Industry-Specific Human Capital

THE JOURNAL OF FINANCE • VOL. LXVIII, NO. 1 • FEBRUARY 2013

Industry-Specific Human Capital, IdiosyncraticRisk, and the Cross-Section of Expected Stock

Returns

ESTHER EILING∗

ABSTRACT

Human capital is one of the largest assets in the economy and in theory may playan important role for asset pricing. Human capital is heterogeneous across investors.One source of heterogeneity is industry affiliation. I show that the cross-section ofexpected stock returns is primarily affected by industry-level rather than aggregatelabor income risk. Furthermore, when human capital is excluded from the assetpricing model, the resulting idiosyncratic risk may appear to be priced. I find that thepremium for idiosyncratic risk documented by several empirical studies depends onthe covariance between stock and human capital returns.

ACCORDING TO TRADITIONAL ASSET pricing theory, investors choose their optimalportfolios by maximizing the expected utility of their lifetime consumption. Inaddition to investments in tradable assets such as stocks and bonds, part oftheir wealth is typically tied up in nontradable assets. A nontradable assetthat forms a significant fraction of wealth for virtually all investors is humancapital. Heaton and Lucas (2000) report that about 48% of household wealth isdue to human capital, while only 6.8% is invested in financial assets. Lustig,van Nieuwerburgh, and Verdelhan (2010) even estimate human capital to be90% of total wealth, while the share of equities is only 2%. This suggests that,in theory, human capital should matter for portfolio choice and asset pricing.

∗Eiling is with the Rotman School of Management, University of Toronto. I would like to thankthe Editor (Campbell Harvey), the Associate Editor, and an anonymous referee for insightfulcomments and suggestions. I am also grateful to Bruno Gerard, Frans de Roon, and Raymond Kanfor many comments and discussions. Furthermore, I thank Lieven Baele, Olesya Grishchenko,Ravi Jagannathan, Frank de Jong, Ralph Koijen, Francis Longstaff, Hanno Lustig, Stijn vanNieuwerburgh, Theo Nijman, Tim Simin, Walter Torous, Kevin Wang, and participants at the2009 American Finance Association meetings, the 2008 European Finance Association meetings,the 2008 Northern Finance Association meetings, the UCLA Anderson School, Tilburg University,Amsterdam University, the Stockholm School of Economics, HEC Paris, HEC Lausanne, ErasmusUniversity, the University of Rochester, the University of Wisconsin–Madison, Rice University,Georgetown University, Rutgers University, the University of Toronto, the Free University ofAmsterdam, and York University for helpful suggestions. I gratefully acknowledge the Award forBest Business Valuation Research Paper at the 2008 NFA meetings. Support for this research hasbeen provided by a grant from the Netherlands Organization for Scientific Research (NWO). Anearlier version of this paper was titled “Can Nontradable Assets Explain the Apparent Premiumfor Idiosyncratic Risk? The Case of Industry–Specific Human Capital.”

43

44 The Journal of Finance R©

Various empirical studies document a relationship between human capi-tal or labor income and equity returns (e.g., Shiller (1995), Campbell (1996),Palacios-Huerta (2003), Lustig and van Nieuwerburgh (2008)).1 Consequently,due to their nontradable human capital, investors are already endowed withcertain exposures to stock returns. To achieve their desired exposures, investorsmay need to adjust their portfolio decisions.

The nature of human capital is investor-specific and depends on, for example,age, education, occupation, or the industry or firm in which the investor works.Heterogeneity in human capital may induce different hedging demands forstocks across investors, due for instance to different levels of labor income riskor differences in correlations between human capital and equity returns. Theeffect of human capital heterogeneity on portfolio decisions is studied by Davisand Willen (2000b), who analyze optimal portfolios for workers with differentoccupations. Empirical asset pricing papers, however, focus on proxies for ag-gregate human capital to explain the cross-section of expected stock returns(e.g., Jagannathan and Wang (1996), Campbell (1996)).

This paper shows that human capital heterogeneity affects the cross-sectionof expected stock returns. I focus on industry-specific human capital.2 In thelabor economics literature, several papers document the existence of significantinter-industry wage differentials (e.g., Katz and Summers (1989), Neal (1995),and Weinberg (2001)), suggesting that labor income and human capital aredetermined in part by industry affiliation. I estimate industry-specific humancapital returns as the contemporaneous growth rate in industry-level laborincome. Based on a mean-variance framework, I first show that the portfolioadjustments for human capital are often significantly different for investorsworking in different industries.

To assess the impact of industry-specific human capital on the cross-sectionof stock returns, I estimate a linear asset pricing model that includes equitymarket returns and multiple human capital factors, corresponding to humancapital returns from different industries. This specification can be motivatedin the context of the Mayers (1972) model. In a single-period mean-varianceframework, investors are endowed with positions in nontradable assets. In theresulting nontradable assets model, expected stock returns are affected by theirexposures to aggregate nontradable asset returns in addition to returns on theequity market portfolio. Aggregate human capital returns are not observableand a commonly used proxy is the growth rate in aggregate labor income(e.g., Jagannathan and Wang (1996)). However, this measure largely ignoresheterogeneity in human capital and assumes that labor income dynamics arethe same across industries, with identical growth and discount rates. I relax

1 Lettau and Ludvigson (2001), Julliard (2004), and Santos and Veronesi (2006) show that futureequity returns can be predicted using variables that are related to human capital.

2 In addition to industry-level heterogeneity in human capital, there may exist important intra-industry variation due to, for example, the firm or occupation. As explained in the following section,the nontradable assets model that I estimate includes a separate factor for each type of humancapital. A natural starting point is to include industry-specific human capital.

Industry-Specific Human Capital 45

this assumption and include industry-specific labor income growth rates asseparate factors in the model.

An asset pricing model with industry-specific labor income risk can also bemotivated based on the literature on heterogeneous agent models with in-complete risk sharing.3 If industry-level labor income risk can be completelydiversified away, only aggregate labor income risk should be priced. However, ifinvestors working in different industries cannot perfectly share their industry-specific labor income risks, industry-level idiosyncratic labor income risk maybe priced as well.

I estimate the model including labor income growth rates from five broadindustries spanning aggregate labor income: goods producing, manufacturing,distribution, services, and the government. I use the value-weighted index ofall stocks traded on the NYSE, Amex, and NASDAQ as a proxy for the tradablemarket portfolio. The main benchmark model includes only one human capitalfactor: aggregate labor income growth. This model is also referred to as thehuman capital Capital Asset Pricing Model (CAPM).

I show that industry-specific human capital significantly impacts the cross-section of returns. When estimating the model for monthly returns on 25 sizeand book-to-market sorted portfolios, three out of five human capital industrieshave significant coefficients. The model captures 61% of the cross-sectionalvariation in returns and the null hypothesis that all pricing errors are zerocannot be rejected. In sharp contrast, aggregate labor income growth is notsignificantly priced and the human capital CAPM has an ordinary least squares(OLS) adjusted-R2 of only 9%. The pricing errors are significantly different fromzero.

Next, I separate industry-idiosyncratic human capital returns from the com-mon component. To this end, I estimate a model that includes aggregate laborincome growth and industry-specific labor income growth rates that are orthog-onal to the aggregate growth rate. Using this alternative model specification, Ifind that the coefficient on aggregate human capital returns is not significant,while again three out of five industries are significantly priced.

The above results suggest that what matters for asset pricing are primarilythe industry-specific labor income risks that are not shared across investors.This finding is robust to using returns on 100 size-beta sorted portfolios as inJagannathan and Wang (1996) and to using quarterly returns. Further, I findthat, even when including orthogonalized returns of a single human capitalindustry, the coefficient on the industry is typically highly significant and theR2 is often substantially higher than for the model with only aggregate humancapital returns.

The poor performance of the human capital CAPM seems to contrast withJagannathan and Wang (1996). An important difference is that they use

3 Several theoretical models show that uninsurable idiosyncratic labor income risk affects as-set pricing and helps to (partially) explain the equity premium puzzle when investors face hightransaction costs (e.g., Heaton and Lucas (1996)) or when labor income shocks are persistent andtheir volatility increases in economic downturns (e.g., Mankiw (1986), Constantinides and Duffie(1996)).


1-month lagged aggregate labor income growth to account for the reportinglag in aggregate labor income data. I focus on contemporaneous growth rates,as investors can observe their own wages in real time. Similar to Heaton andLucas (2000) and Jagannathan, Kubota, and Takehara (1998), I find that thepricing of aggregate labor income growth is very sensitive to the 1-month lag.In sharp contrast, industry-specific labor income growth is robust to timingissues. As a result, while the model with industry-specific labor income growthrates outperforms in both cases, the difference between the models is morepronounced when using contemporaneous labor income growth rates. From aneconomic perspective, this is the most relevant measure.

I compare the performance of the model with industry-specific human capi-tal to a number of well-known asset pricing models. I find that my model hashigher OLS and generalized least squares (GLS) R2s, and lower pricing er-rors, than the static CAPM (Sharpe (1964), Lintner (1965), and Black (1972))and the conditional CAPM of Jagannathan and Wang (1996). The Fama andFrench (1993) three-factor model, including extensions with a momentum fac-tor (Carhart (1997)) and a liquidity factor (Pastor and Stambaugh (2003)),explains a larger share of the cross-sectional variation in average returns onthe 25 size and book-to-market portfolios. However, for 100 size-beta sortedportfolios, these benchmark models have similar R2s and pricing errors to themodel with industry-specific human capital.

In the final part of the paper, I relate human capital to the apparent pre-mium for idiosyncratic risk (IR henceforth). Various papers provide empiricalevidence of a cross-sectional relation between stocks’ idiosyncratic volatilitiesand expected returns (e.g., King, Sentana, and Wadhwani (1994), Malkiel andXu (1997, 2004), Spiegel and Wang (2005), Fu (2009), Ang et al. (2006, 2009)).This creates a puzzle, as true IR should not be priced. Whereas several otherexplanations for this puzzle have been investigated, the link to human capitalhas thus far received little attention.4

Papers documenting a premium for IR typically measure IR as the residualvariance of the CAPM or the Fama and French (1993) three-factor model. Iconfirm a positive premium for IR: I find that portfolios consisting of highIR stocks have higher CAPM and three-factor alphas than those with low IRstocks.5 However, precisely these high IR stocks also have higher exposures

4 Spiegel and Wang (2005) relate IR to liquidity. Baker, Coval, and Stein (2007) use IR as aproxy for differences in opinion. Panousi and Papanikolaou (2012) document a negative relationshipbetween IR and investment. Goyal and Santa Clara (2003), Bali et al. (2005), and Guo and Savickas(2006) examine whether IR can predict market returns. Campbell et al. (2001) and Brandt et al.(2010) examine the time-series properties of IR.

5 Ang et al. (2006, 2009) find a negative relationship between realized IR (estimated usingdaily returns over the past month) and future returns. This result is puzzling, as theories suchas Merton (1987) predict a positive relation when investors underdiversify. Fu (2009) shows thatlagged realized IR is an imprecise measure of expected IR due to its time-varying properties. Usingan EGARCH model, he documents a positive relation between expected IR and expected returns,similar to, for example, King, Sentana, and Wadhwani (1994), Malkiel and Xu (1997, 2004), andSpiegel and Wang (2005). This paper also uses an EGARCH model to estimate IR and confirms thepositive relationship.


to (industry-specific) human capital returns. This can be explained as follows.The benchmark models used to estimate systematic risk (i.e., the CAPM orthe Fama and French (1993) model) do not include human capital. Hence,systematic risk due to (industry-specific) human capital that is not capturedends up in the error term, which thus appears to be systematically priced.Using the nontradable assets model, I show that the resulting “premium” forIR depends on the hedging demand induced by nontradable human capital.My empirical results confirm this: the covariance between CAPM idiosyncraticreturns and industry-specific human capital returns significantly affects thecross-section of expected stock returns. Furthermore, the model with aggregateand orthogonalized industry-specific human capital captures 68% of the cross-sectional variation in returns on 100 size and IR sorted portfolios. Finally, basedon pricing errors of 10 IR sorted portfolios (averaged over all size deciles), Ifind that industry-specific human capital explains 10% to 36% of the premiumfor IR.

The remainder of this paper is structured as follows. Section I presents thenontradable assets model. Section II analyzes industry-specific human capi-tal returns and the corresponding hedging portfolios. Section III presents theempirical analysis of the impact of industry-specific human capital on the cross-section of stock returns. In Section IV, I investigate the link with the premiumfor IR. Section V concludes. An Internet Appendix contains details of the modelderivation, labor income data, and auxiliary results.6

I. Asset Pricing with Nontradable Human Capital: A Simple Model

This section discusses the theoretical framework that serves as a basis forexamining the relation between industry-specific human capital and the cross-section of expected stock returns. In Section IV, I extend this framework toinvestigate the relation with IR. I treat human capital as a nontraded asset,following, amongst others, Mayers (1972), Bottazzi, Pesenti, and van Wincoop(1996), Baxter and Jermann (1997), and Viceira (2001). While investors mayborrow against their future labor income, most would not trade claims againstfuture labor income due to adverse selection and moral hazard problems. Thismakes human capital essentially nontradable.7

Consider a one-period mean-variance framework with N tradable assets andK nontradable assets, similar to Mayers (1972). It is straightforward to showthat an investor’s demand for tradable assets includes hedging demand in-duced by her fixed positions in the nontradable assets, in addition to the usualspeculative demand. Consequently, expected returns on tradable assets (μtr)

6 The Internet Appendix for this article is available online in the “Supplements and Datasets”section at http://www.afajof.org/supplements.asp.

7 Housing and private businesses are two other important nontradable assets that could beincluded in the model. I focus on human capital only, which forms a nonnegligible fraction ofwealth for virtually all investors. Palia, Qi, and Wu (2007) empirically show that, while all threetypes of nontradable assets impact households’ stock market participation and stock holdings,human capital dominates.

http://www.afajof.org/supplements.asp


are linear in their covariances with the tradable market portfolio �tr,mkt and intheir covariances with the returns on nontradable assets �tr,nt.

8 The InternetAppendix derives the following pricing equation:

μtr = γ �tr,mkt + γ �tr,ntqnt, (1)

where γ is the market aggregate risk aversion coefficient and qnt is the K ×1 vector of aggregate wealth due to the nontradable assets divided by thetotal value of tradable assets. I refer to this model as the nontradable assetsmodel. Note that I define the tradable market portfolio as the value-weightedportfolio of all N tradable assets, and I include the returns on nontradableassets separately in the model. An alternative model specification is based onthe return on the total market portfolio including all tradable and nontradableassets. However, this specification is not directly empirically testable, as thereturns on the total market portfolio are not observable.9

Since qnt contains the relative values of the nontradable assets, the pric-ing equation in (1) can be expressed as a two-factor model with returns onthe tradable market portfolio and aggregate returns on all nontradable as-sets as factors. In this paper, I use the model to empirically estimate theimpact of nontradable human capital returns from K different industries onexpected stock returns. The relative values of industry-specific human capi-tal are not observable and are difficult to estimate. Consequently, aggregatingindustry-specific human capital returns is challenging. The existing litera-ture sidesteps this problem by directly estimating aggregate human capitalreturns as the growth rate in aggregate labor income. However, in the nextsection I argue that this approach is problematic if human capital has dif-ferent growth and discount rates across industries of employment. To allowfor heterogeneity in human capital while avoiding the need to estimate itsvalue, I include human capital returns from different industries in the modelseparately.

The pricing equation can be expressed as a multifactor model including amarket beta and K nontradable asset betas:10

E[rtr,i] = βmkt,i

(E[rmkt] − γ

K∑k=1

Cov[rmkt, Rnt,k]qnt,k

)

+K∑

k=1

βnt,k,i(γ Var [Rnt,k]qnt,k

), (2)

8 The tradable market portfolio has weights α. The N × 1 vector of covariances between tradableasset returns and the market portfolio returns is�trα ≡ �tr,mkt. The N × K matrix with covariancesbetween tradable and nontradable asset returns is denoted by �tr,nt and does not contain anyvariances.

9 Roll (1977) argues more generally that, unless all assets are included in the market portfolio,its mean-variance efficiency is not testable.

10 The nontradable assets model is similar to certain models from the international financeliterature; for instance, Errunza and Losq (1985) and De Jong and de Roon (2005). In these partialsegmentation models, domestic investors are restricted from investing in foreign assets.


where βmkt,i ≡ Cov[rtr,i ,rmkt]Var[rmkt]

and βnt,k,i ≡ Cov[rtr,i ,Rnt,k]Var[Rnt,k] . This expression shows

that expected excess returns on tradable assets depend on a “quasi” marketrisk premium (i.e., the expected excess return on the tradable market portfolio,adjusted for its exposure to nontradable asset returns) and a value-weightedsum of “quasi” risk premia on nontradable assets.

In this single-period framework, the motivation to include industry-specifichuman capital in the asset pricing model is empirical, as heterogeneity inhuman capital affects the measurement of human capital returns. An alter-native motivation follows from the literature on heterogeneous agent modelsand the equity risk premium. Various theoretical models show that uninsur-able idiosyncratic labor income risk may help to (partially) explain the equitypremium puzzle in the presence of trading frictions (e.g., Heaton and Lucas(1996)) or persistent labor income shocks that become more volatile duringeconomic downturns (e.g., Mankiw (1986), Constantinides and Duffie (1996),Storesletten, Telmer, and Yaron (2007)).11 This suggests that, when investorscannot perfectly share labor income risk that is specific to their industry ofemployment, industry-level idiosyncratic labor income risk may affect assetpricing. To test the pricing of industry idiosyncratic labor income risk moredirectly, Section III also estimates an alternative model specification that sep-arates the common component in labor income risk from the industry-specificcomponents. The specification includes aggregate labor income growth andindustry-level income growth rates that are orthogonalized to the aggregategrowth rate.

II. Industry-Specific Human Capital Returns

Various papers in the labor economics literature show that industryaffiliation is a major determinant of human capital (e.g., Krueger andSummers (1988), Katz and Summers (1989), Neal (1995), Parent (2000),Weinberg (2001)). Investors working in various industries may face differ-ent amounts of labor income risk, different correlations between their laborincome and equity returns, and variation in the relative values of their hu-man capital. Examples of factors that influence human capital risk include, forinstance, transferability of human capital (e.g., possibilities to move to a dif-ferent sector), the risk that the investor’s human capital becomes obsolete dueto technological developments, or the strength of labor unions. These factorsare likely to be industry-dependent. For instance, consider an investor whoworks in an industry in which human capital is very specialized and not easily

11 The literature on heterogeneous agent models and the equity risk premium is too large toreview here. In general, in heterogeneous agent models, agents trade financial securities to self-insure against idiosyncratic income shocks. To generate a sizeable equity premium, the modelsneed to incorporate sufficient barriers against self-insurance, that is, high transaction costs orpersistent income shocks. Constantinides and Duffie (1996) and Krueger and Lustig (2010) showconditions under which uninsurable idiosyncratic labor income risk does not affect the equitypremium.


transferable to another industry (e.g., an investor working in the investmentbanking industry). She likely faces higher labor income risk, which results inmore adjustments to her stock portfolio to account for her human capital. InSection II.C, I analyze some of the portfolio implications of industry-specifichuman capital. However, my main focus is on the asset pricing implications.

A. Measuring Human Capital Returns

Returns on human capital are difficult to estimate since the cash flow compo-nent is observed (labor income) but not the discount rate component, which isused to calculate the present value of all future labor income, that is, the valueof human capital. To estimate returns on human capital, I follow a similarapproach to Jagannathan and Wang (1996).12 The setup is as follows. Assumethat the expected rate of return on human capital r is constant and per-workerlabor income Lt follows the first-order autoregressive process

Lt = (1 + g)Lt−1 + εt, (3)

where g is the expected growth rate in labor income and εt has a mean of zeroand is independently distributed over time. Human capital wealth is

Whct = Lt

r − g. (4)

Under these assumptions, the return on human capital wealth equals thegrowth rate in labor income. If human capital has the same discount andgrowth rates in all industries, the return on aggregate human capital can becalculated as the growth rate in aggregate labor income. However, if discountrates and growth rates vary across industries, total human capital wealth isaffected by these differences, which are unobservable. Consequently, aggregatehuman capital returns can no longer be calculated as aggregate labor incomegrowth. This paper allows for different labor income processes across industriesby calculating returns on human capital for each industry as the growth ratein industry-level labor income. The main benchmark is aggregate labor incomegrowth.

Jagannathan and Wang (1996) use aggregate labor income with a 1-monthlag to take into account the publication delay for aggregate labor income data.However, as Heaton and Lucas (2000) note, investors observe their own laborincome at the same time they observe stock returns. Hence, from an economicperspective, the contemporaneous labor income growth rate is a more appropri-ate measure of human capital returns. Also, the effect of lagged labor income

12 The literature provides several models for estimating returns on aggregate human capi-tal. These models are based on fairly restrictive assumptions, such as a constant human cap-ital discount rate (Shiller (1995), Jagannathan and Wang (1996)) or a perfect correlation be-tween the discount rates on human capital and stock returns (Campbell (1996)). Lustig and vanNieuwerburgh (2008) investigate the extent to which these models can match consumption dataand find that, while all three models fail, the Jagannathan and Wang (1996) measure comesclosest.


growth on stock returns may be confounded by announcement effects of laborincome or employment data (see also Cochrane (2008)). Therefore, I measurehuman capital returns as the contemporaneous growth rate in labor income.In Section III, I also compare this measure to the 1-month lagged labor incomegrowth rate and show that aggregate human capital returns are particularlysensitive to the timing issue, while industry-specific human capital returns arenot. To diminish the influence of measurement errors, I follow Jagannathanand Wang (1996) and Heaton and Lucas (2000) and use a 2-month movingaverage of Lt. I estimate the returns on human capital for industry k in montht as

Rhck,t = Lk,t + Lk,t−1

Lk,t−1 + Lk,t−2− 1. (5)

B. Labor Income Data and Summary Statistics

I retrieve monthly labor income data from the National Income and ProductAccounts (NIPA) Table 2.7. This table provides monthly wages and salariesfor five industries: goods producing, manufacturing, distribution, service, andgovernment. As these industries span aggregate labor income, I am able toallow for heterogeneity and at the same time include the full universe of humancapital assets in the asset pricing model. I scale wages and salaries by thenumber of workers in the industry, using monthly employment data from theCurrent Employment Statistics survey. The sample period runs from April1959 to December 2009. Further details about the data can be found in theInternet Appendix.

Table I, Panel A reports various descriptive statistics for the monthly data.The average growth rate in aggregate labor income for the United States asa whole is 0.38% per month and its standard deviation is 0.39%. Industry-specific labor income growth is substantially more volatile for the goods pro-ducing industry (0.49%), the manufacturing industry (0.56%), and the serviceindustry (0.63%). The average growth rate in labor income is the highest forthe service industry (0.45%), and the lowest for the distribution industry andthe government (0.36% and 0.37%, respectively). Except for the government,the median and mean returns on industry-specific human capital are nearlyidentical. Furthermore, Wald tests show that the differences in the mean andvariance of labor income growth across industries are statistically significantat the 1% level, and the null hypothesis that average growth rates for all fiveindustries are jointly equal to zero is rejected at the 1% level.

Panel B reports the correlation matrix of the monthly returns. All correla-tions between industry-specific human capital returns are positive and rangefrom 0.038 (services and government) to 0.713 (distribution and services). Thepanel also reports correlations between human capital returns and other as-set pricing factors, which are discussed in Section III.D.13 For aggregate labor

13 This includes the equity market index, the lagged yield spread, the Fama and French (1993)size and value factors, the Carhart (1997) momentum factor, and the Pastor and Stambaugh (2003)liquidity factor.

52 The Journal of Finance R©T

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861.

264.

46−2

2.54

16.5

60.

10R

prem

1.01

0.87

0.47

0.32

3.38

0.97

SM

B0.

210.

053.

10−1

6.85

21.9

90.

06H

ML

0.41

0.41

2.87

−12.

3713.8

70.

16M

om0.

750.

884.

25−3

4.69

18.3

50.

06L

iq0.

000.

665.

69−3

8.21

28.6

20.

01R

hc US

0.38

0.38

0.39

−3.9

93.

100.

34R

hc gds

0.38

0.38

0.49

−1.4

84.

010.

43R

hc man

0.40

0.41

0.56

−5.3

23.

970.

35R

hc dist

0.36

0.36

0.40

−3.4

22.

670.

28R

hc serv

0.45

0.45

0.63

−6.6

35.

490.

26R

hc gov

0.37

0.29

0.40

−1.2

12.

850.

39R

f0.

430.

410.

230.

001.

350.

96H

0:m

ean

Rhc

isze

rofo

ral

l5in

dust

ries

(<0.

001)

H0

:mea

nR

hcis

equ

alfo

ral

l5in

dust

ries

(<0.

001)

H0

:Var

(Rhc

)is

equ

alfo

ral

l5in

dust

ries

(<0.

001)

(Con

tin

ued

)


Tab

leI—

Con

tin

ued

Pan

elB

:Un

con

diti

onal

Cor

rela

tion

Mat

rix

ofM

onth

lyR

etu

rns

onth

eF

acto

rs

r mkt

Rpr

emS

MB

HM

LM

omL

iqR

hc US

Rhc gd

sR

hc man

Rhc di

stR

hc serv

Rpr

em0.

055

SM

B0.

302∗

∗∗0.

085∗

∗H

ML

−0.3

19∗∗

∗−0.0

49−0.2

37∗∗

∗M

om−0.1

39∗∗

∗−0.1

27∗∗

∗−0.0

17−0.1

70∗∗

∗L

iq0.

344∗

∗∗−0.0

330.

169∗

∗∗−0.1

16∗∗

∗−0.0

32R

hc US

0.03

20.

020

0.06

6−0.0

170.

039

−0.0

59R

hc gds

0.02

5−0.0

170.

040

0.05

90.

003

−0.1

19∗∗

∗0.

394∗

∗∗

Rhc m

an0.

053

0.03

40.

101∗

∗−0.0

80∗∗

0.09

2∗∗

−0.0

050.

826∗

∗∗0.

305∗

∗∗R

hc dist

0.00

9−0.0

250.

006

−0.0

470.

071∗

−0.0

180.

842∗

∗∗0.

346∗

∗∗0.

702∗

∗∗R

hc serv

0.04

10.

034

0.02

4−0.0

310.

015

−0.0

250.

885∗

∗∗0.

251∗

∗∗0.

676∗

∗∗0.

713∗

∗∗R

hc gov

−0.0

270.

152∗

∗∗0.

058

0.01

20.

034

−0.1

12∗∗

∗0.

266∗

∗∗0.

074∗

0.05

70.

082∗

∗0.

038


income growth, all correlations are insignificant. For industry-specific laborincome growth rates, several correlations are significant. For example, the cor-relation between human capital returns from the manufacturing industry andthe size factor (SMB) is positive and significant. This is in line with the find-ing that small-size portfolios generally have higher human capital betas thanlarge-size portfolios (Jagannathan, Kubota, and Takehara (1998)).

C. Hedging Demand Due to Human Capital

To further highlight the importance of heterogeneity in human capital re-turns, I analyze how industry-specific human capital affects optimal stockportfolios. As five human capital industries are rather coarse for estimatingportfolio choice implications, in this section I focus on nine industries for whichquarterly labor income data are available from the State Quarterly personalincome tables (provided by the Bureau of Economic Analysis (BEA)). The sum-mary statistics for quarterly labor income growth rates for nine industriesare reported in the Internet Appendix and show similar patterns as monthlyhuman capital returns for five industries.

A natural way to hedge industry-specific human capital risk is to adjustthe industry weights of one’s stock portfolio. Therefore, I create eight equityindustry portfolios that match the industries of the human capital returnsbased on SIC codes, excluding the government. The portfolio returns are basedon all common stocks traded on the NYSE, Amex, and NASDAQ from thereturn files of the Center for Research in Security Prices (CRSP).

The hedging portfolio weights of investor i are given by −�−1tr �tr,ntqi, where

qi contains the value of investor i’s human capital over her financial wealth.14 Iestimate these weights by regressing human capital returns for one particularindustry on a constant and the excess returns on the eight industry equityportfolios. I multiply the regression coefficients by –1, which implies that Iestimate the hedging portfolio weights up to qi.

Table II, Panel A reports the results. Consider a young investor who typicallyhas little financial wealth and the main part of his wealth is due to human cap-ital. Suppose that 90% of his total wealth is due to his human capital and 10%is due to his equity investments (i.e., qi = 9). If he was working in the man-ufacturing industry, his optimal stock portfolio should be adjusted as follows.The coefficient estimates in the fourth column show that the investor shouldunderweight stocks from this own industry by about 27% (3.0% × 9). Due to hishuman capital, he is already exposed to stock returns from the manufacturingindustry and to diversify he optimally invests less in manufacturing stocks. Onthe other hand, stocks from the retail industry form a good hedge against hislabor income risk; he should overweight stocks from this industry by 34.5%.In fact, the column with hedging portfolio weights can be interpreted as the

14 As discussed in the Internet Appendix, qi is a K × 1 vector with investor i’s positions in eachof the K nontradable assets. When the investor works in industry 1, elements 2 to K are zero.


Table IIMatched Human Capital and Equity Industries—Hedging Portfolio

WeightsThis table reports the estimated weights of equity industry portfolios in the hedging portfoliosinduced by nontradable human capital from nine different industries of employment. I create eightequity industry portfolios that are matched by SIC codes with the human capital industries: mining,construction, manufacturing, transportation, wholesale trade, retail trade, finance, and services.In addition, I include human capital from the government. Each month I construct value-weightedindustry equity returns, using all common stocks traded on the NYSE, Amex, and NASDAQ fromthe return files of CRSP. I then calculate quarterly compounded returns in excess of the 3-monthTreasury bill rate from 1959Q3 to 2009Q4. Quarterly human capital returns are calculated as thecontemporaneous growth rate in quarterly per-worker labor income. Panel A reports the hedgingportfolio weights in percentages. The first column gives the weights of the eight equity industriesin the hedging portfolio for an investor who works in the mining industry. The subsequent columnspresent hedging portfolio weights for investors working in other industries. These weights areestimated up to q, which is the value of the investor’s human capital over her financial (equity)wealth. The weights are estimated based on an OLS regression of human capital returns on aconstant and excess returns on the eight industry equity portfolios. ∗∗ and ∗ denote significance atthe 5% and 10% levels, based on Newey and West (1987) standard errors with six lags. The lastrow of Panel A reports the p-values (in parentheses) for the Wald test that all hedging portfolioweights in that column are jointly equal to zero. Panel B reports p-values (in parentheses) for theWald tests of the null hypothesis that the hedging portfolio weights for a pair of human capitalindustries are equal. The Wald tests are based on a White covariance matrix.

Panel A: Hedging Portfolio Weights (in %)

mining constr manuf transp wholes retail finance serv gov

mining −2.75 −2.25∗∗ 0.65 0.39 0.79 −0.02 3.88 0.90 −0.67constr −0.47 0.60 −0.27 0.52 0.58 −0.04 −1.86 0.42 −0.32manuf 0.64 4.32∗ −3.00 −0.39 −1.73 −0.57 −6.39 0.21 2.03transp −2.88 −0.77 0.57 3.23∗ 1.04 0.11 0.05 0.49 3.75∗∗wholes −0.25 0.02 −0.41 0.64 0.23 −0.56 −2.41 0.53 1.61retail −5.04 −0.58 3.83∗∗ 0.03 2.76∗ 0.21 4.82 1.97 −0.71finance 5.74 1.03 0.37 −1.42 −1.78 0.00 −3.70 −0.81 −1.80serv −0.20 −1.67 −1.74∗ −2.07 −1.61∗ 0.75 2.51 −2.55∗∗ −1.35p-value (0.412) (0.360) (0.417) (0.664) (0.349) (0.998) (0.289) (0.366) (0.170)

Panel B: p-values of Wald test H0 : HC Industries i and j Have the Same Hedging Portfolios

mining constr manuf transp wholes retail finance serv gov

mining (0.301) (0.198) (0.198) (0.117) (0.465) (0.318) (0.103) (0.103)constr (0.056) (0.035) (0.009) (0.035) (0.015) (0.006) (0.195)manuf (0.118) (0.557) (0.042) (0.139) (0.443) (0.097)transp (0.712) (0.306) (0.066) (0.641) (0.458)wholes (0.275) (0.042) (0.770) (0.126)retail (0.247) (0.316) (0.206)finance (0.028) (0.113)serv (0.057)


adjustments that an industry pension fund should incorporate for its members’human capital. Note that, for about half of the industries, investors should un-derweight stocks in their own industry.

The table shows that, next to their economic significance, several individualportfolio weights are also statistically significant. However, the null hypothesisthat all hedging portfolio weights are jointly equal to zero cannot be rejected,suggesting that the portfolio weights are estimated with considerable noise. Inaddition, the analysis assumes that correlations between human capital andequity returns are constant over the full sample period. The Internet Appendixreports a robustness test in which the hedging portfolio weights are estimatedseparately for the first and second half of the sample period. I find that thenull hypothesis that all weights are zero can be rejected for three and fourhuman capital industries, respectively. Next, I perform Wald tests of the nullhypothesis that workers from two different industries have the same hedgingportfolios, that is, I test whether the different columns in Panel A are equal.Panel B of Table II shows that, for the resulting 36 pairwise tests, the null canbe rejected 12 times, suggesting there is considerable heterogeneity in humancapital hedging portfolios across industries of employment.

A related paper, Davis and Willen (2000b) analyzes portfolio implicationsof heterogeneity in human capital at the occupational level.15 The authorsshow that the covariances between occupation-level income shocks and equityreturns for the closest matched industry are positive for 9 of the 10 occupationsunder consideration. They then calibrate optimal portfolio weights based on alife cycle portfolio choice model. The menu of tradable assets includes eitherown-industry equity returns or equity market returns, and returns on size-based and value-based portfolios. The analysis presented in this section isbased on a simpler single-period model. In addition to own-industry equityreturns, I also consider other industries in the menu of tradable assets. Thisallows me to examine how industry-specific human capital affects the industrycomposition of one’s equity portfolio.

III. Industry-Specific Human Capital and theCross-Section of Stock Returns

I examine the impact of industry-specific human capital on expected stockreturns, based on the multi-beta specification in expression (2). The model iscompared to various benchmark models, including one with aggregate laborincome growth.

15 Based on a life-cycle model, Davis and Willen (2000a) examine labor income risk hedging forsynthetic persons based on birth cohort, education, and gender. They show that introducing newfinancial assets, such as an equity portfolio that matches the industry composition of the personsin the cohort, leads to substantial welfare gains. Fugazza, Giofre, and Nicodano (2011) argue thatthe optimal portfolios of pension funds vary depending on the industry in which the members work.


A. Econometric Approach

I test all models using the two-stage cross-sectional regression method (e.g.,Black, Jensen, and Scholes (1972), and Fama and MacBeth (1973)). While acommon approach is to use multiple regression betas in the first stage, this hasan important drawback. Unless the factors are uncorrelated, first-stage betasdepend on the other factors included in the multiple regression. This compli-cates model selection based on estimated factor risk premia (e.g., Jagannathanand Wang (1998), Cochrane (2005, p. 261), Kan and Robotti (2011)). Also, thenontradable assets model in (2) is expressed in terms of simple regressionbetas. Therefore, I follow Chen, Roll, and Ross (1986) and Jagannathan andWang (1996) and use simple regression betas to determine whether a factoris priced in the presence of other factors. As the matrix of simple betas is alinear transformation of the matrix of multiple betas, the errors and R2s ofthe cross-sectional regression are the same as when using multiple regressionbetas.

Throughout the paper, I estimate betas by performing OLS regressions overthe full sample period.16 I then run a cross-sectional regression of the averageexcess returns on all N assets on a constant and the betas. The standard errorsare adjusted for sampling error in the betas following Jagannathan and Wang(1998), who show that, in the presence of conditional heteroskedasticity, Famaand MacBeth (1973) standard errors do not necessarily overreject in finitesamples. Therefore, following Jagannathan, Kubota, and Takehara (1998) andLettau and Ludvigson (2001), I report the classical Fama–MacBeth t-statistics(t-valueFM) in addition to the adjusted t-statistics (t-valueJW ).

A useful diagnostic statistic to evaluate and compare the different modelsis the OLS adjusted-R2 of the cross-sectional regression, which I calculateas in Jagannathan and Wang (1996). In addition, I report the GLS R2 as analternative measure of model fit, as suggested by Kandel and Stambaugh (1995)and Lewellen, Nagel, and Shanken (2010). The GLS R2 is related to a factor’sproximity to the minimum-variance boundary. Finally, I report the square rootof the average squared pricing error (“rmspe”) and the F-statistic of the testof whether the average pricing error equals zero.17 In a robustness check, I

16 The original Fama and MacBeth (1973) approach uses beta estimates based on the previous60 months. However, the estimated cross-sectional regression coefficients are generally not con-sistent when using rolling betas (Kan and Robotti (2012)). I follow, among others, Black, Jensen,and Scholes (1972) and Jagannathan and Wang (1996), and use full sample betas. The InternetAppendix shows that the relative performance of the models based on 60-month rolling windowbetas is similar.

17 In general, the test statistic for the test that the pricing errors are zero is given byT e′ V (e)+ e ∼ χ2

N−M−1, where e is the vector of OLS pricing errors for all N test assets, V (e)is its estimated covariance matrix, and V (e)+ denotes its pseudo inverse. The number of factorsin the model is denoted by M. I estimate V (e) as in Kan and Robotti (2012), which is robust inthe presence of conditional heteroskedasticity. I use an approximate F-test for better finite-sampleproperties. The test statistic is approximately FN−M−1,T −N+1 distributed.


include portfolio characteristics in the cross-sectional regressions as anothertest of model misspecification.

B. Portfolio Returns

I estimate the asset pricing models for three sets of equity portfolio returns.First, I consider the well-known 25 size and book-to-market sorted (size-BM)equity portfolios, constructed as in Fama and French (1992, 1993). As theseportfolios are known to have a strong factor structure (Lewellen, Nagel, andShanken (2010)), I also consider 100 size-beta sorted portfolios, constructedas in Fama and French (1992) and Jagannathan and Wang (1996). Third, inSection IV, I consider returns on 100 size and IR sorted equity portfolios.

Before performing cross-sectional regressions, I first test the significanceof the human capital betas as suggested by Kan and Zhang (1999). Humancapital betas are difficult to estimate accurately (Jagannathan, Kubota, andTakehara (1998)). The two main reasons are that labor income is relativelystable over time and labor income data may suffer from measurement error.18

Nevertheless, Wald tests reveal that the betas are often jointly significant. Itest whether the exposures to a certain type of human capital (i.e., aggregate orindustry-specific) are jointly equal to zero or whether they are all equal for theequity portfolios under consideration. The results are reported in the InternetAppendix. For the 25 size-BM portfolios, both null hypotheses can be rejectedfor aggregate human capital as well as human capital from the service industryand the government. For the 100 size-beta portfolios, both null hypotheses canbe rejected for all types of human capital returns. These results imply thatthe labor income growth series are unlikely to be useless factors. Moreover,there are strong economic motivations for including human capital in an assetpricing model.

Finally, given the relatively high correlation between human capital returnsfrom different industries, as reported in Table I, a possible concern is thatthe human capital betas are highly correlated. One of the assumptions of thecross-sectional regressions is that the matrix [ ιN B] has full column rank,where ιN is an N-dimensional vector of ones and B is an N × M matrix withthe test assets’ betas with respect to all M factors in the model. I test the nullhypothesis that [ ιN B] has less than full column rank, using the test proposedby Cragg and Donald (1997) and modified by Gospodinov, Kan, and Robotti(2010).19 The Internet Appendix shows that the null can be rejected for the100 size-beta sorted portfolios, but not for the 25 size-BM sorted portfolios.While this does not necessarily imply that the null is true, the results for the25 size-BM portfolios should be interpreted with some caution.

18 In Section IV, I report individual human capital betas for 10 IR sorted portfolios, and in theInternet Appendix I report human capital betas for 100 size-IR portfolios.

19 I thank Raymond Kan for showing me how to perform the rank test.


C. Cross-Sectional Regressions

C.1. Aggregate versus Industry-Specific Labor Income Growth Rates

I estimate the nontradable assets model, which includes a beta with respectto the equity market portfolio and betas with respect to industry-specific laborincome growth rates:

E[rtri ] = c0 + cmktβmkt,i +

5∑k=1

chck β

hck,i, (6)

where βmkt,i is estimated as the slope coefficient of an OLS regression of the ex-cess returns on portfolio i on a constant and the returns on the value-weightedCRSP index in excess of the 30-day T-bill rate, and βhc

k,i is estimated as the slopecoefficient in a regression of the excess portfolio returns on a constant and thelabor income growth rate in industry k. The main benchmark model includesaggregate instead of industry-specific labor income growth rates

E[rtri ] = c0 + cmktβmkt,i + chc

U SβhcU S,i. (7)

Expression (7) is also known as the human capital CAPM (e.g., Jagannathanand Wang (1996), Lettau and Ludvigson (2001)). While the cross-sectional re-gression model is the same as that of the nontradable assets model when K = 1,the human capital CAPM has a slightly different motivation. This model as-sumes that human capital is tradable. As its weight in the market portfolio isunknown, aggregate human capital returns are added as an additional factor.In contrast, in the nontradable assets model, additional factors arise due tohedging demand induced by investors’ nontradable human capital.

Table III, Panel A reports the cross-sectional regression results for the 25size-BM portfolios. The model with industry-specific human capital has an OLSadjusted-R2 of 61% and a GLS R2 of 25%. The square root of the mean squaredpricing error (“average pricing error” in short) equals 0.12% and the null hy-pothesis that all pricing errors jointly equal zero cannot be rejected. Basedon Fama–MacBeth standard errors, the cross-sectional regression coefficientsof human capital from the goods producing, manufacturing, and distributionindustries are significant. For the first two industries, the coefficients are nolonger significant when considering adjusted t-statistics.

In sharp contrast, the model with aggregate labor income growth capturesonly 9% of the cross-sectional variation in average returns. The GLS R2 is 13%.The model has an average pricing error of 0.20% and the null hypothesis thatall pricing errors are equal to zero is rejected. Furthermore, the cross-sectionalregression coefficient of aggregate labor income growth is not statistically sig-nificant, with t-values close to one.

These results highlight the importance of allowing for heterogeneity in hu-man capital. On the basis of aggregate labor income growth rates, one mayerroneously conclude that human capital does not affect expected stock re-turns, while industry-specific human capital appears to play a significant role.


Table IIICross-Sectional Regressions for 25 Size-BM Portfolios: Aggregate

versus Industry-Specific Human CapitalThis table compares three asset pricing models with aggregate and industry-specific labor incomegrowth rates for five industries: goods producing, manufacturing, distribution, services, and gov-ernment. The first model is based on E[rtr,i] = c0 + cmktβmkt,i + chc

U SβhcU S,i,where rtr,i is the excess

return on portfolio i, i = 1, . . . ,N, rmkt is the excess return on the value-weighted CRSP index,Rhc

U S is the growth rate in aggregate per-worker labor income, and βmkt,i (βhcU S,i) is estimated as

the slope of the OLS regression of rtr,i on a constant and rmkt (RhcU S). The second model is based

on E[rtr,i] = c0+cmktβmkt,i+∑K

k=1 chck β

hck,i, where Rhc

k is the labor income growth rate for industry k.Panel A uses contemporaneous labor income growth, which is the main measure used in this paper.Panel B uses a 1-month lag, similar to Jagannathan and Wang (1996). The third model in Panel Ais based on E[rtr,i] = c0+cmktβmkt,i+chc

U SβhcU S,i+

∑Kk=1 chc⊥

k βhc⊥k,i , where Rhc⊥

k is the contemporaneouslabor income growth rate for industry k , which is orthogonalized to Rhc

U S. All betas are calculated asslope coefficients in simple regressions including a constant and the relevant Rhc

k . The table reportsresults based on excess returns on 25 size-BM sorted portfolios, constructed as in Fama and French(1992, 1993), from April 1959 to December 2009. The models are estimated using the Fama andMacBeth (1973) procedure. First, simple betas are estimated using time-series regressions overthe full sample period. Next, average returns are regressed on a constant and the cross-section ofbetas. The table reports cross-sectional regression coefficients estimates, Fama–MacBeth t-values(t-valueFM, in parentheses), t-values that have been adjusted for estimation error in the betas us-ing the Jagannathan and Wang (1998) adjustment (t-valueJW , in parentheses), the cross-sectionalregression’s OLS adjusted-R2 calculated as in Jagannathan and Wang (1996), and below that theGLS R2. The last column reports the square root of the mean squared pricing error (“rmspe”) andbelow that (in square brackets) the F-statistic of the test of H0 : all pricing errors equal zero. Thistest is robust to estimation error in the first-stage betas and conditional heteroskedasticity.

Panel A: Cross-Sectional Regressions for 25 Size-BM Portfolios, Contemporaneous Rhc

c0 cmkt chcU S chc

gds chcman chc

dist chcserv chc

gov R2ols(gls) rmspe

c (× 102 ) 1.53 −0.92 0.17 9.35% 0.20%t-valueFM (4.34) (−2.36) (1.37) 12.53% [2.37]t-valueJW (3.38) (−1.99) (1.18)c (× 102 ) 1.20 −0.94 0.44 0.61 −0.68 −0.23 −0.04 60.92% 0.12%t-valueFM (4.33) (−2.50) (2.66) (2.79) (−3.77) (−0.83) (−0.42) 24.88% [0.96]t-valueJW (2.31) (−1.40) (1.55) (1.46) (−1.86) (−0.49) (−0.24)c (× 102 ) 1.29 −1.02 −0.18 0.64 0.28 −0.13 0.06 0.19 60.10% 0.12%t-valueFM (4.67) (−2.70) (−1.53) (3.57) (3.35) (−2.25) (0.68) (1.37) 29.43% [0.79]t-valueJW (2.18) (−1.32) (−0.76) (1.62) (1.68) (−1.07) (0.32) (0.68)

Panel B: Cross-Sectional Regressions for 25 Size-BM Portfolios, Lagged Rhc

c0 cmkt chcU S chc

gds chcman chc

dist chcserv chc


c (× 102 ) 1.29 −0.71 0.33 19.18% 0.19%t-valueFM (3.53) (−1.81) (2.27) 10.63% [2.10]t-valueJW (2.42) (−1.37) (1.69)c (× 102 ) 1.46 −0.84 0.73 1.04 −0.42 −0.64 0.16 48.46% 0.14%t-valueFM (4.51) (−2.31) (4.57) (3.17) (−1.92) (−2.27) (1.36) 22.33% [0.65]t-valueJW (2.08) (−1.05) (2.07) (1.35) (−0.73) (−0.84) (0.60)


The weak performance of the model with aggregate labor income growthseems to contrast with findings in Jagannathan and Wang (1996) andLettau and Ludvigson (2001). However, they are in line with Fama andSchwert (1977), who find little empirical support for the Mayers (1972) modelwith aggregate labor income growth as a proxy for human capital returns.Jagannathan and Wang (1996) use 1-month lagged labor income growth toaccount for the reporting lag in aggregate labor income data. As discussed inSection II, I use contemporaneous growth rates. This is the economically morerelevant measure, because investors can observe their own labor income inreal time. For comparison, Panel B of Table III reports the results when us-ing 1-month lagged labor income growth rates. In this case, the coefficient onlagged aggregate labor income growth is significant and the model captures19% of the cross-sectional variation in returns. The nontradable assets modelwith lagged industry-specific labor income growth rates continues to have ahigher OLS adjusted-R2 of 48%. Additionally, all industries except for the gov-ernment have significant coefficients. The GLS R2 of this model is also higherand the average pricing errors are lower. The sensitivity of aggregate laborincome growth to the timing of returns suggests that the pricing of lagged ag-gregate labor income growth may be due to announcement effects of aggregatelabor market data. This is also noted by Jagannathan, Kubota, and Takehara(1998), Heaton and Lucas (2000), and Cochrane (2008). In contrast, the abilityof the model with industry-specific human capital to capture the cross-sectionof average returns even improves when using contemporaneous rather thanlagged labor income growth rates. The Internet Appendix discusses the impactof the timing of human capital returns in greater detail and shows that theresults are similar when using quarterly returns.

As mentioned earlier, for the 25 size and book-to-market portfolios, common-ality in betas may complicate the interpretation of the estimated cross-sectionalregression coefficients. For example, note that in Table III not all coefficientsfor industry-specific human capital have the expected positive sign. Table IV,Panel A reports the cross-sectional regression results for an alternative set ofportfolios, namely, 100 size-beta sorted portfolios, for which the null hypothesisof the Cragg and Donald (1997) test can be rejected. The performance of themodel with aggregate labor income growth is better for this set of test assets.The coefficient on aggregate labor income growth is positive and significant,and the OLS R2 is 31%. However, the GLS R2 is close to zero (1.10%). Whenincluding industry-specific human capital returns, both R2s increase to 61%and 12%, respectively. Based on unadjusted t-statistics, human capital fromthe goods producing, service, and government industries is significant at the1%, 5%, and 1% levels, respectively. After adjusting the t-statistics for estima-tion error in the betas, the goods producing and government industries remainsignificant at the 1% and 5% levels. The coefficient estimates are 0.0032 and0.0019.20

20 The models in Tables III and IV have positive and significant estimates of the intercept, whileit should be zero when using excess returns. Also, the market risk premium estimates are negative


Table IVCross-Sectional Regressions for 100 Size-Beta Portfolios: Aggregate

versus Industry-Specific Human CapitalThis table reports results for monthly excess returns on 100 size-beta portfolios from April 1959to December 2009, constructed as in Fama and French (1992) and Jagannathan and Wang (1996).Panel A reports the results for the human capital CAPM (equation (7)), the nontradable assetsmodel with industry-specific human capital (equation (6)), and a model with aggregate and or-thogonalized industry-specific human capital (equation (8)). Human capital returns are calculatedas contemporaneous labor income growth rates. Simple betas are estimated using time-seriesregressions over the full sample period. Average returns are then regressed on a constant andthe cross-section of betas. The table gives cross-sectional regression coefficient estimates, Famaand MacBeth (1973) t-values (t-valueFM, in parentheses), Jagannathan and Wang (1998) adjustedt-values (t-valueJW , in parentheses), the cross-sectional regression’s OLS adjusted-R2, the GLSR2, the square root of the mean squared pricing error (“rmspe”), and below that the F-statisticof the test of H0 : all pricing errors equal zero. Panel B first repeats the industry-specific humancapital risk premia estimates from Panel A, where ∗∗∗ and ∗∗ indicate significance at the 1% and 5%levels based on adjusted t-values. In the nontradable assets model, these coefficients are estimatesof γVar(Rhc

k )qk, where γ is the coefficient of risk aversion and qk is the value of human capitalin industry k over the market value of all tradable assets. The implied qk is based on γ = 5 andassuming that the three insignificant risk premia estimates equal zero. Next, the panel sets γ = 10and calculates qk for these three industries (assuming they have equal qk s) such that the sum of allqk equals that of the base case. Below, the panel reports the implied risk premia. Finally, the threeinsignificant risk premia estimates are set at two standard errors above their point estimates fromthe base case. Below, the panel reports the implied qk , for γ = 10.

Panel A: Cross-Sectional Regressions for 100 Size-Beta Portfolios

c0 cmkt chcU S chc

gds chcman chc

dist chcserv chc


c (× 102 ) 1.01 −0.45 0.37 30.65% 0.18%t-valueFM (5.86) (−1.87) (2.95) 1.10% [1.16]t-valueJW (3.75) (−1.36) (2.27)c (× 102 ) 0.73 −0.10 0.32 0.03 0.09 −0.35 0.19 60.99% 0.14%t-valueFM (4.81) (−0.44) (4.16) (0.19) (0.87) (−2.55) (2.63) 11.82% [0.94]t-valueJW (3.51) (−0.33) (2.99) (0.14) (0.60) (−1.49) (2.09)c (× 102 ) 0.71 −0.11 0.03 0.21 −0.04 0.00 −0.14 0.06 61.89% 0.13%t-valueFM (4.78) (−0.48) (0.45) (3.63) (−0.80) (0.08) (−2.47) (0.90) 12.04% [1.00]t-valueJW (3.59) (−0.37) (0.37) (2.74) (−0.58) (0.06) (−1.94) (0.65)

Panel B: Economic Interpretation of CSR Coefficients

gds man dist serv gov∑K

k=1 qk γ

Base case:c (× 102 ) 0.32∗∗∗ 0.03 0.09 −0.35 0.19∗∗stdev(Rhc) 0.49% 0.56% 0.40% 0.63% 0.40%implied q 26.86 0.00 0.00 0.00 23.05 49.91 5

Experiment 1: adjusting the relative values of human capitaladjusted q 13.43 8.32 8.32 8.32 11.53 49.91 10implied c (× 102 ) 0.32 0.26 0.13 0.33 0.19

Experiment 2: adjusting the estimated risk premiaadjusted c (× 102 ) 0.32 0.39 0.38 0.12 0.19implied q 13.43 12.38 23.79 2.99 11.53 64.12 10


To interpret the magnitudes of these estimated human capital risk premia,it is useful to consider the nontradable assets model in expression (2). Accord-ing to the model, the cross-sectional regression coefficients chc

k are estimates ofγVar[Rnt,k]qnt,k, that is, the risk aversion coefficient multiplied by the varianceof human capital returns and the value of human capital over the value of allstocks. Panel B of Table IV reports the implied relative values of industry-specific human capital (i.e., qnt,k), given the estimated risk premia fromPanel A, the variance of human capital returns, and a risk aversion coeffi-cient of five. First, I assume that the risk premia estimates that are not sta-tistically significant are equal to zero. The implied relative values of humancapital in the goods producing and government industries are qgds = 26.9 andqgov = 23.1. While the value of human capital cannot be observed, Lustig, vanNieuwerburgh, and Verdelhan (2010) estimate that about 90% of total wealthis due to human capital (in line with Jorgenson and Fraumeni (1989) andPalacios (2010)), while only 2% is due to equities.21 This would lead to an ag-gregate measure of q of 45, which is relatively close to the sum of the impliedvalues of qgds and qgov. These findings show that the two human capital riskpremia estimates are reasonably in line with the model for a risk aversioncoefficient of five.

The above calculations should be interpreted with some caution, as theyeffectively assume that the value of human capital in the remaining threeindustries equals zero. To examine the impact of nonzero risk premia for humancapital from the manufacturing, distribution, and service industries, I performtwo simple experiments. First, I calculate the maximum human capital valuein the three industries that would still lead to a plausible total relative valueof human capital. Since for a risk aversion coefficient of five the sum of qgds andqgov is already above 45, I use a risk aversion coefficient of 10, which lowersthe sum of qgds and qgov to 25. I make the simplifying assumption that thethree remaining industries have equal values of q. Keeping the total value ofhuman capital the same as in the base case (

∑Kk=1 qk = 49.9) leads to qman =

qdist = qserv = 8.3. Panel B of Table IV shows that the implied risk premia giventhese values of q are 0.26%, 0.13%, and 0.33%, respectively, which are similarto the regression coefficient estimates of the goods producing and governmentindustries.

The second experiment adjusts the risk premia estimates of the three indus-tries by setting them two standard errors above their point estimates (basedon Jagannathan and Wang (1998) adjusted standard errors). Using γ = 10, I

(similar to, for example, Fama and French (1992), Jagannathan and Wang (1996), Lettau andLudvigson (2001)). In the Internet Appendix I estimate these models imposing a zero intercept.The resulting estimates of cmkt are always positive and often significant. This suggests that thenonzero estimates of the intercepts could be related to the similarity in market betas for many ofthe portfolios.

21 This implies that the value of equity is approximately 20% of all nonhuman wealth, whichis roughly in line with several studies that use the Survey of Consumer Finances data to analyzethe composition of households’ financial wealth (e.g., Poterba and Samwick (2001) and Heaton andLucas (2000)).


find that the implied values of q are higher, leading to a total relative value ofhuman capital of 64.1. A risk aversion coefficient of 13 would bring the totalvalue down to 49, as in the base case.

This discussion suggests that the economic magnitudes of the two signifi-cant human capital risk premia estimates are reasonable for a risk aversioncoefficient of five. When allowing for nonzero human capital risk premia in theremaining three industries as well, economic magnitudes are plausible for arisk aversion coefficient of at least 10.

C.2. Aggregate and Orthogonalized Industry Human Capital Returns

To separate the common component from the industry-specific components inlabor income growth, I estimate the following alternative model specification:

E[rtr,i] = c0+cmktβmkt,i+chcU Sβ

hcU S,i+

K∑k=1

chc⊥k βhc⊥

k,i . (8)

Aggregate labor income growth RhcU S is used as a proxy for the common compo-

nent. The orthogonalized industry-specific human capital returns for industryk (Rhc⊥

k ) are estimated as the residual of a regression of Rhck on a constant and

RhcU S. The slope coefficient of a time-series regression of rtr,i on a constant and

Rhc⊥k is denoted by βhc⊥

k,i .As discussed in Section I, several heterogeneous agent models show that

idiosyncratic labor income risk may affect asset pricing. Intuitively, when in-vestors cannot perfectly share their industry-level labor income risk, industry-specific idiosyncratic labor income risks may affect expected returns, in addi-tion to aggregate labor income risk. The model specification above allows meto test more directly whether industry-level idiosyncratic labor income risksare priced. An additional advantage of removing the common component fromthe industry-specific human capital returns is that it results in substantiallylower correlations between the orthogonalized industry-specific human capitalreturns, which range between –0.44 (service and government) and 0.028 (goodsproducing and distribution).

The results are reported in Table III, Panel A (for 25 size-BM portfolios)and Table IV, Panel A (for 100 size-beta portfolios). In both panels, the co-efficient on aggregate labor income growth is close to zero and insignificant.On the other hand, exposures to industry-specific orthogonalized human capi-tal returns significantly affect the cross-section of expected stock returns. Forthe 25 size-BM portfolios, the coefficients on the goods producing, manufac-turing, and distributive industries are significant, while for the 100 size-betaportfolios, the coefficients on the goods producing and service industries aresignificant. As expected, the R2s are almost identical to those of the modelswith industry-specific human capital returns only. These findings emphasizethat what matters for expected stock returns are mainly the industry-specifichuman capital risks that cannot be shared, rather than labor income risk thatis common to all investors.


D. Comparison with Alternative Asset Pricing Models

Next, I compare the performance of the model with (orthogonalized) industry-specific human capital to five well-known asset pricing models. I first estimateall models for the 25 size-BM portfolios. The results are reported in Table V,Panel A.

I start with the traditional static CAPM:

E[rtri ] = c0 + cmktβmkt,i. (9)

Panel A documents the well-known result that this model fails to capturethe returns on the 25 size-BM portfolios. The estimated market price of riskcmkt is negative and insignificant. The OLS and GLS R2s are 8.6% and 11%,respectively.

I also consider the conditional CAPM, as in Jagannathan and Wang (1996).They show that, when betas and expected returns vary over time, the condi-tional CAPM can be expressed as an unconditional multifactor model, whichincludes the market beta and a so-called premium beta that measures thebeta-instability risk:

E[rtri ] = c0 + cmktβmkt,i + cpremβprem,i, (10)

where βprem,i is measured with respect to the 1-month lagged yield spreadbetween Moody’s Baa- and Aaa-rated corporate bonds from the Federal ReserveBulletin. The estimated cprem is positive and significant. The OLS R2 is 31%and the GLS R2 is 11%.

Next, I consider the Fama and French (1993) three-factor model (referred toas FF3), which is based on the following cross-sectional regression model:

E[rtri ] = c0 + cmktβmkt,i + csmbβsmb,i + chmlβhml,i, (11)

where βsmb,i is estimated as the slope coefficient of a simple regression of theportfolio returns on a constant and the Fama and French (1993) size factorSMB, and βhml,i is estimated similarly using the value factor HML. Both factorsare downloaded from French’s website. Perhaps not surprisingly, the FF3 modelbetter explains the cross-section of returns on the 25 size-BM sorted portfoliosthan the models discussed so far. The OLS and GLS R2s are higher (71%and 34%), and both SMB and HML have significant and positive risk premiaestimates.

The following benchmark model also includes a momentum factor:

E[rtri ] = c0 + cmktβmkt,i + csmbβsmb,i + chmlβhml,i + cmomβmom,i, (12)

where βmom,i is the slope coefficient with respect to Mom, the momentum factorproposed by Carhart (1997), which is also downloaded from Kenneth French’swebsite. Table V shows that the momentum factor is significant and positive,and the R2s improve slightly compared to the FF3 model (75% and 41%).

Various papers show that aggregate liquidity is a priced risk factor (e.g.,Pastor and Stambaugh (2003), Acharya and Pedersen (2005), Korajczyk and


Table VCross-Sectional Regressions: Comparison with Alternative Asset

Pricing ModelsThis table evaluates five benchmark asset pricing models for monthly excess returns on 25 size-BM equity portfolios (Panel A) and 100 size-beta sorted portfolios (Panel B), from April 1959 toDecember 2009. The first model is the static CAPM. The second model is the conditional CAPM fromJagannathan and Wang (1996): E[rtr,i] = c0 + cmktβmkt,i + cpremβprem,i,where Rprem,t−1 is the laggedyield difference between Moody’s Baa- and Aaa-rated corporate bonds and βprem,i is calculated asthe slope of the OLS regression of rtr,i,t on a constant and Rprem,t−1. The three remaining modelsare based on the following cross-sectional regression model: E[rtr,i] = c0 + cmktβmkt,i + csmbβsmb,i +chmlβhml,i + cmomβmom,i + cliqβliq,i,where βsmb,i and βhml,i are estimated as the slope coefficients withrespect to the Fama and French (1993) size and value factors SMB and HML, βmom,i is estimated asthe slope coefficient of an OLS regression of rtr,i,t on a constant and the Carhart (1997) momentumfactor, and βliq,i is estimated as the slope coefficient on the Pastor and Stambaugh (2003) liquidityfactor. I consider the Fama and French (1993) three-factor model that only includes the firstthree factors, as well as the four-factor model including momentum and a model including all fivefactors. The liquidity factor is available for a shorter sample period, from August 1962 to December2008. The cross-sectional regression model is estimated using the Fama and MacBeth (1973)procedure. The table gives estimates of the cross-sectional regression coefficients, the correspondingFama–MacBeth t-values (t-valueFM, in parentheses), Jagannathan and Wang (1998) adjusted t-values (t-valueJW , in parentheses), the cross-sectional regression’s OLS adjusted-R2 calculated asin Jagannathan and Wang (1996), and below that the GLS R2. In the last column, the table reportsthe square root of the mean squared pricing error (“rmspe”) and below (in square brackets) theF-statistic of the test of H0 : all pricing errors are equal to zero. This test is robust to estimationerror in the first-stage simple betas as well as conditional heteroskedasticity.

Panel A: Cross-Sectional Regressions for 25 Size-BM Portfolios

c0 cmkt cprem csmb chml cmom cliq R2ols(gls) rmspe

c (× 102 ) 1.20 −0.51 8.57% 0.21%t-valueFM (3.23) (−1.24) 10.50% [2.68]t-valueJW (3.15) (−1.22)c (× 102 ) 1.73 −1.45 0.61 31.13% 0.18%t-valueFM (4.89) (−3.76) (4.10) 10.89% [1.18]t-valueJW (2.60) (−2.21) (2.58)c (× 102 ) 1.15 −0.69 0.41 0.38 71.27% 0.11%t-valueFM (4.23) (−1.78) (2.76) (2.72) 33.51% [2.10]t-valueJW (4.24) (−1.74) (2.51) (2.73)c (× 102 ) 0.49 0.87 0.32 1.08 3.27 74.65% 0.10%t-valueFM (1.49) (1.49) (2.07) (4.53) (3.66) 41.41% [1.46]t-valueJW (1.15) (1.12) (1.36) (3.16) (2.72)c (× 102 ) 0.73 −0.39 0.29 0.76 1.99 2.38 78.06% 0.10%t-valueFM (2.17) (−0.58) (1.72) (3.18) (2.29) (1.90) 46.14% [1.35]t-valueJW (1.76) (−0.49) (1.19) (2.53) (1.92) (1.56)

Panel B: Cross-Sectional Regressions for 100 Size-Beta Portfolios


c (× 102 ) 0.67 0.01 −1.02% 0.22%t-valueFM (3.81) (0.02) 0.00% [1.44]t-valueJW (3.81) (0.02)

(Continued)


Table V—Continued

Panel B: Cross-Sectional Regressions for 100 Size-Beta Portfolios


c (× 102 ) 0.70 −0.49 0.50 37.25% 0.18%t-valueFM (4.01) (−1.97) (3.52) 0.19% [0.87]t-valueJW (2.66) (−1.40) (2.58)c (× 102 ) 0.65 −0.24 0.45 0.37 63.36% 0.13%t-valueFM (3.77) (−0.72) (2.81) (1.64) 5.23% [1.44]t-valueJW (3.87) (−0.71) (2.75) (1.73)c (× 102 ) 0.58 0.03 0.47 0.41 0.74 64.63% 0.13%t-valueFM (3.12) (0.07) (3.02) (1.74) (1.94) 12.16% [1.31]t-valueJW (2.88) (0.06) (2.83) (1.55) (1.78)c (× 102 ) 0.58 −0.07 0.46 0.37 0.98 0.40 64.76% 0.13%t-valueFM (3.18) (−0.15) (2.80) (1.59) (2.70) (0.60) 12.85% [1.33]t-valueJW (2.82) (−0.12) (2.40) (1.30) (2.28) (0.53)

Sadka (2008)). In the final benchmark model, I include the Pastor andStambaugh (2003) liquidity factor.22 I estimate the following five-factor model:

E[rtri ] = c0 + cmktβmkt,i + csmbβsmb,i + chmlβhml,i + cmomβmom,i + cliqβliq,i. (13)

The results in Panel A show that the coefficient estimate cliq is marginallysignificant based on the unadjusted t-statistic, and the OLS and GLS R2sincrease slightly compared to the four-factor model (78% and 46%).

Panel B reports the results based on the 100 size-beta sorted portfolios. Thepoor performance of the static CAPM is even more dramatic, with R2s close tozero. Furthermore, the coefficient on the liquidity factor loses significance. Theranking of the models based on R2s and pricing errors is similar to Panel A.

Overall, the results in Table V show that a model with (orthogonalized)industry-specific human capital returns compares reasonably well to the fivebenchmark models. The model easily outperforms the static and conditionalCAPM, and has similar R2s and pricing errors as the models with size, value,momentum, and liquidity factors when estimated for 100 size-beta sorted port-folios. For the 25 size-BM portfolios, the latter three models capture 11% to18% more of the cross-sectional variation in stock returns.

E. Robustness Check

This section briefly discusses a number of robustness checks. The results anda more detailed discussion can be found in the Internet Appendix. First, theresults are robust to using quarterly instead of monthly returns.

22 The liquidity factor is downloaded from Pastor’s website. The factor is only available fromAugust 1962 to December 2008. Therefore, model specifications that include the liquidity factorare estimated for this shorter sample period.


Second, I include one human capital industry at a time to address possibleconcerns that the outperformance of the model with industry-specific humancapital is due to the larger number of factors. While the OLS R2s are adjustedfor the degrees of freedom, they may not completely control for the difference inthe number of factors. The resulting model includes the market return, aggre-gate labor income growth, and orthogonalized human capital returns for oneindustry. Using the 25 size-BM portfolios as test assets, I find that the coef-ficient on orthogonalized human capital is significant for all industries. Also,for all industries except manufacturing, the OLS R2 is substantially higherthan for the model with only aggregate labor income growth. For instance,adding orthogonalized human capital returns of the goods producing industryincreases the R2 from 9% to 47%. The results for the 100 size-beta portfoliosare similar. These findings confirm that the higher OLS adjusted-R2s of themodel with industry-specific human capital are not merely due to the largernumber of factors.

Third, I add the factors of the benchmark models (i.e., the yield spread, size,value, momentum, and liquidity) to the models with human capital returns.The significance of aggregate and industry-specific human capital is not af-fected much. I find that the momentum factor loses significance when addedto industry-specific human capital returns. Momentum also becomes insignif-icant when added to aggregate human capital for the 100 size-beta portfolios.All other factors remain at least marginally significant.

Finally, as suggested by Jagannathan and Wang (1998), I include firm char-acteristics in the cross-sectional regressions. If the model is correctly specified,characteristics should not have any explanatory power. I find that average logfirm size and book-to-market ratios are significant in the cross-sectional re-gressions with both aggregate and industry-specific human capital, suggestingthat the models do not pass this model misspecification test. Nevertheless, two(respectively three) human capital industries remain significant.

IV. Human Capital and the Premium for Idiosyncratic Risk

The results presented in Section III support an asset pricing model that in-cludes industry-specific labor income growth rates. In this section, I examinethe consequences of ignoring human capital in an asset pricing model. In par-ticular, I link (industry-specific) human capital to the premium for IR that hasbeen documented in the literature.

According to modern portfolio theory, investors should not receive compensa-tion for stocks’ IR, since this can be diversified away. However, various empir-ical papers report evidence of a cross-sectional relation between IR (measuredas the CAPM or FF3 model residual volatility) and expected returns. Amongothers, King, Sentana, and Wadhwani (1994), Malkiel and Xu (1997, 2004),Spiegel and Wang (2005), and Fu (2009) find a positive relationship. This isin line with the theoretical models of Levy (1978), Merton (1987), and Malkieland Xu (2004) in which investors underdiversify due to market frictions. Incontrast, Ang et al. (2006, 2009) document a negative relationship, based onrealized residual volatility using daily data over the past month. Fu (2009)


shows that this is an imprecise measure of expected idiosyncratic volatilitybecause of its time-varying nature. Using an Exponential GARCH model toestimate expected idiosyncratic volatility, he finds a positive relationship.23

Testing whether IR, measured as the residual volatility of a particular assetpricing model, is priced can be interpreted as a test of model misspecification.If the model captures all systematic risk, residual volatility should not affectexpected returns.24 However, if the model fails to capture all systematic risk,part of that risk ends up in the error term and the resulting IR may appearto be priced. The results presented in Section III show that industry-specifichuman capital affects expected returns. Therefore, a natural follow-up questionis: what happens if human capital is ignored in the asset pricing model? Couldthis induce a relation between the model’s residual volatility and expectedreturns? Before analyzing these issues empirically, I first demonstrate theintuition theoretically, using the nontradable assets model.

A. Idiosyncratic Risk in the Nontradable Assets Model

If systematic risk is measured using the CAPM, the resulting idiosyncratic(i.e., residual) variance equals

�ε = �tr − βmktσ2mktβ

′mkt.

In the absence of nontradable assets (i.e., qnt = 0), the tradable market portfoliois an appropriate benchmark for measuring systematic risk and �ε is the trueIR, which does not affect expected returns. However, in the presence of non-tradable assets, the CAPM does not capture all systematic risk and�ε containssystematic risk due to nontradable assets. Consequently, �ε affects expectedreturns. This can be seen by rewriting expression (1) as

μtr = βmktμmkt + γ �εH,where H = �−1tr �tr,ntqnt. (14)

This alternative specification of the nontradable assets model shows that ex-pected returns are affected by CAPM residual risk, depending on the aggregatehedging demand induced by nontradable assets (−H). To empirically investi-gate the link between IR and nontradable human capital, it is convenient toexpress equation (2) as follows:

E[rtr,i] = βmkt,i E[rmkt] + γ

K∑k=1

Cov[ei, Rhck ]qhc

k , (15)

where ei,t = rtr,i,t − βmkt,irmkt,t, that is, asset i’s residual return with respectto the tradable market portfolio. This expression explicitly shows how the id-iosyncratic return with respect to the CAPM can enter the pricing equation,

23 Also, Bali and Cakici (2008) report that the sign and magnitude of the results in Ang et al.(2006) depend on data frequency, portfolio weighting schemes, and portfolio breakpoints.

24 This argument can also be made when investors underdiversify, for instance, due to transac-tion costs. If the model incorporates these market frictions, idiosyncratic risk with respect to theadjusted measure of systematic risk should not affect expected returns.


depending on its covariance with the returns on (industry-specific) human cap-ital. The model can be tested using a cross-sectional regression including themarket beta and the covariance between CAPM residuals and human capitalreturns. Section IV.C discusses the results.

B. Returns on Idiosyncratic Risk Sorted Portfolios

To empirically investigate the impact of IR on the cross-section of expectedreturns and the link with (industry-specific) human capital, I construct 10 IRsorted portfolios, controlling for size. To this end, I first construct 100 size andIR sorted stock portfolios using all common shares traded on the NYSE, Amex,and NASDAQ (from CRSP).25 I estimate firm-level idiosyncratic volatility asthe market model residual variance, which is in line with equation (14). As arobustness check, I estimate IR as the residual variance of the FF3 model.Following Spiegel and Wang (2005) and Fu (2009), I estimate monthly IRusing an EGARCH model (Bollerslev (1986), Nelson (1991)). For each stock,using all available monthly returns with a minimum of 60 observations, I es-timate nine EGARCH(p,q) models, for (p,q) ∈ {1,2,3}. I select the model withthe lowest Akaike Information Criterion. Each month I double-sort stocks intosize and IR deciles. The breakpoints are based on NYSE stocks only. I calcu-late value-weighted returns on the resulting 100 portfolios and subtract the1-month T-bill rate.26 The Internet Appendix reports summary statistics andCAPM alphas of the full set of 100 size-IR sorted portfolios. I construct 10 IRsorted portfolios by averaging over all size deciles within each IR decile.

Sorting stocks based on idiosyncratic volatility leads to a substantial spreadin the portfolio characteristics. Table VI, Panel A shows that the time-seriesaverage excess returns are increasing in IR and range from 0.30% per month forthe low IR portfolio to 1.28% per month for the high IR portfolio. This is in linewith Fu (2009) and Spiegel and Wang (2005), who report similar large returnsfor portfolios consisting of high IR stocks. Panel A shows that the standarddeviation of the portfolio returns ranges from 3.32% (low IR) to 8.88% (highIR) per month. By construction, the size of the portfolios is similar, althoughthe average size of the low IR portfolios slightly exceeds that of the high IRportfolios.

Portfolios with higher IR stocks also have higher market betas, but this can-not fully account for the return difference between high and low IR portfolios. I

25 A potential concern when investigating IR for portfolio returns is that, in portfolios, stocks’idiosyncratic risks are diversified away. However, the premium for IR that is predicted by thenontradable assets model does not concern true diversifiable IR, but systematic risk not capturedby the CAPM, which should be present in portfolio returns.

26 Since the parameters of the EGARCH model are estimated over the full sample period, the100 size-IR portfolios do not form a true trading strategy. This could be solved by estimating theEGARCH model for each stock for each month, using all returns prior to that month. However, thiswould require estimation of a much larger number of EGARCH models. Also, the main purpose ofthe 100 size-IR portfolios is to examine the contemporaneous link with human capital returns andnot to design a trading strategy based on idiosyncratic volatility. Fu (2009) finds similar resultsbased on full sample or expanding window estimates.


Table VITen Idiosyncratic Risk Sorted Portfolios: Summary Statistics and

Human Capital BetasThis table reports summary statistics and human capital betas of excess returns on 10 idiosyncraticrisk (IR) sorted portfolios from April 1959 to December 2009. Every month, all stocks traded on theNYSE, Amex, and NASDAQ are sorted into size deciles based on their market capitalization at thebeginning of the month. Within each size decile, the stocks are then sorted into IR deciles basedon the estimated conditional idiosyncratic volatility for that month. This double sorting results invalue-weighted returns on 100 size-IR sorted portfolios. Breakpoints are determined using NYSEstocks only. Idiosyncratic volatility is estimated as the residual volatility of the market model. Foreach asset, monthly idiosyncratic volatility is estimated using an EGARCH model for all availablereturns. Returns on the 10 IR sorted portfolios are calculated as the average return over all sizedeciles for a given IR decile. Panel A reports summary statistics (mean, median, standard deviation,average log size (in log $ thousands), and average conditional idiosyncratic volatility of the stocks ineach portfolio), the CAPM market beta, and the alphas of time-series regressions with respect to theCAPM, the Fama–French three-factor model, and the Carhart four-factor model. Panel B reportshuman capital betas, which are calculated based on a simple regression of excess stock returns ona constant and human capital returns. Human capital returns are estimated as contemporaneouslabor income growth rates. Panel C reports the covariance between the CAPM residual return andhuman capital returns. All panels report the results for the 10 IR sorted portfolios, as well as forthe difference between the highest and lowest IR portfolios (H-L). ∗∗∗,∗∗, and ∗ denote significanceat the 1%, 5%, and 10% levels, respectively, based on a Newey and West (1987) adjustment withfour lags. Tests for differences in human capital betas are based on a White covariance matrix. Thelast row of Panel B reports corresponding t-values in parentheses.

Panel A: Summary Statistics of 10 Idiosyncratic Risk Sorted Portfolios

Mean Median Stdev avg IR βmkt αC APM αFF3 α4F(%) (%) (%) avg Size (%) (%) (%) (%)

Low IR 0.30 0.51 3.32 12.73 4.21 0.68 0.00 −0.16∗∗∗ −0.16∗∗∗2 0.44 0.76 3.95 12.73 5.65 0.82 0.09 −0.11∗ −0.10∗3 0.47 0.89 4.33 12.71 6.50 0.90 0.08 −0.13∗∗ −0.11∗∗4 0.53 0.87 4.65 12.70 7.24 0.97 0.11 −0.11∗ −0.075 0.57 0.94 4.95 12.69 7.97 1.04 0.12 −0.09 −0.046 0.60 0.83 5.24 12.68 8.75 1.09 0.12 −0.10∗ −0.027 0.61 0.97 5.58 12.67 9.65 1.17 0.10 −0.11∗ −0.038 0.69 0.81 6.09 12.66 10.79 1.27 0.14 −0.06 0.089 0.71 1.11 6.74 12.64 12.52 1.38 0.12 −0.07 0.11∗High IR 1.28 1.11 8.88 12.60 18.41 1.66 0.56∗∗ 0.50∗∗∗ 0.77∗∗∗H-L 0.98 0.61 5.55 −0.12 14.20 0.98 0.56∗∗ 0.66∗∗∗ 0.93∗∗∗

Panel B: Human Capital Betas

βhcU S βhc

gds βhcman βhc

dist βhcserv βhc

gov

Low IR −0.10 0.18 0.04 −0.30 0.04 −0.502 0.06 0.25 0.11 −0.18 0.09 −0.423 0.20 0.35 0.19 −0.12 0.17 −0.404 0.21 0.30 0.16 −0.19 0.15 −0.285 0.29 0.42 0.30 −0.12 0.19 −0.326 0.44 0.42 0.38 −0.04 0.23 −0.177 0.54 0.48 0.46 −0.02 0.31 −0.058 0.62 0.46 0.49 −0.08 0.34 −0.039 0.81 0.60 0.62∗ −0.07 0.43 0.12High IR 1.74∗ 0.81 1.39∗ 0.28 0.88 0.45

(Continued)


Table VI—Continued

Panel B: Human Capital Betas

βhcU S βhc

gds βhcman βhc

dist βhcserv βhc

gov

H-L 1.84∗∗ 0.63 1.36∗∗ 0.58 0.85∗ 0.95t-value (2.43) (1.10) (2.19) (0.84) (1.82) (1.27)

Panel C: Cov[e, Rhc] × 105

RhcU S Rhc

gds Rhcman Rhc

dist Rhcserv Rhc

gov

Low IR −0.545 0.051 −0.799 −0.588 −0.646 −0.4792 −0.366 0.152 −0.750 −0.413 −0.592 −0.2783 −0.194 0.342 −0.591 −0.324 −0.385 −0.2134 −0.230 0.183 −0.783 −0.445 −0.538 0.0245 −0.134 0.444 −0.445 −0.344 −0.430 −0.0166 0.050 0.399 −0.261 −0.227 −0.345 0.2607 0.165 0.515 −0.109 −0.206 −0.136 0.4818 0.239 0.393 −0.149 −0.325 −0.114 0.5699 0.459 0.674 0.105 −0.322 0.113 0.873High IR 1.725 1.022 2.150 0.189 1.575 1.544H-L 2.270 0.971 2.949 0.776 2.221 2.023

find that time-series alphas with respect to the CAPM are generally increasingin IR. While low IR portfolios do not have significant alphas with respect tothe CAPM, the highest IR portfolio has a significant alpha of 0.56% per month.The difference between the top and bottom portfolios, that is, the “premium”for IR, is significant at the 5% level. Furthermore, the table reports alphas withrespect to the FF3 model and the four-factor model that includes momentum.The premium for IR cannot be explained by these models. In fact, the differ-ences between alphas of the high and low IR portfolios are even larger. In theInternet Appendix, I estimate IR as the residual variance of the FF3 model.The resulting premium for IR is highly significant at 0.91% per month. Thesefindings confirm the positive relation between IR and expected returns that isreported in various papers.

C. Empirical Results

The results presented in this section display a link between human capitaland the premium for IR. First, I find that high IR stocks have higher expo-sures to human capital returns. Next, the model with orthogonalized industry-specific human capital returns explains 68% of the cross-sectional variation inreturns on 100 size-IR sorted portfolios. Third, the covariance between CAPMresidual returns and human capital returns is increasing in IR and is signifi-cantly priced in the cross-section of returns.


C.1. Human Capital Betas

Table VI, Panel B reports human capital betas of 10 IR sorted portfolios,showing that the betas are increasing in IR. The differences between low andhigh IR portfolios are substantial. For example, the lowest IR portfolio has abeta with respect to human capital from the manufacturing industry of 0.04,while the beta of the highest IR portfolio is 1.39. The difference between thesebetas is significant at the 5% level. The difference between betas of high and lowIR portfolios is also statistically significant for aggregate labor income growthand labor income growth from the service industry.27 Hence, stocks with higherIR have higher exposures to human capital returns. Precisely these stocks havehigher alphas with respect to the CAPM, FF3, and four-factor models. In otherwords, the apparent premium for IR is larger for stocks with higher exposuresto human capital.

C.2. Cross-Sectional Regressions

I examine the extent to which the nontradable assets model with industry-specific human capital can explain the cross-section of returns on IR sortedportfolios, based on returns on 100 size-IR portfolios. First, I find that thenull hypothesis of the Cragg and Donald (1997) test can be rejected at the1% level. Also, the null hypotheses that all betas are zero or equal acrossthe 100 portfolios are both rejected for all types of human capital.28

I estimate the three models with aggregate and (orthogonalized) industry-specific labor income growth rates, that is, equations (6), (7), and (8). The resultsare presented in Table VII, Panel A. These findings confirm that the model withindustry-specific human capital outperforms the model with aggregate labor in-come growth. The OLS adjusted-R2 is 60% versus 36%, and the GLS R2 is morethan twice as high. All human capital industries have at least marginally sig-nificant coefficients, while the coefficient on aggregate labor income growth isnot significant. The model with aggregate and orthogonalized industry-specificlabor income growth captures 68% of the cross-sectional variation in returns.

Panel B reports the results of the five benchmark models discussed inSection III. The model with industry-specific labor income growth has simi-lar OLS R2s as the conditional CAPM (65%), four-factor (64%), and five-factor(59%) models. However, these benchmark models have lower GLS R2s. Thestatic CAPM and FF3 models have lower OLS R2s (36% and 44%, respec-tively). The Internet Appendix reports robustness checks similar to those forthe 25 size-BM and 100 size-beta portfolios.

27 The Internet Appendix shows similar results for human capital betas of all 100 size-IR sortedportfolios.

28 These results are reported in the Internet Appendix.


Table VIICross-Sectional Regressions for 100 Size-IR Sorted Portfolios

This table reports cross-sectional regression results for monthly excess returns on 100 size-IRportfolios from April 1959 to December 2009. Panel A reports the results for three different mod-els with human capital returns: the human capital CAPM with aggregate labor income growth(equation (7)), the nontradable assets model with industry-specific human capital (equation (6)),and a model with aggregate human capital and industry-specific human capital returns that havebeen orthogonalized to the aggregate human capital returns (equation (8)). Monthly human capi-tal returns are calculated as the contemporaneous growth rate in per-worker labor income, usinga 2-month average. Panel B reports results for five benchmark models: the static CAPM (equa-tion (9)), the conditional CAPM (equation (10)), the Fama and French (1993) three-factor model(equation (11)), the four-factor model including the Carhart (1997) momentum factor (equation(12)), and the four-factor model augmented with the Pastor and Stambaugh (2003) liquidity factor(equation (13)). The models are estimated using the Fama and MacBeth (1973) procedure. The slopecoefficient βmkt,i is estimated using an OLS regression of ri,t (i =1, . . . ,100) on a constant and rmkt,t,using returns over the full sample period. The other betas are estimated similarly. The table givesestimates of the cross-sectional regression coefficients, the corresponding Fama–MacBeth t-values(t-valFM, in parentheses), and the Jagannathan and Wang (1998) adjusted t-values (t-valJW , inparentheses). The table also reports the cross-sectional regression’s OLS adjusted-R2 calculated asin Jagannathan and Wang (1996) and below that the GLS R2. The last column reports the squareroot of the mean squared pricing error (“rmspe”) and below that (in square brackets) the F-statisticof the test of H0: all pricing errors are equal to zero. This test is robust to estimation error in thefirst-stage simple betas as well as conditional heteroskedasticity.

Panel A: Models Including (Industry-Specific) Human Capital

c0 cmkt chcU S chc

gds chcman chc

dist chcserv chc


c (× 102) −0.19 0.67 0.17 36.43% 0.36%t-valFM (−1.21) (2.72) (1.37) 6.93% [3.48]t-valJW (−1.01) (2.56) (1.41)c (× 102) −0.39 0.72 0.40 0.29 −0.74 −0.41 0.15 59.91% 0.28%t-valFM (−2.59) (2.99) (3.44) (2.05) (−6.01) (−2.55) (1.66) 14.65% [1.20]t-valJW (−1.11) (1.52) (1.85) (0.94) (−2.86) (−1.28) (0.88)c (× 102) −0.65 0.98 −0.33 −0.11 −0.23 −0.21 −0.36 −0.57 68.01% 0.25%t-valFM (−4.55) (4.13) (−4.49) (−1.27) (−4.62) (−5.92) (−5.81) (−8.40) 20.18% [1.84]t-valJW (−2.56) (2.33) (−1.84) (−0.65) (−1.73) (−2.15) (−1.80) (−2.73)

Panel B: Alternative Asset Pricing Models


c (× 102) −0.45 0.97 35.94% 0.37%t-valFM (−2.02) (3.29) 3.24% [4.02]t-valJW (−2.07) (3.41)c (× 102) −0.06 0.16 0.50 64.50% 0.27%t-valFM (−0.31) (0.63) (5.17) 11.25% [1.95]t-valJW (−0.19) (0.41) (3.42)c (× 102) −0.23 0.57 0.38 0.28 43.67% 0.34%t-valFM (−1.58) (1.83) (2.22) (1.34) 4.56% [4.42]t-valJW (−1.56) (1.83) (2.38) (1.43)

(Continued)


Table VII—Continued

Panel B: Alternative Asset Pricing Models


c (× 102) 0.17 −0.36 −0.27 −0.54 −3.26 63.97% 0.27%t-valFM (1.02) (−0.96) (−1.83) (−2.06) (−6.48) 6.50% [3.05]t-valJW (0.57) (−0.50) (−1.17) (−0.87) (−4.19)c (× 102) −0.16 2.12 0.08 0.17 −2.21 −6.35 58.74% 0.26%t-valFM (−1.02) (5.33) (0.50) (0.63) (−4.17) (−8.40) 9.68% [1.81]t-valJW (−0.53) (2.79) (0.28) (0.30) (−2.41) (−5.03)

C.3. The Covariance between CAPM Residual Returns and Human CapitalReturns

According to the nontradable assets model expressed as in equation (15),the covariance between CAPM idiosyncratic returns and human capital re-turns affects expected stock returns. Panel C of Table VI reports estimates ofCov[ei, Rhc

k ] for the 10 IR sorted portfolios. I find that for the lowest IR portfo-lios, Cov[ei, Rhc

k ] is always negative (except for the goods producing industry),while for the highest IR portfolios it is always positive. In all cases, the covari-ance is increasing in IR. This confirms the patterns in human capital betas.According to expression (15), Cov[ei, Rhc

k ] should be priced in the cross-sectionof returns. Therefore, I estimate the following cross-sectional regression:

E[rtr,i] = ψ0 + ψmktβmkt,i +K∑

k=1

ψkCov[ei, Rhck ], (16)

where βmkt,i is the estimated slope coefficient of a regression of rtr,i on a constantand rmkt, and ei is the time-series regression’s residual. The intercept ψ0 shouldbe zero. If the apparent premium for IR is related to the presence of nontradableassets, ψk should be nonzero. Table VIII reports the results.

I find that the cross-sectional regression coefficients ψk are highly significantfor industry-specific human capital for four industries. For aggregate labor in-come growth, the coefficient is not significant. Estimates of the intercept arenegative, and for the model with industry-specific human capital it is statisti-cally significant. In Panel B, I rerun the cross-sectional regressions imposingthe restriction that the intercept equals zero. The R2 is now measured as oneminus the sum of squared errors divided by the sum of squared average re-turns. The coefficient with respect to Cov[ei, Rhc

U S] for aggregate human capitalis positive and marginally significant. For industry-specific human capital,the coefficients for all industries except for services are significant. The OLSadjusted-R2s remain high. These results confirm that the apparent premiumfor IR is related to nontradable human capital.

According to expression (15), the cross-sectional regression coefficientsψk areestimates of γqhc

k . When restricting the intercept to zero, which is in line with


Table VIIINontradable Human Capital and the Apparent Premium for

Idiosyncratic RiskThis table reports tests of the cross-sectional regression model: E[rtr,i] = ψ0 + ψmktβmkt,i+∑K

k=1 ψkCov[ei, Rhck ], where rtr,i is the excess return on portfolio i, rmkt is the excess return on

the value-weighted CRSP index, βmkt,i is the slope of an OLS regression of rtr,i on a constant andrmkt, ei is the residual excess return of portfolio i with respect to the market model, and Rhc isthe return on human capital, estimated as the contemporaneous growth rate in per-worker laborincome (aggregate or industry-specific). The model is estimated using monthly excess returns on100 size and IR sorted equity portfolios using the Fama and MacBeth (1973) procedure. The termsβmkt,i and Cov[ei, Rhc

k ] are estimated using time-series regressions over the full sample period. Inthe second stage, average excess portfolio returns are regressed on the cross-section of betas andcovariance estimates. t-values (in parentheses) are adjusted using Newey–West with four lags.Panel A reports the results of the unrestricted cross-sectional regressions, while Panel B restrictsthe intercept to zero. The table reports OLS cross-sectional regression’s adjusted-R2s and GLSR2s. In Panel A, the OLS adjusted-R2 is calculated as in Jagannathan and Wang (1996). In PanelB, the R2s are based on the (weighted) sum of squared mean returns on the test assets instead oftheir variance.

Panel A: Results Unrestricted Cross-Sectional Regressions

ψ0 ψmkt ψhcU S ψhc

gds ψhcman ψhc

dist ψhcserv ψhc

gov R2ols(gls)

ψ −0.00 0.01 108.92 36.43%t-value (−1.07) (2.91) (1.34) 6.93%ψ −0.00 0.01 171.46 92.05 −464.03 −103.81 90.32 59.91%t-value (−2.32) (2.90) (3.12) (2.09) (−5.08) (−2.50) (1.58) 14.65%

Panel B: Results Restricted Cross-Sectional Regressions: ψ0= 0

ψ0 ψmkt ψhcU S ψhc

gds ψhcman ψhc

dist ψhcserv ψhc

gov R2ols(gls)

ψ 0 0.01 161.36 76.99%t-value n.a. (2.65) (1.72) 3.23%ψ 0 0.00 171.47 126.09 −482.65 −70.63 135.89 85.05%t-value n.a. (1.77) (3.12) (2.62) (−5.24) (−1.56) (2.34) 9.68%

the model, the coefficient on aggregate human capital is positive and significantat 161. Assuming again that qhc = 45 for aggregate human capital results inan implied coefficient of risk aversion of 3.6, which is a reasonable value. Themagnitudes for the industry-specific coefficients are more difficult to interpret.Four out of five industries have significant coefficients, but the coefficient forthe distribution industry is negative. The positive coefficients range from 126to 171, which would result in reasonable relative values of human capital (qhc

k )only for a risk aversion coefficient of 10.

D. Analysis of Cross-Sectional Regression Pricing Errors

Arguably, human capital is not the only missing factor from the CAPM.Therefore, in this section I examine the fraction of the premium for IR that


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Figure 1. Realized average returns versus fitted expected returns. Each scatter plot re-ports the realized full sample average portfolio excess returns against the fitted expected excessportfolio returns (in percentages) for 10 IR sorted equity portfolios, constructed as in Table VI.The fitted value for the expected excess portfolio return E[rtr

i ] is based on the estimates of eightdifferent models: the static CAPM (equation (9)), the human capital CAPM with aggregate laborincome growth (equation (7)), the nontradable assets model with industry human capital (equa-tion (6)), a model with aggregate human capital and orthogonalized industry-specific labor incomegrowth (equation (8)), the conditional CAPM (equation (10)), the Fama and French (1993) three-factor model (equation (11)), a four-factor model including the Carhart (1997) momentum factor(equation (12)), and a five-factor model including the Pastor and Stambaugh (2003) liquidity factor(equation (13)). The cross-sectional regressions are estimated for the 10 IR sorted portfolios aug-mented with 25 size and book-to-market sorted portfolios. Human capital returns are estimated asthe contemporaneous growth rate in per-worker labor income, based on a 2-month moving average.The straight line is the 45-degree line through the origin. The models are estimated using Famaand MacBeth (1973), where βmkt,i is estimated as the slope of an OLS regression of ri,t (i = 1, . . . . ,35) on a constant and rmkt,t. The other betas are estimated similarly.

can be explained by the nontradable assets model with industry-specific hu-man capital. To this end, I analyze the pricing errors of IR sorted portfo-lios. The typical approach based on time-series regression alphas cannot beused because human capital is not a tradable factor. Therefore, I analyze pat-terns in the pricing errors based on cross-sectional regressions. The results in


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Figure 1. Continued.

Table VII show that the model with (orthogonalized) industry-specific laborincome growth rates has lower average pricing errors on 100 size-IR portfoliosthan the human capital CAPM, static CAPM, and FF3 model. To analyze pat-terns in individual pricing errors, I focus on 10 IR sorted portfolios, which areaveraged over all size deciles. This allows me to examine the relation betweenthe pricing errors and IR, while controlling for size effects.

First, I add these 10 portfolio returns to the 25 size-BM sorted portfoliosand estimate the cross-sectional regressions for the resulting set of 35 portfolioreturns. Figure 1 shows scatter plots of the average realized excess returnsversus the fitted expected excess returns for the 10 IR sorted portfolios. Thisfigure provides a visual impression of the model fit. If all points are on the45-degree line through the origin, the model prices all IR sorted portfolioscorrectly. There is one portfolio in particular that has substantial pricing errors:the highest IR portfolio. The failure of the CAPM to price this portfolio is anindication of the apparent premium for IR. The fitted expected returns based onthe CAPM are comparable for the 10 IR sorted portfolios; the 10 dots are onlyslightly upward sloping. Similar results obtain for the model with aggregate


Table IXAnalysis of Cross-Sectional Regression Pricing Errors

This table reports pricing errors of 10 IR sorted portfolios, based on cross-sectional regressions.In Panel A, the 10 IR sorted portfolios are added to 25 size and book-to-market sorted portfoliosand the cross-sectional regressions are estimated for the resulting set of 35 portfolios. In PanelB, the cross-sectional regressions are estimated for 110 portfolios: the 10 IR sorted portfoliosand 100 size-beta portfolios. The 10 IR sorted portfolios are constructed as in Table VI and theother portfolio returns are constructed as in Tables III and IV. The panels report the individualpricing errors (in percentages) of the 10 IR sorted portfolios, as well as the difference betweenthe highest IR and the lowest IR portfolio (H-L). The corresponding t-values (in parentheses) arebased on the asymptotic covariance matrix of the cross-sectional regression’s pricing errors (see, forexample, Kan and Robotti (2012)). The cross-sectional regressions are estimated using the Famaand MacBeth (1973) methodology. Both panels report pricing errors for the following eight models:the static CAPM (equation (9)), the human capital CAPM with aggregate labor income growth(equation (7)), the nontradable assets model with industry-specific human capital (equation (6)),a model with aggregate human capital and industry-specific human capital returns that havebeen orthogonalized to the aggregate human capital returns (equation (8)), the conditional CAPM(equation (10)), the Fama and French (1993) three-factor model (equation (11)), the Carhart (1997)four-factor model (equation (12)), “4F”, and the four-factor model augmented with the Pastor andStambaugh (2003) liquidity factor (equation (13)), “5F.” Human capital returns are estimated asthe contemporaneous growth rate in per-worker labor income, based on a 2-month moving average.

Panel A: Pricing Errors (%) of 10 IR Portfolios When Added to 25 Size-BM Portfolios

Aggr Ind Aggr HC CondCAPM HC HC +Ind⊥ CAPM FF3 4F 5F

Low IR −0.25 −0.26 −0.19 −0.19 −0.34 −0.06 −0.11 −0.062 −0.14 −0.14 −0.04 −0.05 −0.22 −0.04 −0.07 −0.053 −0.13 −0.13 −0.07 −0.08 −0.19 −0.08 −0.10 −0.084 −0.09 −0.08 −0.03 −0.05 −0.11 −0.07 −0.08 −0.075 −0.07 −0.05 −0.06 −0.06 −0.08 −0.06 −0.07 −0.046 −0.05 −0.04 0.01 0.00 −0.09 −0.09 −0.10 −0.067 −0.06 −0.04 −0.05 −0.03 −0.09 −0.11 −0.11 −0.118 0.00 0.03 −0.03 −0.04 −0.02 −0.08 −0.10 −0.039 −0.01 0.02 −0.15 −0.14 −0.02 −0.11 −0.14 −0.07High IR 0.49 0.49 0.31 0.28 0.43 0.44 0.38 0.46H-L 0.74 0.75 0.50 0.47 0.78 0.50 0.49 0.51t-value (7.41) (7.47) (5.29) (5.72) (6.26) (9.03) (8.41) (9.43)

Panel B: Pricing Errors (%) of 10 IR Portfolios When Added to 100 Size-Beta Portfolios

Aggr Ind Aggr HC CondCAPM HC HC +Ind⊥ CAPM FF3 4F 5F

Low IR −0.34 −0.33 −0.26 −0.26 −0.33 −0.30 −0.30 −0.302 −0.21 −0.20 −0.15 −0.15 −0.20 −0.18 −0.19 −0.193 −0.19 −0.19 −0.13 −0.13 −0.16 −0.16 −0.18 −0.164 −0.13 −0.10 −0.07 −0.07 −0.06 −0.09 −0.12 −0.125 −0.10 −0.07 −0.05 −0.04 −0.04 −0.06 −0.09 −0.086 −0.07 −0.07 −0.05 −0.04 −0.06 −0.05 −0.06 −0.057 −0.07 −0.07 −0.05 −0.03 −0.06 −0.03 −0.07 −0.098 0.01 0.02 0.06 0.06 0.00 0.04 0.02 0.039 0.02 0.02 0.03 0.05 0.01 0.04 0.02 −0.01High IR 0.57 0.34 0.55 0.56 0.41 0.54 0.50 0.36H-L 0.90 0.68 0.81 0.82 0.74 0.84 0.80 0.66t-value (9.44) (5.96) (6.79) (7.37) (4.73) (9.26) (7.01) (7.40)


labor income and for the conditional CAPM. For the other models, the fittedreturns fall closer to the 45-degree line, although all models have difficultiespricing the highest IR portfolio. The models with (orthogonalized) industry-specific human capital have the lowest pricing errors for the high IR portfolio.

Table IX, Panel A reports the individual pricing errors for all models. Thebottom two rows report the difference between the pricing errors of the high-est and lowest IR portfolios (H-L), and the corresponding t-statistics. For theCAPM, the difference in pricing errors is 0.74% per month. This alternativeapproach to estimating the premium for IR results in a higher estimate thanbased on the time-series alphas presented in Table VI. The human capitalCAPM with aggregate human capital returns leads to a slightly higher esti-mate of H-L compared to the CAPM, which is 0.75%. In sharp contrast, thepremium for IR is reduced substantially to 0.50% when the model includesindustry-specific human capital and even further to 0.47% for the model withaggregate and orthogonalized industry labor income growth. Based on these es-timates, the nontradable assets model with (orthogonalized) industry-specifichuman capital can reduce the premium for IR by 36%. The benchmark modelshave H-L estimates that range from 0.49% (four-factor model) to 0.78% (con-ditional CAPM). The premium remains statistically significant for all modelspecifications.

As a robustness check, I estimate the pricing errors of the 10 IR sortedportfolios when added to the 100 size-beta portfolios. The results are reportedin Panel B. Similar to Panel A, H-L is positive and highly significant for allmodels. For the CAPM, the estimated “premium” for IR is 0.90%. In this panel,the model with aggregate labor income growth leads to a lower H-L estimatethan the model with industry-specific human capital returns (0.68% vs. 0.81%).According to these estimates, the premium for IR is reduced by 10% to 25%when including human capital in the model.

In sum, while human capital is arguably not the only missing factor fromthe CAPM, an analysis of pricing errors on 10 IR sorted portfolios reveals thatthe model with industry-specific human capital can explain 10% to 36% of the“premium” for IR.

V. Conclusion

Human capital, one of the main components of wealth, is heterogeneousacross investors. This paper shows that human capital heterogeneity at theindustry level affects the cross-section of stock returns. Industry-specific laborincome dynamics and human capital discount rates affect the measurement ofhuman capital returns. This is largely ignored in the commonly used proxy foraggregate human capital returns, which is based on aggregate labor incomegrowth. Furthermore, several heterogeneous agent models show that uninsur-able idiosyncratic labor income risk may affect asset pricing. This suggeststhat, if investors cannot completely share their industry-specific labor incomerisks, these risks may be priced.

I estimate a linear asset pricing model that includes growth rates in industry-level rather than aggregate labor income, in addition to the returns on the


equity market portfolio. In cross-sectional regressions, several human capitalindustries have significant coefficients, while the coefficient on aggregate laborincome growth is often close to zero. Also, allowing for industry-level humancapital heterogeneity increases the cross-sectional R2 substantially: from 9% to61% for 25 size and book-to-market sorted portfolios. These results show thatwhat matters for the cross-section of expected stock returns are primarily theindustry-specific human capital risks rather than aggregate labor income risk.

Next, I relate human capital to the premium for IR that is documentedin various empirical papers. I show, both theoretically and empirically, that,when (industry-specific) human capital is excluded from the benchmark used tomeasure systematic risk, the resulting residual risk affects the cross-section ofexpected returns. The magnitude of the IR premium depends on the exposureto human capital returns.

Initial submission: June 30, 2009; Final version received: June 20, 2012Editor: Campbell Harvey

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Industry-Specific Human Capital