The Value Premium

Source: Zhang, L. (2005). Journal of Finance 60(1), 67–103. DOI: 10.1111/j.1540-6261.2005.00725.x

TL;DR

A risk-based, investment-based theory of why value stocks earn higher expected returns than growth stocks. In a neoclassical (q-theory) production economy, costly reversibility (cutting capital is more expensive than expanding it) plus a countercyclical price of risk make assets in place riskier than growth options — especially in bad times when risk is most painfully priced — so value firms command a premium. The value anomaly "arises naturally in the neoclassical framework with rational expectations," with no behavioral assumptions.

The question

Why do value stocks earn higher average returns than growth stocks? Conventional wisdom (e.g., Grinblatt-Titman, Gomes-Kogan-Zhang 2003) holds that growth options are "leveraged" on assets in place and therefore riskier — which would imply growth, not value, earns more. Zhang asks what the neoclassical world actually implies for risk and expected return, and shows the conventional intuition is wrong.

The model

A competitive-equilibrium production economy where heterogeneous firms make optimal capital-investment decisions facing convex but asymmetric adjustment costs, against an exogenous countercyclical price of risk (pricing kernel) and aggregate/idiosyncratic productivity shocks. Two features drive the result:

Costly reversibility: disinvestment costs more than investment, so in bad times value firms (asset-heavy, low growth) are stuck with unproductive capital and cannot easily shed it.

Countercyclical price of risk: risk aversion / risk premia are high in recessions.

Together these make value firms' dividends and returns covary more with bad times, raising their risk exactly when the price of risk is high. Growth firms invest more in good times and their returns covary little with booms. The value premium = risk dispersion between value and growth × the price of risk; time-varying price of risk lets a large average premium coexist with a low unconditional beta spread (bad times are rarer and shorter, so high bad-times dispersion is offset by low/negative good-times dispersion). The model is calibrated at monthly frequency and solved/simulated numerically.

Key predictions

The calibrated model reproduces existing regularities and yields new refutable hypotheses, including:

Value is riskier than growth, especially in bad times (conditional, not unconditional, risk).

High book-to-market signals persistently low profitability; low B/M persistently high profitability.

The expected value premium is high when the value spread (cross-sectional B/M dispersion) is wide, and the two are positively related over time.

Value and expected-return relations should appear across industries; industry cost of capital rises with industry book-to-market.

A high average value premium coexists with a low/near-zero unconditional market-beta spread between value and growth.

Empirical status

Motivated the investment-based / q-factor literature (Hou-Xue-Zhang 2015 q-factors; Fama-French CMA investment factor). Subsequent work (e.g., Petkova-Zhang 2003) supports conditional, countercyclical value betas. The value premium itself is robustly documented (Fama-French 1992, 1993), and a longer 1927–2001 sample shows a value-minus-growth unconditional beta spread of about 0.41 (vs. ~0 in Fama-French's 1963–1991 sample), consistent with the model's emphasis on conditional risk.

Limitations

Calibration-dependent; whether the mechanism quantitatively matches the data in magnitude is debated.

Partial-equilibrium pricing kernel (price of risk exogenous), not derived from preferences in general equilibrium.

Behavioral explanations (extrapolation; Lakonishok-Shleifer-Vishny 1994) fit some facts the risk story struggles with — the value debate remains unresolved.

Key references

Zhang, L. (2005) — The Value Premium — Journal of Finance

Lakonishok, J., Shleifer, A. & Vishny, R. (1994) — Contrarian Investment, Extrapolation, and Risk — Journal of Finance

Fama, E. & French, K. (1992) — The Cross-Section of Expected Stock Returns — Journal of Finance

Hou, K., Xue, C. & Zhang, L. (2015) — Digesting Anomalies: An Investment Approach — Review of Financial Studies

Provenance: verified/generated from the paper's full text.