Knowledge that Transforms

A simple, necessary and sufficient condition is derived under which portfolios that are mean-variance efficient on a before-tax basis are also efficient on an after-tax basis and vice-versa. Under this condition and the hypothesis that investors demand after-tax efficient portfolios, the ‘no-tax’ form of the Capital Asset Pricing Model provides an accurate description of equilibrium asset returns even though investors in the economy may be subject to a wide variety of tax rates on dividends and capital gains. Evidence reported by Black and Scholes (1974), however, makes the condition for equivalence of before and after-tax efficiency empirically implausible. The paper thus concludes with a characterization of some essential differences between before and after-tax efficient portfolios and of the after-tax efficiency losses associated with before-tax efficient portfolios. The relation of these results to the issue of corporate dividend policy choices is also discussed.

Dual fund shares allow individuals to satisfy their divergent preferences for the ordinary income and the capital gains components of return. Institutional restrictions on short selling are shown to permit discounts on dual funds to fluctuate within wide bounds. However, these fluctuations are shown to be consistent with informational efficiency. The average discount is shown to have a contemporaneous association with net redemptions of diversified open-end funds. It is shown that the high turnover of dual fund portfolios is not warranted by their portfolio performance and causes redistributions of wealth between income and capital shareholders.

Assuming continuous trading in continuous time with Brownian motion processes, the basic capital asset pricing model of Sharpe, Lintner, and Mossin is developed under arbitrary distributions of investors' beliefs consistent with available information. Results on the processing of information are reported, and properties of investors' portfolios are derived.

A general formula is derived for the price of a security whose value under specified conditions is a known function of the value of another security. Although the formula can be derived using the arbitrage technique of Black and Scholes, the alternative approach of continuous-time portfolio strategies is used instead. This alternative derivation allows the resolution of some controversies surrounding the Black and Scholes methodology. Specifically, it is demonstrated that the derived pricing formula must be continuous with continuous first derivatives, and that there is not a ‘pre-selection bias’ in the choice of independent variables used in the formula. Finally, the alternative derivation provides a direct proof of the Modigliani-Miller theorem even when there is a positive probability of bankruptcy.

The relative performance of several portfolio selection strategies is assessed empirically. These strategies vary in sophistication from a ‘naive’ strategy of maintaining equal dollar investments in each stock available to a strategy that periodically uses updated parameter estimates to calculate new optimal proportions of portfolio value to be invested in the stocks available. Although it is to be expected a priori that relatively sophisticated strategies will perform at least as well as the more naive strategies, implementation costs will clearly differ across strategies and across investor-specific parameters such as total portfolio value. Thus estimation of the various strategies' performance gross of these costs is a necessary consideration in rational strategy selection by any given investor.

The option pricing model developed by Black and Scholes and extended by Merton gives rise to partial differential equations governing the value of an option. When the underlying stock pays no dividends – and in some very restrictive cases when it does – a closed form solution to the differential equation subject to the appropriate boundary conditions, has been obtained. But, in some relevant cases such as the one in which the stock pays discrete dividends, no closed form solution has been found. This paper shows how to solve these equations by numerical methods. In addition, the optimal strategy for exercising American options is derived. A numerical illustration of the procedure is also presented.

The State of Maine recently imposed an additional regulation on the maturity of small loans offered by finance companies, presumably to protect the consumer. The effectively restricted the maturity of these high interest rate loans to 36 months. Within five years, the number of licensees (finance company offices) declined from 116 to 24. Within another five years, all of these lenders had completely ceased operations. Hypotheses on the effect and value to consumers of the regulation are stated operationally and tested empirically. This study includes estimation of the loan companies' cost function, (accounting) profit rates and output and a survey of the individuals directly affected by the demise of the companies. The analysis indicates (1) that the maturity restriction made ordinary operations unprofitable, (2) why this occurred, and (3) that half of the consumers did not obtain funds elsewhere.

Nonsynchronous trading of securities introduces into the market model a potentially serious econometric problem of errors in variables. In this paper properties of the observed market model and associated ordinary least squares estimators are developed in detail. In addition, computationally convenient, consistent estimators for parameters of the market model are calculated and then applied to daily returns of securities listed in the NYSE and ASE.

We estimate the extent to which various assets were hedges against the expected and unexpected components of the inflation rate during the 1953–1971 period. We find that U.S. government bonds and bills were a complete hedge against expected inflation, and private residential real estate was a complete hedge against both expected and unexpected inflation. Labor income showed little short-term relationship with either expected or unexpected inflation. The most anomalous result is that common stock returns were negatively related to the expected component of the inflation rate, and probably also to the unexpected component.

In this paper, we develop a Capital Asset Pricing Model (CAPM) using a mean-lower partial moment framework. We explicitly derive formulae for the equilibrium values of risky assets that hold for arbitrary probability distributions. We show that when the probability distributions and portfolio returns are either normal, stable (with the same characteristic exponent between 1 and 2 and the same skewness parameter, not necessarily zero), or Student-t distributions, our CAPM reduces to the traditional mean-scale CAPM's. Consequently, since the traditional equilibrium models are special cases of our model, the mean-lower partial moment framework is guaranteed to do at least as well in explaining market data. As an application of our theory, we derive an acceptance criterion for capital investment projects and note that corporate finance theory results developed, for example, in the well-known mean- variance framework carry over to the mean-lower partial moment framework.