Japanese Economic Review

How to Cite

QIN, J. (2002), Human-Capital-Adjusted Capital Asset Pricing Model. Japanese Economic Review, 53: 182198. doi: 10.1111/1468-5876.00222

Author Information

Ritsumeikan University, Kusatsu City, Shiga-ken

The author is very grateful for useful comments from two anonymous referees. He also thanks Hiroyasu Akakabei, Masayuki Ikeda, Shinsuke Ikeda, Nabil El-Maghrebi, Kazuhiko Nishina, Masamitsu Ohnishi, Susumu Saito, Yoshio Tabata, Yasuhiko Tanigawa, and Yoshiro Tsutsui for their helpful discussions and suggestions. Financial support from the Zengin Foundation of the Japanese Banks Association and from a Nanzan University research subsidy are also gratefully acknowledged.

See e.g. Fama (1991) for a useful discussion on stock market anomalies, and Mehra and Prescott (1985). Weil (1992) and Hansen and Jagannathan (1991) for the «premium puzzle» and the «risk-free rate puzzle».

Roll (1977) argues that one possible reason for the poor performance of the CAPM is that the value-weighted index of stocks is a poor proxy for the portfolio of aggregate wealth. In the case of Japan, according to the Japan Statistical Yearbook (1999). national income amounted to a total of 389,703 billion Japanese yen in 1996, of which 279,414 billion (71.7%) represented wages and salaries, 22,653 billion (5.8%) accounted for property income and 87,636 (22.5%) billion represented entrepreneurial income. Dividend income, which is included in property income, represented only 5758 billion yen (1.5%) of the total national income.

Jagannathan and Wang (1996) find that the conditional CAPM explains 30%, and 50% when human capital betas are included, of the cross-sectional variation in average returns of 100 stock portfolios. Jagannathan et al. (1998) find that the R 2 statistic rises from 2% to 75% when human capital beta is added into the conventional CAPM.

There are some previous studies of human capital valuation. For example, in Richard (1975). which examines the problem of investment and consumption in the case of constant labour income and uncertain lifetime, the value of human capital is determined according to the price of life insurance. Bodie et al. (1992) investigate the effect of the labourleisure choice in a framework similar to that of the present paper; under the assumption that human capital can be valued as if it were traded in markets, they give the value function of human capital without strict proof. In Svensson and Werner (1993). which considers incomplete markets, the value function of human capital is determined such that, if a claim on an individual’s labour income were added into security markets and were priced by that function, this individual would be willing to hold the entire claim. Recently, Koo (1998) has investigated the effect of market imperfection and derived the value function of human capital following the approach of Svensson and Werner (1993). The present paper differs from these studies in that it derives the no-arbitrage price of human capital with option pricing methods. For a detailed discussion on this paper’s approach of human capital valuation, see Qin (2000) .

Some studies extend the CCAPM to account for uninsurable labour income risk. For example, Weil (1992) studies the effect of uninsurable income risk on asset pricing in a two-period model. Heaton and Lucas (1996) consider the case where individuals face transitory shocks, transaction costs and borrowing and lending constraints. Constantinides and Duffie (1996) focus on the case where idiosyncratic shocks have permanent effects on human capital. Recently, Cuoco (1997) proved the existence of an optimal consumption policy in the presence of portfolio constraints, and derived an equilibrium model that relates the price of a security to both its consumption beta and the shadow prices of the constraints. The present paper differs from these studies in that it is a generalization of the CAPM.

This paper assumes complete markets. However, with little modification, the present analysis can be extended to the case of incomplete markets where investment opportunities depend on state variables that are not spanned by securities. In such cases, a multi-beta asset pricing model can be derived in which market beta, human capital beta and state-variable betas are included. This paper argues that allowing for stochastic investment opportunities without state variable specifications has few economic implications; hence it assumes complete markets to simplify the analysis.

This paper’s assumption of labour income can also be interpreted as the economy’s labour input co-moving with its capital stock level.

In fact, the asset pricing model of the present paper does not depend on specific valuation function of human capital; it depends only on the assumption that human capital can be replicated by a self-financing strategy in security markets. Hence, as long as labour income satisfies some regulating conditions that insure the existence of replicating strategies for human capital, the major results of the paper will hold with little modification. For a general method of human capital replication and valuation, see Qin (2000). where the assumption of (2) and some other specifications of labour income are treated as special cases.

Here, what needs to be replicated is a flow of labour income, not an amount of cash paid at a single date. The replicating strategy is self-financing, not with the usual meaning, but in the sense that that there is neither cash inflow nor cash outflow except for the initial investment and the cash flow to be replicated. Similar definitions of self-financing strategy are adopted in the case of pricing American options that are written on dividend-paying stocks. For a detailed discussion, see e.g. Karatzas (1988) and Qin (2000) .

?H i /?S =a i ₀ T t (d ₁ )ds. H i /?t =a i C (S ,T t )b i e r (T t ). , and. 2 H i /?S ?t =a i (d ₁ )|_{s =T t} . where () denotes the density function of the standard normal distribution.