Bruce D. Fielitz

Long-term dependence in common stock returns

The efficient market, martingale model of security price movements requires that the arrival of new information be promptly arbitraged away. A necessary and sufficient condition for the existence of an arbitraged price is that statistical dependence among prices must decrease very rapidly. If persistent statistical dependence is present, the arbitraged price changes do not follow a martingale and should have an infinite variance. Using a technique for detecting long-term dependence, called R/S analysis, 200 daily stock return series are studied; many series are characterized by long-term dependence. Thus, in the presence of long-term dependence, the martingale model does not hold. Also, the distribution of security returns is non-normal stable Paretian as opposed to Gaussian.

Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns

Abstract The form of the distribution underlying common stock returns has many implications for financial modeling. Among the frequently proposed models for stock return distributions is the family of stable distributions. Numerous studies of stock return distributions have also proposed various types of mixtures of normal distributions. This article examines the characteristics of several different combinations of mixtures of normal and stable distributions, and compares them with actual stock price distributions. The principal tests applied are based on the stability-under-addition property of stable distributions.

Asymmetric Stable Distributions of Stock Price Changes

Abstract This note presents evidence that the asymmetric members of the stable family of distributions are appropriate for describing changes in stock prices.

The Behavior of Stock-Price Relatives-A Markovian Analysis

This paper presents a method of Markovian analysis of changes in the natural logarithms of stock prices over time. It examines 200 stocks from the New York Stock Exchange for the period December 23, 1963, to November 29, 1968, and defines a set of three states up, down, small change for the process in terms of the mean absolute deviation of changes in the natural logarithms of prices. This definition of the set of states allows both the magnitude and the direction of change to be incorporated in the analysis. Standard statistical tests for stationarity and dependence in vector and individual-process Markov-chain models are employed for both fixed-and variable-time data the latter refers to highs for a day or week interval. In addition, a method for testing the homogeneity of the vector Markov chain is given. Empirical results for the vector-process model suggest that price movements appear to be described by a first-or higher-order nonstationary Markov chain. Tests also indicate that the vector-process Markov chain is heterogeneous. Empirical results for the individual-process Markov-chain model suggest that an individual stock has a short-term memory with respect to daily price relatives, i.e., the process is first-or higher-order. However, the corresponding process lacks stationarity. No dependency appears to exist for a weekly time lag.

The Effect of Long Term Dependence on Risk-Return Models of Common Stocks

In a previous paper the authors have shown that common stock returns are characterized by a phenomenon called long term dependence. The present paper discusses the implications of the presence of long term dependence for existing risk-return models in finance. Specifically, it is shown that (1) risk rankings of stocks or portfolios tend to vary with the differencing interval chosen to measure security returns, (2) efficient portfolios vary with the differencing interval selected, and (3) the unrealistic, homogeneous time horizon assumption of the capital asset pricing model must be retained in order for the model to hold.

Method-of-moments estimators of stable distribution parameters

A method is developed for estimating the four parameters of stable Paretian distributions. Based on a procedure proposed by an earlier researcher but never developed, the method proves to be mathematically simple and easy to apply. The method is extensively tested and sampling properties of the estimators are studied, providing approximate confidence intervals for the estimators.

Managing cash flow risks in stock index futures

1 74 m 5 T he DurDose of this DaDer is to orovicle inI I I I 53 5 stitutional users of stock index futures contracts with an analytical model for assessing and monitoring their potential funds or liquidity needs during the implementation of index futures trading programs, Regardless of the particular use of stock index futures that is employed, managers are finding that considerable attention must be devoted to monitoring the cash flow resulting from the daily resettlement of these contracts. A lack of attention to this often overlooked aspect of futures trading has the potenti,d for catching the manager cash short, thereby necessitating selling equity holdings or closing some of the futures position action that can have damaging implications for portfolio performance. The paper is organized as follows. First, we briefly review some of the many uses of stock index futures in portfolio management and describe thle important relationship that daily resettlement will have in conjunction with these strategies. We then introduce a model that has been used previously in the futures literature for describing optimal margin setting behavior on the part of the exchanges. We adapt this model to the problem at hand and generate a set of tables that provides managers with the necessary liquidity requirements they should maintain, given the probability they are willing to accept of exhausting the liquidity pool and given their portfolio’s size, in-

New Evideince of Persistence in Stock Returns

38 E T he tendency for stock prices to display perisistent strength or weakness is inconsistent with the random walk model of security prices. The random walk model states that the price change or return for a security over any time period is independent of all previous prices; thus, knowledge of past prices is of no help in determining future price behavior. In order for stock prices to follow a strict random walk, it is necessary that there be no dependence at all between successive price changes. Most people would agree, however, that stock prices do follow a random walk, for all practical purpose:;, if the dependence between successive price changes is small and dies out quickly as the time lag between price changes increases. In order to demonstrate empirically that the random walk model is not applicable to stock prices, we must show that (1) the dependence between successive values is non-negligible or (2) the dependence does not die out quickly as the time lag increases. Previous empirical investigations of the dependence in common stock prices have usually relied on estimation of the first few serial correlation coefficients; these correlations are generally found to be close to zero. They then couple this :-esult with the assumption that any slight dependence uncovered by the serial correlation

Abstract: A Multiple Discriminant Analysis of Technical Indicators on the NYSE

This study investigates the ability of daily technical indicators to predict the direction of change in the Standard and Poors 500 Index (as measured by price relatives). Two sets of variables widely used by technical analysts are employed, and are designated “regular†variables and “percentage†variables. Examples of relevant “regular†variables are: volume; proportion of stocks advancing, declining, and remaining unchanged; off-lot purchases, sales, and short-sales; and new highs and new lows.