Idiosyncratic Cash Flows and Systematic Risk

• Published date: 01 February 2016
• Author: YURI TSERLUKEVICH,ILONA BABENKO,OLIVER BOGUTH
• DOI: http://doi.org/10.1111/jofi.12280
• Date: 01 February 2016

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 1 •FEBRUARY 2016

Idiosyncratic Cash Flows and Systematic Risk

ILONA BABENKO, OLIVER BOGUTH, and YURI TSERLUKEVICH∗

ABSTRACT

We show that unpriced cash flow shocks contain information about future priced risk.

A positive idiosyncratic shock decreases the sensitivity of firm value to priced risk

factors and simultaneously increases firm size and idiosyncratic risk. A simple model

can therefore explain book-to-market and size anomalies, as well as the negative

relation between idiosyncratic volatility and stock returns. Empirically, we find that

anomalies are more pronounced for firms with high idiosyncratic cash flow volatility.

More generally, our results imply that any economic variable correlated with the

history of idiosyncratic shocks can help to explain expected stock returns.

IT IS WELL ESTABLISHED that, under standard asset pricing assumptions, only

systematic risk is priced. In this paper, we argue that unpriced idiosyncratic

cash flow shocks can also be important for asset prices as they contain valuable

conditioning information in a dynamic asset pricing framework. In particular,

we show that the conditional beta with respect to any priced source of risk

depends directly on the history of firm-specific shocks. We use this insight to

provide risk-based explanations for several anomalies in the cross-section of

equity returns, including the widely documented value and size effects, the

negative relation between idiosyncratic volatility and stock returns, and the

underperformance following investment and equity issuance.1

To understand why firm-specific shocks are useful as conditioning informa-

tion, consider a firm with two divisions. Suppose the profit of the first division

depends exclusively on idiosyncratic profitability shocks and the profit of the

∗All authors are with the W.P.Carey School of Business at Arizona State University. The authors

thank Ken Singleton (the Editor) and two anonymous referees as well as Jonathan Berk; Sreed-

har Bharath; Scott Cederburg; Darrell Duffie; Laurent Fr´

esard; Robert Hodrick; Søren Hvidkjær;

Rajnish Mehra; Kristian Miltersen; Dimitris Papanikolaou; Lasse Pedersen; Mark Rubinstein;

Toni Whited; and seminar participants at Arizona State University, Copenhagen Business School,

Erasmus University, New Economic School, Stanford University, University of Arizona, Univer-

sity of California at Berkeley, University of Luxembourg, University of Maryland, University of

Minnesota, University of Rochester, the 2013 meetings of the Western Finance Association and

the European Finance Association, and the 2013 UBC Summer Finance Conference. The authors

have no conflicts of interest, as identified in the Disclosure Policy.

1In the cross-section, firms with small market capitalization and a high ratio of fundamentals

to price tend to have high stock returns (Banz (1981), Graham and Dodd (1934)). Fama and

French (1992) provide a detailed analysis of both the value and the size premium. Ang et al.

(2006) document that high idiosyncratic volatility predicts low returns. Among others, Loughran

and Ritter (1995), Daniel and Titman (2006), and Pontiff and Woodgate (2008)showthatstocks

underperform following equity issuance.

DOI: 10.1111/jofi.12280

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426 The Journal of Finance R

second division is driven only by systematic shocks. This firm can be viewed as

a portfolio of a zero-beta asset and a risky asset. When a positive idiosyncratic

shock occurs, the size of the zero-beta asset increases, making it a larger frac-

tion of the total portfolio value. As a result, overall firm beta decreases, as do ex-

pected stock returns. Therefore, any firm characteristic correlated with the his-

tory of idiosyncratic cash flow shocks can help explain expected stock returns.

In a more general setting, we show that beta is invariant with respect to

idiosyncratic shocks only in the special case in which profits are the product

of idiosyncratic and systematic profitability shocks. Multiplicative production

functions of this type are used extensively in the literature because of their

tractability properties (see, for example, Gomes, Kogan, and Zhang (2003),

Carlson, Fisher, and Giammarino (2004), Zhang (2005), and Cooper (2006)).2

Therefore, without additional features such as operating leverage, time-varying

price of risk, or investment options, market betas are independent of firm-

specific shocks.

Using this insight, we build a simple model in which firm value is additive in

two types of shocks and only systematic risk is priced. We first consider a firm

consisting entirely of assets in place. We show that, in the simple benchmark

model, firm characteristics are related to expected returns in the cross-section.

All else being equal, firms with larger idiosyncratic cash flows have larger

market capitalization and lower book-to-market, and at the same time have

lower equity betas. As a result, large firms and growth firms have low expected

returns.

Similarly, we obtain a negative relation between idiosyncratic volatility and

expected stock returns, a puzzling empirical finding in Ang et al. (2006)that

presents a challenge to risk-based explanations of expected stock returns. In

our one-factor model, a history of favorable idiosyncratic shocks decreases the

relative magnitude of the systematic profit component, thereby increasing id-

iosyncratic stock return volatility and lowering beta. Importantly,idiosyncratic

risk is not priced in our framework, but it is negatively correlated with system-

atic risk and can therefore predict returns.

The model, which incorporates systematic and idiosyncratic cash flow shocks,

also adds to our understanding of the relation between growth options and

risk. Since investment options are levered claims on assets in place, they are

usually considered more risky than installed capital.3We demonstrate that

the relation between options and risk depends on the type of investment op-

tion. In particular, while growth options linked to systematic shocks increase a

firm’s risk, growth options linked to idiosyncratic profitability shocks have the

opposite effect. Somewhat surprisingly,however, the exercise of both systematic

2Notable exceptions are Brennan (1973) and Bossaerts and Green (1989), who model dividends

as the sum of persistent idiosyncratic shocks and a single systematic shock. In particular,Bossaerts

and Green (1989) derive two-factor arbitrage pricing theory restrictions on dynamic equilibrium

asset returns to explain the abnormally high January returns of small stocks.

3The existing literature shows that this relation can be reversed in the presence of operating

leverage or adjustment costs. See, among others, Carlson, Fisher, and Giammarino (2004), Zhang

(2005), Cooper (2006), and Novy-Marx (2011).

Idiosyncratic Cash Flows and Systematic Risk 427

and idiosyncratic growth options always leads to a decline in a firm’s system-

atic risk as long as the firm finances new investment with equity. Thus, our

model also accounts for the observed poor stock return performance following

seasoned equity offerings (Loughran and Ritter (1995)).

Furthermore, growth options magnify the value and size premiums in the

model and give rise to time-varying price-earnings ratios. There are two rea-

sons for these effects. First, options make firm value and conditional beta more

sensitive to profitability shocks, as irreversible investment options grow in

value exponentially (Dixit and Pindyck (1994)). Second, firms optimally exer-

cise their investment options, and as a result lower their risk, only when their

market capitalization is high. We show that the nonlinear exposure of growth

options to the underlying profitability shock can generate price-earnings ratios

that negatively predict returns.

The intuition developed in this paper applies to any setting with a single

source or multiple sources of priced risk. As in previous studies, size and value

effects are not anomalous relative to the correctly specified asset pricing model

and appear only when not all sources of priced risk are accounted for correctly,

as in Berk (1995). Reconciling the predictions of our model with the empirical

evidence on value, size, and idiosyncratic volatility anomalies relative to the

capital asset pricing model (CAPM) thus relies on imperfect measurement of

risk, and in particular on differences between conditional and unconditional

betas, as discussed in Gomes, Kogan, and Zhang (2003). Lewellen and Nagel

(2006) argue that the conditional CAPM cannot match the magnitude of ob-

served anomalies because the variation in estimated betas is not sufficiently

large. However, betas are likely to be mismeasured because either asset pricing

tests fail to use all conditioning information (Hansen and Richard (1987)) or

the proxy for the market portfolio is imperfect (Roll (1977)).

We use analytical solutions from the model to simulate firms’ stock returns

and examine the fit between the model-generated and empirically observed

data. Our analysis of the simulated data indicates that the model can produce

reasonable value and size effects in cross-sectional Fama and MacBeth (1973)

regressions even when we explicitly control for empirically estimated betas. For

example, we find a size premium of 0.48% per month for the decile of stocks with

the smallest market capitalization relative to the largest decile. Sorting based

on book-to-market ratio, price-earnings ratio, and idiosyncratic volatility yields

return differentials of similar magnitudes. Value and size anomalies are more

pronounced when growth options are valuable. These results are consistent

with empirical evidence in Da, Guo, and Jagannathan (2012) and Grullon,

Lyandres, and Zhdanov (2012), who argue that the poor empirical performance

of the unconditional CAPM is largely attributable to real options.

In addition to explaining established asset pricing anomalies, our model

produces novel empirical predictions. In particular, the model suggests that

asset pricing anomalies are stronger when a significant part of cash flows is

idiosyncratic in nature. We test this prediction using portfolios of stocks sorted

by the volatility of their idiosyncratic cash flows and by firm characteristics

such as size and book-to-market. We find that that size and book-to-market