Knowledge that Transforms

Both the Roll and the Geske equations for the valuation of the American call option on a stock with known dividends are incorrectly specified. This note presents the corrected valuation formula, explains the misspecifications and provides a numerical example.

The study examines the impact of convertible security calls on securityholder's wealth. On average common stock values fall by approximately two percent at the announcements of convertible debt calls, but common stockholder's wealth is unaffected by convertible preferred stock calls. These findings are consistent with a corporate tax effect. A small average decrease in firm value is also found at the announcements of convertible debt calls. The study raises, but leaves unanswered, the interesting question of what motivates managers to make capital structure decisions that reduce stockholder wealth and firm value.

The paper examines the optimal behavior of a single dealer who is faced with a stochastic demand to trade (modeled by a continuous time Poisson jump process) and facing return risk on his stock and on the rest of his portfolio (modeled by diffusion processes). Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealer's expected utility of terminal wealth as a function of the state in which he finds himself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined.

Miller and Scholes have shown that under certain conditions the Federal Income Tax taxes dividend income at a rate no higher than the rate on capital gains. Tabulations of actual 1977 tax returns show that the special circumstances under which this can occur apply to recipients of two and one half percent of dividend income and that no dominant role may therefore be ascribed to their hypothesis in the determination of corporate dividend policy.

This study examines the empirical relationship between the return and the total market value of NYSE common stocks. It is found that smaller firms have had higher risk adjusted returns, on average, than larger firms. This ‘size effect’ has been in existence for at least forty years and is evidence that the capital asset pricing model is misspecified. The size effect is not linear in the market value; the main effect occurs for very small firms while there is little difference in return between average sized and large firms. It is not known whether size per se is responsible for the effect or whether size is just a proxy for one or more true unknown factors correlated with size.