The composite measures of investment performance: the reward-to-variability index, by Sharpe ([29], [30]) and Lintner [23], and the reward-to-volatility index, by Treynor [33], were developed after Markowitz ([24], [25]) and Tobin [32] popularized the mean-variance framework of analyzing the problems of certain investments. Since these are ex ante measures they are not directly applicable to the evaluation of ex post performance. A theoretical basis for doing so has been provided by Jensen ([17], [18]) who also developed another composite performance measure, the predictability index. In practice, these composite measures have been found to have problems. Foremost, they have been observed to exhibit systematic biases. Various causes of the biases have been proposed. These are: the existence of unequal lending and borrowing rates, the failure to consider higher moments of return distributions, and the elusive “true” holding period.

The purposes of this article are two. Some extensions to Mayers’ [1] classical work on portfolio building in the presence of nonmarketable assets are presented. In addition the implications of certain simple forms of taxation and redistribution are investigated.

The problem of the portfolio demand for money was first rigorously studied by Tobin [22]. It has been analyzed since then, by Hicks [8] and Arrow [1], among many others. Many interesting results and implications regarding liquidity preference and risk-taking are derived in these studies. However, the effect of purchasing power risk on liquidity preference has been overlooked in these studies.

Most research in modern portfolio theory and capital market theory is based on investor selection of portfolios that are efficient in the sense that they are not dominated by other portfolios in terms of their risk-expected return characteristics. The most widely used measure of portfolio risk is the variance about the mean of the exante distribution of portfolio returns. The theoretical framework from which this measure of risk is usually derived was initially suggested by Markowitz [12], and is by now well known. Although variance has the attention of most researchers, another measure, semivariance, had some early support from Markowitz himself, and from Quirk and Saposnik [17], Mao [10], and others. Semivariance as a measure of risk can be derived from the same theoretical framework as is variance; it requires only a slightly different utility function. The semivariance of returns of portfolio p below some point h is defined as

where fp (R) represents the probability density function of returns for portfolio p. Semivariance portfolio theory is enjoying something of a revival in the works of Porter [15, 16], Hogan and Warren [6] and Klemkosky [8], and semivariance capital market models have been developed by Hogan and Warren [7] and Greene [5].

The solution to the problem of portfolio choice is relevant in a positive financial economics context because it provides models of individual maximizing behavior which when aggregated to the level of the market provide models of equilibrium asset pricing. These models generally assume that the parameters of the probability distribution of security returns are known to individual investors. In practice, however, the individual has to estimate these parameters. To the extent that there is parameter uncertainty or “estimation risk”, what are the observable implications of a market equilibrium derived on the assumption that the information set of all investors is equivalent to a given set of sample data?

In a past issue of the Journal of Financial and Quantitative Analysis, Norstrπm [7] has presented a very simple sufficient condition for detecting whether a given pattern of cash flows over time has a unique nonnegative internal rate of return. Nor strum's condition is now widely cited in the literature and included in stock computer routines for analyses using the internal rate of return. See, e.g., de Faro [5] and Newnan [6].

In the literature dealing with bond price volatility, there have been two divergent approaches. On the one hand, theoretical papers have looked at bond price volatility in the instantaneous framework of the calculus. Using the derivative of bond price (P) with respect to yield to maturity (y), it has been shown that volatility is linearly related to this derivative (dP/dy). (See [10].)

In a recent issue of this journal Barnea [1] presented an empirical study of the impact of a specialist (market-maker) on the variability of the price of a stock. He concludes with others that “the chief cost of dealing with a market maker is the difference between the theoretical but unobservable equilibrium price and the transaction price, rather than the bid-ask spread.” This paper presents a rigorous dynamic model in which the specialist, who is uncertain about the future arrival of tenders, determines transaction prices periodically over the trading day. The structure of the model permits a direct comparison of the specialist's prices to the “equilibrium price,” to be defined below, and also to what prices would be in the absence of a specialist.

The widespread notion that dollar-cost averaging can help an investor minimize the risk of investing all of one's capital in the market at an inappropriate time is aptly stated by Malkiel [4, p. 242]:

Periodic investments of equal dollar amounts in common stocks can substantially reduce (but not avoid) the risks of equity investment by insuring that the entire portfolio of stocks will not be purchased at temporarily inflated prices. The investor who makes equal dollar investments will buy fewer shares when prices are high and more shares when prices are low.

This paper develops an exact theoretical test of the presence or absence of a filter effect for a portfolio of securities and a general number of different filter sizes. It is a natural development from Praetz [8], which obtained exact expressions for the mean and variance of rates of return of the investment strategies under filter tests assuming the underlying stochastic process is a random walk. These expressions showed that expected returns from filter strategies are, in fact, less than the return from a buy-andhold alternative with which filter returns are usually compared.

From its beginnings in sixteenth century southern Germany, Professor Landes traces the development of the personal timepiece industry to France, where the design of watches as items of personal adornment reached its peak; to England, where precision in timekeeping and rationalization of manufacture were developed to new heights; to Switzerland, where manufacture on a mass scale for a highly diverse market was attained; and, finally, to America, where the technique of assembling mechanical devices from precision-machined interchangeable parts was applied to watchmaking with the same success it had achieved in less demanding applications. He discusses the sociological factors that produced the Swiss industry in a region of seemingly little promise, and demonstrates how these factors made the Swiss more successful than the Germans, French, or English.