Markov Chains and Regression toward the Mean

Using the theory of stationary Markov chains, we uncover a previously unknown property of the behavior of betas. Specifically, if the cross-sectional distribution of betas is stationary over time, then the set of firms that remain in an arbitrarily chosen beta interval between one period and the next will not regress toward the mean. This surprising result occurs in spite of the well-known fact that the set of all the firms in the interval will exhibit the regression tendency. Our empirical tests indicate that betas behave in remarkable accordance with this prediction.     

Precautionary saving and partially observed income

I propose an intertemporal precautionary saving model in which the agent's labor income is subject to (possibly correlated) shocks with different degrees of persistence and volatility. However, he only observes his total income, not individual components. I show that partial observability of individual components of income gives rise to additional precautionary saving due to estimation risk, the error associated with estimating individual components of income. This additional precautionary saving is higher, when estimation risk is greater. Compared with a precautionary agent who is otherwise identical, but ignores estimation risk, the rational agent consumes less at the beginning of his life, but consumes more later, because of larger wealth accumulated from savings for estimation risk. The utility cost of ignoring estimation risk is also quantified in closed form.     

The estimation of mortality and other decremental probabilities

Abstract

The standard actuarial methods of estimating the age-specific one-year probabilities of death in a given community were developed—for the most part, many years ago-with large bodies of observations in mind. Although the familiar “exposed to risk” procedure is known to provide unbiased estimates only when a rather dubious assumption is made about the progression of the instantaneous death-rate (the force of mortality) over the year of age (Cantelli, 1914) it is still the most widely used method of estimation. This is partly because the age-to-age increment in human mortality is relatively small—so that assumptions about its mathematical form are unimportant—and partly because suggested methods of estimation based on more “realistic” assumptions are usually laborious to apply to thousands of observations.     

Firm specific and macro herding by professional and amateur investors and their effects on market volatility

We find a herding tendency among both amateur and professional investors and conclude that the propensity to herd is lower in the professionals. These results are obtained both when we consider herding into individual stocks and herding into stocks in general. Herding depends on the firm’s systematic risk and size, and the professionals are less sensitive to these variables. The differences between the amateurs and the professionals may be attributable to the latter’s superior financial training. Most of the results are consistent with the theory that herding is information-based. We also find that the herding behavior of the two groups is a persistent phenomenon, and that it is positively and significantly correlated with stock market returns’ volatility. Finally, herding, mainly by amateurs, causes market volatility in the Granger causality sense.