All returns great and small: measuring the impact of issues and repurchases on stock returns

When a company issues or repurchases stock at other than market prices a transfer of wealth occurs between equityholder groups such as common shareholders and stock-optionholders. This creates a gap between rates of return earned by common shareholders and rates of return earned by all equityholders that reaches 0.120 percent per month on average (95 percent CI = 0.103 to 0.136 percent per month) for U.S. industrial companies over 1983-1998. The gap, which is due mostly to stock issued at a discount, is inversely related to book-to-market equity and is strongest in March, June, September and December. (Seattle, January 2007)

Equity returns in leveraged risky businesses: simple analytics within CAPM

In a one-period limited liability economy, in which securities are fairly priced according to the CAPM, two, and only two, firm-specific characteristics affect stock returns: bankruptcy risk and cyclicality. The effects of expected cash flows, business risk, and leverage on returns are entirely subsumed by bankruptcy risk. The expected return on equity conditional on the return on the market converges asymptotically to -1. The resulting curvature in the shape of expected returns becomes more pronounced as either bankruptcy risk or cyclicality increases, and is entirely consistent with tenets of the CAPM. (Seattle, August 2006; presentation)

Limited liability, the CAPM and speculative grade firms: a monte carlo experiment

Assuming that investors have limited liability has strong implications for asset pricing: it allows equity to be valued as a call option within the CAPM’s framework; predicts that investors who ignore bankruptcy will find an upward bias in the intercept of stocks’ characteristic lines; and is consistent with the detection of a variety of return anomalies related to size, leverage and business risk, all of which are subsumed by financial distress. Monte Carlo experiments show that these predicted anomalies are significant for speculative grade firms: when bankruptcy risk is 5% (20%), correlation between free cash flows and the market 40%, and the market premium 9%, OLS underestimates true equity beta by 10% (23%) and unconditional expected returns on equity by 164 bp (384 bp) per year. (Seattle, August 2004)

Towards establishing a rationale for distress-related CAPM anomalies, I derive a model of expected returns on common equity that combines features of the diversification and option perspectives on asset pricing. The model demonstrates that traditional measures of systematic risk and expected returns fail to take proper account of bankruptcy risk, and points out the necessary adjustments in the context of a single-period CAPM. The analysis also leads to maximum likelihood estimators for bankruptcy risk and cyclicality implicit in stock return distributions, and delineates a unique role for accrual accounting data in valuation. (Fontainebleau, May 2002; presentation)

Bankruptcy happens: a study of the mechanics of distress-driven CAPM anomalies

After incorporating bankruptcy risk into estimates of expected returns I show that traditional CAPM measurement techniques are biased, and that the magnitude and sign of the errors incurred depends on levels of distress and cyclicality. The analysis leads to maximum likelihood estimators for probability of bankruptcy and cyclicality implicit in stock return distributions. These results are consequential for studies of distress-related CAPM anomalies. They also indicate that there is a unique role for accrual accounting data in valuation to the extent that they lead to more forward-looking measures of distress and cyclicality than models based on historical rates of return. (Fontainebleau, December 2001)

An explanation for bankruptcy’s risk-return paradox

The admission of bankruptcy risk into a single-period CAPM economy leads to two surprising results. First, OLS beta is a biased measure of systematic risk. Second, the expected return conditional on the market is no longer a linear function of beta alone. Instead, it is a linear function of the ratio of conditional to unconditional expected dividends and of that ratio times beta. In this economy very distressed firms should underperform the market because of their high option values and strong contributions to portfolio diversification. This is confirmed by empirical tests that replicate Dichev’s paradox. (Fontainebleau, November 2001)

Understanding anomalous stock market prices

A model of the firm that admits bankruptcy sheds light on the often puzzling behavior of asset prices vis-à-vis the CAPM. Option-like stock price features are obtained within the CAPM’s equilibrium framework by taking into account the limited liability of shareholders. This yields several properties of beta that have been demonstrated empirically. The central result is that the OLS estimator of beta is unable to reflect properly the likelihood of bankruptcy, and therefore produces biased estimates of beta in a way that is consistent with stock return anomalies. Alternative estimators for beta are proposed. (State College, June 1994)

An economic story for beta

A model of the firm that allows the possibility of bankruptcy with limited liability leads to expressions for beta and equity value as a function of financial risk, business risk, and the correlation between the firm’s payoff and the market’s rate of return. This produces two new results. The first is a valuation formula with characteristics similar to those obtainable under the option pricing model, but derived strictly within the CAPM’s equilibrium framework. This also reproduces several properties of beta which have been demonstrated empirically. The second contribution is an expression for systematic risk “as observed” by analysts who cannot properly assess the likelihood of bankruptcy from historical rates of return. This suggests that the OLS estimator for beta is severely biased for certain firms, and yields predictions about the sign and magnitude of the bias. Alternative estimators for beta are proposed. (State College, May 1994)

The Importance of beta: making sense of the cross-section of expected stock returns

Beta is important in explaining the cross-section of stock returns, with the sign and almost with the magnitude predicted by the CAPM. In 302 monthly regressions of stock returns on beta alone, the coefficient of beta is significantly positive at the 5% level 205 times. When size and book-to-market equity are included in the regression, beta is significant 214 times, about 1.7 times as often as size and book-to-market equity. This is at odds with recent claims that beta is irrelevant. The reason for this difference of opinion is that standard tests based on the sign of the mean coefficient of beta are misspecified. Our test requires that the coefficient of beta be capable of tracking realized market premia over time, instead of requiring that it should be a good estimator of the expected market premium. Additional evidence on the CAPM is obtained from a breakdown of average slopes by calendar month: beta has the right sign and magnitude almost every month of the year, book-to-market less than half the time; size only during the first quarter. (State College, September 1994)