We present sufficient conditions for taxable investors to be indifferent to dividends despite tax differentials in favor of capital gains (Strong Invariance Proposition). The conditions include two ‘seemingly unrelated’ provisions of the Internal Revenue Code: (1) the limitation of interest deductions to investment income received and (2) the tax-free accumulation of wealth at the before-tax interest rate on investments in life insurance. Although we use insurance for simplicity in the proof, many tax-equivalent investment vehicles now exist, notably pension funds. Our analysis suggests that the personal income tax is approaching a consumption tax with further drift likely.

A series of empirically refutable generalized two parameter asset pricing models that linearly relate risk and return are identified for the power (and quadratic) utility members of the linear risk tolerance capital asset pricing models. Five possible power utility models and the mean variance model are tested to determine whether one model might provide a more accurate description of security pricing. The major empirical result is that the data do not allow us to distinguish between the models.

This article re-examines the magnitude of stockholder gains from merger. To measure stockholder gains we employ four alternative two-factor market-industry models in combination with a matched non-merging control group. The four two-factor models are based on either the capital asset pricing model or Black's (1972) zero-beta model combined with two alternative industry factors. The four models are shown to produce generally consistent results. However, the results from a two-factor model are sometimes different from the results of a simpler one-factor model. Also, the introduction of a third factor, the non-merging control group, is shown to have a substantial impact on performance measurement.

Ex post efficient proxies for the market portfolio are tested against the equal weight proxy. The equal weight proxy outperforms the others when the criterion is squared error of conditional prediction of returns. The ex post efficient proxies use maximum likelihood estimates of return. Stein estimates of return will generally be different from the maximum likelihood estimates and they necessarily correspond to market proxies which are not efficient ex post. In other words, there generally exists a better, inefficient, proxy than an ex post efficient proxy when the criterion is squared error of conditional prediction of return.

The new ‘supershare’ securities proposed by Hakansson (1977, 1976) are subject to the same sort of rickless-hedge combinations as are other forms of secondary securities such as stock options. In consequence, the prices of supershares must, even in the absence of distributional assumptions, obey certain pricing relationships with each other and with the underlying primary security. When the primary security is assumed in addition to follow a geometric Brownian motion process, exact supershare valuation formulae of the Black-Scholes (1973) type are obtained. The ‘hedge portfolio algebra’ of Garman (1976) is employed to make the analysis concise.

The Black-Scholes equation for the price u(x,t) of a call option for a single share of common stock with dividend policy d(x,t) is 12σ2x2uxx+(rx−d(x,t))ux−ru−ut=0, 0 extlessx, 0 extlesst extlessT, with boundary conditions u(x,0)=max(0,x−E), 0≤x, u(0,t)=0, 0≤t≤T. The coefficients are unbounded and the equation is not uniformly parabolic. We prove an existence (and recall a uniqueness) theorem for a class of equations with boundary conditions that includes the Black-Scholes equation. These may be used to show that an American option must, or will not, sell for the same price as a European option.

The Black-Scholes option pricing model, as generalized for dividend payments by Merton, is used to calculate implied variances of future stock returns. These variances are found to be better predictors of future stock return variances than those obtained from historic stock price data. A trading strategy is developed that exploits the informational content of the implied variances. The trading strategy, contrary to the efficient market hypothesis, produces abnormally high returns.