Knowledge that Transforms

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.

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.

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 formula for the price of default-free discount bonds of all maturities is found using a Black- Scholes type of arbitrage model which is based on the assumption that a portfolio of three default-free discount bonds of distinct maturities can be managed to be a perfect substitute for any other default-free discount bond. The formula relates the price of bonds to the real rate of interest, the anticipated rate of inflation and the equilibrium prices of interest rate and inflation risks. Bond prices are shown to be the expected value of the sure nominal proceeds of the bond discounted to the present at a random discount rate. It is shown that the unbiased expectations hypothesis is in general inconsistent with this model.

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.

This paper explores investors portfolio behavior when security returns can be described by one of the forms of the CAPM model and investors pay taxes. The conditions under which an investor holds the market portfolio are explored. In addition the extent to which securities are held in proportions which differ from market weights are shown to be functions of tax rates, dividend policies, and the variance covariance structure between all securities.

In this paper the lower boundary conditions for traded options are derived and subjected to empirical testing. Two hypotheses are formulated based on the theoretical conditions and tested on data on call options traded on the Chicago Board Options Exchange. The first hypothesis argues that the stock and options markets are well synchronized so that simultaneous closing prices are within the theoretical boundaries. The evidence in the ex post test is inconsistent with this hypothesis. The second hypothesis claims the markets to be efficient. The tests are directed toward the question whether arbitrage profits could actually have been made on the Exchange by exploiting the violations of the dominance condition. The tests, carried out as ex ante tests, indicate that positive profits could have been exploited on the average, but the magnitude of the average was small relative to the dispersion of the yields.

Since early 1956 Citizens Utilities Company has had two classes of common stock which are virtually identical in all respects except dividend payout. One class pays only stock dividends, the other class pays only cash dividends, and the corporate charter requires that the dividends per share on the two classes be of equivalent value. Under an I.R.S. ruling granted to Citizens Utilities in 1955 and a ‘grandfather clause’ in the 1969 Tax Reform Act, the stock dividends are not taxable as ordinary income. (No other publicly held firm has such a ruling and, in general, the 1969 Act made stock dividends of this type taxable.) Given these circumstances, the price-dividend history of the Citizens Utilities shares provides a view of the effects of alternative payout policies which, to an exceptional degree, is free of confounding factors. Close examination of this history implies that, if anything, claims to cash dividends have commanded a slight premium in the market over claims to equal amounts (before taxes) of capital gains.

This is the second part of a study about common stock returns around split events (Part I) and dividend change events (Part II) as revealed in the 1947–1967 experience of the New York Stock Exchange (NYSE). Part I is the subject of a companion article in this issue of the Journal. The evidence about splitting stocks was found in many ways consistent with the efficient capital markets hypothesis, slightly method-dependent and time-dependent to an appreciable degree. By contrast, the results from Part II presented below point to persistent inefficiencies in the market. In almost any way one looks at the stocks' residuals in the months following the selected dividend changes, decreases in particular, they turn out abnormally large. The interpretation is advanced that, on the average, the NYSE under-reacts when dividend changes are announced. The possibility is also recognized that unexplored basic problems with the residual approach could account for the abnormal results.