisdorfer is from the University of Connecticut. Amit Goyal is from Swiss Finance In-

stitute at the University of Lausanne. Alexei Zhdanov is from Penn State University. We are

grateful for the constructive feedback and suggestions from the anonymous referees, the Associate

Editor, and Editors Kenneth Singleton and Stefan Nagel. We also thank Yakov Amihud, Malcolm

Baker, John Campbell, Clifton Green, Amiyatosh Purnanandam (our AFA discussant), Norman

Sch¨

urhoff, and seminar participants at Bar-Ilan University, Emory University, Florida State Uni-

versity,HKUST, Interdisciplinary Center Herzliya, NTU, NUS, Penn State University, University

of Connecticut, University of Pireaus, University of Texas at Dallas, University of Warwick, and

Virginia Tech University for helpful comments. All remaining errors are our own. Amit Goyal

would like to thank Rajna Gibson for her support through her NCCR-FINRSK project. We have

read the Journal of Finance’s disclosure policy and have no conflict of interests to disclose.

DOI: 10.1111/jofi.12748

845

846 The Journal of Finance R

Our paper addresses the question of whether analysts and investors incorpo-

rate this option-based approach in their equity valuations, and whether their

failure to do so gives rise to misvaluation.

While the option to default is a key characteristic of equity, standard stock

valuation techniques such as multiples valuation or discounted cash flow do

not explicitly account for this option. Using these techniques therefore can

lead to under- or overvaluation, especially among stocks with a relatively high

default option value (stocks with greater prospects of default or exit). We build

a structural equity valuation model that explicitly accounts for the value of the

option to default (or abandon the firm). We then use our option-based valuation

model to identify potential misvaluation of equity by examining whether our

model can predict future stock returns, and whether its predictive ability is

driven by the mispricing of default options.

Our model shares features with other structural valuation models of debt

and equity such as endogenous default (see Leland (1994) and a number of

models that followed).1It also implicitly accommodates the path-dependence

of Brockman and Turtle (2003) (due to an additional financial distress cost in

low cash flow states). Our model further allows for different tranches of debt

with different maturities and additional costs of financial distress. Our model

does not incorporate some features that have received considerable attention in

corporate finance literature such as investments or managerial entrenchment

(see Ozdagli (2010) for a more carefully calibrated model of default), as it

focuses specifically on valuing the default option. Notably, we use firm-specific

accounting inputs when implementing the model and hence are able to generate

firm-level valuations. To the best of our knowledge, our paper is the first to

employ a structural option pricing model of default on a large cross section of

stocks to value equity and measure potential misvaluation at the firm level.

Leaving the details of our model for later, we start our analysis by sorting all

stocks each month into decile portfolios according to the ratio of the model value

to market value of equity.2We find that most misvalued stocks, either over- or

undervalued, are smaller, are more volatile, are less liquid, have lower analyst

coverage with higher analyst forecast dispersion, and have lower institutional

ownership than more fairly valued stocks, indicating that the former stocks are

more difficult to value. Excess returns on these stocks show patterns consistent

with our valuation model. The monthly excess return for the most overvalued

decile of stocks is 0.51%, while that for the most undervalued decile of stocks

is 1.15%.

An analysis of factor loadings reveals that our strategy loads strongly

on well-known anomalies of size, value, momentum, and profitability in an

1For example, Goldstein, Ju, and Leland (2001) develop a model with dynamic refinancing,

Hackbarth, Miao, and Morellec (2006) model the effect of time-varying macroeconomic conditions,

and Bharma, Keuhn, and Strebulaev (2010) embed a structural model of credit spreads in a

consumption-based asset pricing model.

2Sorts based on differences between model value and market value are often used in the liter-

ature. See, for example, D’Mello and Shroff (2000), Claus and Thomas (2001), Dong et al. (2006),

and P´

astor, Sinha, and Swaminathan (2008).

Equity Misvaluation and Default Options 847

interesting way. Overvalued stocks are closer to small,value, past return loser,

and unprofitable stocks than are undervalued stocks. Nevertheless, alphas

from a variety of factor models are positive and strongly statistically signif-

icant. For example, the four-factor alpha for the overvalued decile of stocks is

−0.24%, while that for the undervalued decile stocks is 0.67%. The long-short

strategy that buys stocks that are classified as undervalued by our model

and shorts overvalued stocks thus generates a four-factor annualized alpha of

about 11%. These results are stronger for equal-weighted portfolios (four-factor

annualized alpha of about 16%). Our results are robust to the horizon effects

discussed in Boguth et al. (2016), conditional alphas as in Boguth et al. (2011)

and Cederburg and O’Doherty (2016), various subsamples, and longer holding

periods, and are also confirmed using Fama and MacBeth (1973) regressions.

Motivated by the patterns in factor loadings, we next explore the role of the

default option more directly by investigating how the returns generated by

the model vary across stocks with characteristics related to the default option.

We focus on four firm characteristics in this exercise: financial distress, size,

volatility, and profitability. Specifically, we first sort all stocks into quintiles

based on each of these characteristics. We then double-sort all stocks within

each quintile into quintiles according to the model-to-market value ratio. The

fraction of the default option value in the total model equity value clearly

indicates a relation between the importance of the default option and each

of the characteristics. Most notably, for the top distress quintile, the option

to default accounts on average for 35.9% of equity value, compared to only

19.2% for the least distressed stock quintile (these numbers also reflect the

value of the abandonment option, which is always positive in our model as

long as fixed costs are nonzero). The difference in the fraction of the default

option between the two extreme size quintiles is 11%, between the two extreme

volatility quintiles is 15%, and between the two extreme profitability quintiles

is 7%. These relations justify the use of these characteristics, and also support

the reliability of our model.

The returns generated by the model also exhibit a clear pattern across the

four characteristics. For example, within the top distress quintile, undervalued

stocks earn a monthly four-factor alpha that is 1.19% higher than that earned

by overvalued stocks. The equivalent difference within the bottom distress

quintile is only 0.26%. The model’s returns are also much higher among highly

volatile stocks, with the four-factor alpha of the long-short strategy equal to

1.38% for the most volatile stocks, but only 0.39% for the least volatile stocks.

The effect of firm size, however, is much weaker and not always monotonic: the

model’s four-factor alpha is 0.75% for small firms and 0.43% for large firms.

This is consistent with the fairly low difference in the fraction of the default

option between small and large stocks. For profitability-sorted portfolios, we

see a reduction in the four-factor alpha of the long-short strategy from 1.09%

for the least profitable stocks to 0.69% for the most profitable stocks.

The positive effect of firm characteristics, especially distress and volatility,

on the model’s performance strongly suggests that the option to default is a

primary driver of the predictive ability of the model for future stock returns. To