Stock return, inflation, and the Du Pont identity.

Author:Yi, Taihyeup David


A vast of research has been done to identify what risk factors determine asset returns since the Sharpe (1965) and Lintner (1965) capital asset pricing model was developed. Fama and French (1993) argue that the higher average returns on small stocks and high book-to-market stocks are possible risk factors that may explain asset returns that are not captured by the market risk. On the basis of Jegadeesh and Titman (1997)'s momentum effect where short-term winners performed better than short-term losers, Carhart (1997) shows that the effect should be an additional factor in explaining asset returns. Chen, Novy-Marx, and Zhang (2010) claim that the Fama-French model cannot explain cross-sectional patterns, documenting anomalies where asset returns are positively related to short-term prior returns and earnings surprises, and are negatively related to financial distress, net stock issues, and asset growth. They introduce a new three-factor model from q-theory where the expected asset returns depend on the market factor, an investment factor, and a return-on-assets (ROA) factor, showing that the model explains better the aforementioned anomalies than the Fama-French and the Carhart models.

The Du Pont identity indicates that the return on equity (ROE) is determined by ROA and financial leverage where ROA is a product of profit margin and an asset turnover. Controlling for market risk and firm size, Bhandari (1988) shows that the expected stock returns are positively related to financial leverage. However, Fama and French (1992) document that the book-to-market risk factor incorporates the leverage effect. Previous research on a relation between asset betas and financial leverage is mixed. Kaplan and Stein (1990) and Grullon and Michaely (2004) find a negative relation while Healy and Palepu (1990) and Kadlec (1994) find a positive relation. Based on a time-series approach, Korteweg (2004) finds that an increase in financial leverage in an exchange offer is associated with a decrease in asset betas, and vice versa, and that expected risk premiums for highly levered firms are too low. In addition, Cai and Zhang (2009) show that stock prices are significantly negatively affected by an increase in the financial leverage ratio of firms with limited debt capacity, supporting the pecking order theory where the increase may lead to future underinvestment.

On the basis of the market risk, ROA, and financial leverage factors in the traditional and recent asset pricing models, I develop the following model:

(1) [R.sub.i,t] = [a.sub.0,i] + [a.sub.1,i][ MRP.sub.t] + [a.sub.2i] [PM.sub.t] + [a.sub.3,i] [AT.sub.t] + [a.sub.4,i] [EM.sub.t]

where [R.sub.i,t] is an excess stock return over the one-month Treasury bill rate, [MRP.sub.t] is the market risk premium, PMt is profit margin, [AT.sub.t] is an asset turnover, and [EM.sub.t] is an equity multiplier as a measure of financial leverage. Note that ROA is a product of profit margin and an asset turnover. I find that most of the coefficients of the market risk premium and an asset turnover are significantly different from zero, supporting the factor model of Chen, Novy-Marx, and Zhang (2010).

The Fisher effect says that an asset return moves one on one with expected inflation. However, most evidence is inconsistent with the effect that nominal stock returns are negatively related to expected inflation. To resolve the empirical puzzle, Fama (1981) uses a proxy hypothesis where inflation is a proxy for real activity. The negative relation occurs because stock price and inflation react in an opposite direction to a change in expected future output. Boudoukh, Richardson, and Whitelaw (1994) find cross-sectional differences in the covariance between expected inflation and nominal returns. Their results suggest that the stock returns of non-cyclical industries co-vary...

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