Firm size, book-to-market ratio and the macroeconomic environment: theory and test

Abstract

Many studies find that stock returns are related to firm size and the book-to-market ratio. This article provides a theoretical explanation for this phenomenon. We show that profit maximizing homogenous firms should converge to a stable long-run equilibrium in which firm's capital size and growth rates are shaped by the economic environment, and both influence stock returns. Our evidence shows firm convergence towards the optimum profitability size in a changing equilibrium. Firm characteristics reflect sensitivity to the macroeconomic environment. Our model and empirical tests demonstrate a linkage between this sensitivity and the relationship of returns to market value and book-to-market.

Notes

¹ Depreciation here is economic, rather than an accounting measure.

² We do not present derivations in this article due to space constraints. The detailed explanation of the theory is available on request from the authors.

³ Assume that the price of the unit of capital is $1 and there is no borrowing. In practice, B _t is a noisy estimator of firm size K _t .

⁴ Using more elaborate models, Russett and Slemrod (1993) investigate propensity to save and Gilchrist and Williams (2000) relate productivity, investment and macroeconomic conditions.

⁵ We are using the company β to control for market risk, since our theoretical model assumes all companies have the same risk.

⁶ Several alternative proxies give similar empirical results.

⁷ Lagged deviation from optimal capital is used so that the condition exists at the beginning of the measured return period.

⁸ To the best of our knowledge, we are the first to use this variable in asset pricing. Whereas inflation or market return characterize overall economic conditions, HITECH specifically characterizes computer-driven technological growth. HITECH gives information about the technological growth for the economy as a whole, whereas FF variables represent individual firm sensitivities to economic conditions.

⁹ COMPUSTAT has market βs only for 1999–2004, which is much shorter than the rest of the annual dataset; thus, we computed market βs for 1986–1998. We used annualized monthly total returns (COMPUSTAT mnemonic: TRT1Y) for all companies and the S&P 500 index (COMPUSTAT mnemonic: i0003). The β is calculated for a 5-year (60-month) lagged time period. If less than 60 months of data is available, β is calculated for as few as 12 months.

¹⁰ http://www.federalreserve.gov.

¹¹ http://www.bls.gov.

¹² www.economagic.com.

¹³ Large returns result from small companies, such as technology firms, which grew very rapidly. We checked these firms for the accuracy of returns and sensitivity to their exclusion, finding little difference in empirical results.

¹⁴ To ensure that our results are not affected by survivorship bias, we used the following procedure for the inclusion of companies in the dataset. If a data point (a company) contains market values and accounting variables sufficient to calculate the relevant size proxy (e.g. if total assets are available when size is proxied by total assets), it is included in the dataset. If in year (t) all required data are available for a company, and not available in year (t + 1) and thereafter, we set market value for year (t + 1) as zero and the corresponding stock return as −100%.

¹⁵ Financials and utilities are omitted. For firms in the financial sector, capital has different interpretation from the rest of the economy. Utilities are heavily regulated and may have different capital investment characteristics than firms operating in a less regulated market environment.

¹⁶ The total number of observations across the eight sectors is 82 683, which is 78.9638% of the total dataset consisting of 104 710 observations.

¹⁷ Our base case measure of capital investment was total assets. As a robustness test, we used different measures. They include total assets, total liabilities, market value of shares, number of employees and gross property, plant and equipment. In all cases we obtained similar results.

¹⁸ We also tried two other proxy variables. They were the size of the company with the highest return in year t, and variable MHDS (median value for total assets for companies in the highest decile of stock returns). In both cases we obtained results consistent with those presented here.

¹⁹ As a robustness test, we used DEVSIZE for the whole sample as an independent variable in Equation 18, used DEVSIZE_t instead of DEVSIZE_{t −1}, and obtained consistent results.

²⁰ The technology bubble of 1995–2000 should bias the results in the opposite direction from what the theory predicts. During this period small technology companies were earning high-stock returns, and therefore we would expect to see a negative relationship between returns and SIZE HITECH. However, our estimates for SIZE HITECH for the whole sample and industry sectors energy, industrials, information technology and telecommunication services are positive, as predicted. We argue that this indicates support for our model, and our results might have been stronger if there had been no technology bubble in the late 1990s.

²¹ Certainly, it is possible that the theoretical model needs refinement to adequately describe firm production and growth. Several factors could affect the results. First, the theoretical model is derived under the assumption of certainty; adding uncertainty may yield different conclusions. Next, we assume only one type of technological change and one production function with homogenous firms, which is not the case in the real world. The effect of using these assumptions on the model's ability to capture the properties of the economy remains unclear. Finally, using accounting proxies introduces estimation errors, and the direction of these errors is unknown.