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This paper evaluates a nonparametric sign test for abnormal security price performance in event studies. The sign test statistic examined here does not require a symmetrical distribution of security excess returns for correct specification. Sign test performance is compared to a parametric t-test and a nonparametric rank test. Simulations with daily security return data show that the sign test is better specified under the null hypothesis and often more powerful under the alternative hypothesis than a t-test. The performance of the sign test is dominated by the performance of a rank test, however, indicating that the rank test is preferable to the sign test in obtaining nonparametric inferences concerning abnormal security price performance in event studies. [ABSTRACT FROM AUTHOR]

Studies of size and earnings/price ratio effects together have produced contradictory results. Does one effect subsume the other or are there two separate effects?. This paper demonstrates that equity returns are related to both size and earnings/price ratio as well as the month of January. Reinganum [20] and Basu [4] are reexamined to find the reasons for their contradictory results. Reinganum's finding that size subsumes earnings/price ratio is caused by a fortuitous choice of methods. Basu's finding that earnings/price ratio subsumes size appears to be sample-specific. This paper examines the implied standard deviation (ISD) estimated from transactions data on options, using the Black-Scholes pricing model. It was found that the distribution of the ISD is symmetric, though not normal. Also, the ISD based on the last daily observation deviates significantly from the daily average ISD. It is suggested that the daily average is a more reliable estimate of the standard deviation. [ABSTRACT FROM AUTHOR]

This paper reexamines, at a range of investment horizons, the asymmetric dependence between hedge fund returns and market returns. Given the current availability of hedge fund data, the joint distribution of longer-horizon returns is extracted from the dynamics of monthly returns using the filtered historical simulation; we then apply the method based on copula theory to uncover the dependence structure therein. While the direction of asymmetry remains unchanged, the magnitude of asymmetry is attenuated considerably as the investment horizon increases. Similar horizon effects also occur on the tail dependence. Our findings suggest that nonlinearity in hedge fund exposure to market risk is more short term in nature, and that hedge funds provide higher benefits of diversification, the longer the horizon. [ABSTRACT FROM AUTHOR]

A fundamental statistical test of serial independence developed by Ashley and Patterson (1986) to examine a possible form of serial dependence in daily stock returns is shown to be improperly constructed. As a consequence, the significance probabilities that they obtain are overstated. This paper presents a corrected version of their test. The test statistic obtained after correction is shown to possess the same limiting distribution as the Kolmogorov-Smirnov test statistic. Applying the corrected test procedure to data identical to that used by Ashley and Patterson, we find that their original null hypothesis can no longer be rejected at conventional significance levels. [ABSTRACT FROM AUTHOR]

Event studies generally seek to measure abnormal security performance associated with firm-specific events. In principle, estimators of and tests for abnormal performance should appropriately reflect cross-sectional dependence between abnormal returns to different securities. Joint generalized least squares provides a natural framework for developing such estimators and tests. This paper derives a joint generalized least squares estimator and related test statistic applicable in the typical event study context. Simulation techniques comparable to those of Brown and Warner [2] are used to assess the frequency distribution of the estimator and power of the test statistic. Several simpler procedures are simulated for comparison. The results provide no evidence that joint generalized least squares is superior to simpler procedures. [ABSTRACT FROM AUTHOR]

Daily cash forecasting generally requires some method to reflect day-of-month and day- of-week effects. It requires the resolution of multiple seasonals, a problem given scant treatment in the econometrics literature. This paper first presents multiplicative and mixed-effects specifications of day-of-month and day-of-week effects as alternatives to the additive specifications. Then, several important estimation issues pertinent to each specification are investigated, namely collinearity, holiday effects, length-of-month distortion, varying weekly-monthly pattern mix, and daily-monthly consistency. The paper develops a broad class of distribution-based linear forecasting models in great generality similar to the way that Box and Jenkins provide a broad class of time- series models that can be specialized via parameter selection (specification). In our case, parameter selection (specification) gives particular members of the linear class of distribution models. A particular version can be tested against an alternative specification via hypothesis tests on model parameters. [ABSTRACT FROM AUTHOR]

Stable distributions are becoming increasingly popular as appropriate models for stock price changes and other economic phenomena. As a result, there is an expanding body of literature on inferential procedures for this family of distributions. Computationally simple estimators for the parameters of symmetric stable distributions have been provided by Fama and Roll. Little attention, though, has been given to goodness-of-fit tests for members of this family other than the normal. It is the purpose of this paper to discuss simple goodness-of-fit hypothesis tests using kurtosis, b2, to distinguish among members of the stable family. The b2 tests of hypothesis comprise: 1) a null normal versus a non-normal symmetric stable alternative; 2) a null nonnormal symmetric stable versus a normal alternative; and 3) a null nonnormal stable versus another non-normal stable alternative. Tables that give the percentage points of b2 and that are necessary for these tests of hypothesis are given. Apart from providing critical values for the tests, the tables allow the researcher to calculate the power. It will be seen that the b2 test exhibits excellent power. It is then hoped that computational convenience will make b2 an important tool for researchers and practitioners in finance. It is also hoped that the procedures we provide will aid these researchers and practitioners in the construction of appropriate financial models. [ABSTRACT FROM AUTHOR]

The article discusses changes in stock prices and asymmetric stable distributions by making 200 dependent stock samples into independent samples as a way of understanding probability distribution. A table is provided that details the outliers in the securities market and showing the expected and mean number of observations. The results of this experiment indicate that daily residual stock returns are linked to the nonnormal group of stable distributions. The article concludes that risk estimates that are culled from standard deviations are useless and that other suggestions for risk measures cannot be used in the case f asymmetric stable distributions, making asymmetric measures an unlikely choice to describe stock price changes.

Certainly, the concept of skewness of returns and its role in the context of portfolio analysis has gained increasing attention in recent literature. Witness the studies by Alderfer and Bierman, Arditti, Jean, and Simonson. Each of these studies has treated skewness as the third moment of a series expansion—accordingly, skewness has been measured and interpreted as a logical extension of the traditional two-dimensional return-versus-standard deviation analysis of security evaluation. The purpose of this note is to illustrate that the measurement of skewness is more sample sensitive than similar measurements for the mean and standard deviation. In particular, skewness measures will be shown to be highly sensitive to both the size of the differencing interval and the initialization point. [ABSTRACT FROM AUTHOR]

The article focuses on the cost implications of fluctuating demand. It states that in a market characterized by fluctuations in demand, businesses need to minimize total cost functions associated with probability distribution production and produce a probability distribution of outputs. It suggests that using a static total cost function would thus be different from a cost function that resulted from production of a stable level of output and would also overstate the total costs of suboptimum and superoptimum outputs. It claims that pricing policies and profit maximizing decisions should reflect the cost effects from output variability.

Markowitz's [2] portfolio selection model was originally concerned with financial investments, but the model's implications for capital budgeting are now well recognized. Markowitz's basic idea is that the optimal portfolio for an investor is not simply any collection of good securities, but a balanced whole, providing the investor with the best combination of “return” and “risk.” Return and risk are to be measured by the expected value and variance of the probability distribution of portfolio return. Although financial writers have generally accepted Markowitz's measure of return, they have not been completely satisfied with his suggested measure of risk [1]. In fact, Markowitz himself had reservations about choosing variance as a measure of risk.1 Besides variance, he considered five other alternative measures of risk:(1) The expected value of loss;(2) The probability of loss;(3) The expected absolute deviation;(4) The maximum expected loss; and(5) The semivariance. [ABSTRACT FROM PUBLISHER]

The article focuses on using investment portfolios in risk management. The effect on the variance of an investment fund through adding dependent investments is considered. A trend in risk analysis focuses on the mean and variance of the probability distribution of returns. The author notes that a person looking to avoid risk should search for negatively correlated investments. Another method of reducing risk is to find independent investments, limited by information and transaction costs, and bring them into an investment portfolio. Risk can also be reduced by adding investments with less positive correlations.

We propose a model of volatility tail behavior in which investors display aversion to both low-volatility and high-volatility states, and hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors who have heterogeneity in beliefs about volatility outcomes and maximize their utility by choosing volatility-contingent cash flows. Our empirical examination suggests that the model is better suited to reproduce data features in the left tail of the volatility distribution, both qualitatively and quantitatively. [ABSTRACT FROM AUTHOR]

We study individual portfolio choice in a laboratory experiment and find strong evidence for heuristic behavior. The subjects tend to focus on the marginal distribution of an asset, while largely ignoring its diversification benefits. They follow a conditional 1/n diversification heuristic as they exclude the assets with an “unattractive” marginal distribution and divide the available funds equally between the remaining “attractive” assets. This strategy is applied even if it leads to allocations that are dominated in terms of first-order stochastic dominance and is clearly irrational. In line with these findings, we find that framing and problem presentation have substantial influence on portfolio decisions. [ABSTRACT FROM PUBLISHER]

Arithmetic Asian options are difficult to price and hedge as they do not have closed-form analytic solutions. The main theoretical reason for this difficulty is that the payoff depends on the finite sum of correlated lognormal variables, which is not lognormal and for which there is no recognizable probability density function. We use elementary techniques to derive the probability density function of the infinite sum of correlated lognormal random variables and show that it is reciprocal gamma distributed, under suitable parameter restrictions. A random variable is reciprocal gamma distributed if its inverse is gamma distributed. We use this result to approximate the finite sum of correlated lognormal variables and then value arithmetic Asian options using the reciprocal gamma distribution as the state-price density function. We thus obtain a closed-form analytic expression for the value of an arithmetic Asian option, where the cumulative density function of the gamma distribution, G(d) in our formula, plays the exact same role as N(d) in the Black-Scholes/Merton formula. In addition to being theoretically justified and exact in the limit, we compare our method against other algorithms in the literature and show our method is quicker, at least as accurate, and, in our opinion, more intuitive and pedagogically appealing than any previously published result, especially when applied to high yielding currency options. [ABSTRACT FROM AUTHOR]

To date, a number of studies involving the use of bond prices and/or returns have utilized the published prices of trades on the New York and other exchanges. These exchange quotes reflect the odd-lot activities of individual investors and account for only a negligible portion of the trading in listed issues. In contrast, the vast majority of listed corporate trading occurs over-the-counter and involves round-lot trades between institutions. Given differences in market characteristics, odd-lot exchange prices may differ substantially from those in the round-lot institutional market. This study compares exchange quotations from Moody's Bond Record with prices assigned by Merrill Lynch's institutional pricing service and uses each set of prices to calculate return and risk measures. Institutional (Merrill Lynch) bond prices are shown to be systematically greater than exchange (Moody's) prices. In addition, bond returns based on Merrill Lynch prices are shown to yield significantly higher beta and R² estimates, as well as significantly lower standard deviation and residual risk estimates. [ABSTRACT FROM AUTHOR]

Using a technique based upon the behavior of the sample standard deviation as the sample size increases, we have rejected the hypothesis that security return distributions have an infinite variance. Our findings indicate that while the variance of return is finite, it changes over time in a complex fashion. This finding has important implications for future research in finance, both empirical and theoretical. Specifically, the need for a better understanding of those factors which influence return variability is clear. Further, statistical techniques used in conjunction with security returns must be robust with respect to parameter shifts. [ABSTRACT FROM AUTHOR]

The article focuses on the relationship between heterogenous expectations of the return and asset prices of a security. Particular attention is given to explore the impact of return distribution changes on asset prices along with the defining of investor probability distributions in environments of diverging opinions. Empirical research is conducted offering explicit correlations between security returns and investor expectations in various environments of permitted, restricted or forbidden short-selling.

The article presents an exploration into the empirical relationships between the alternative portfolio risk evaluation and selection models of mean-lower partial moment and mean-variance sub-forms of the capital asset pricing model (CAPM). Results are given, with moderating considerations outlining the assumptions of underlying positive or negative distribution skewness of returns, highlighting scenarios of significant differences between the two in their variance slope and intercept calculations.

The empirical distributions of price changes for measured over calendar time yield a higher frequency of observations near the mean and at the tails than would be expected for a normal distribution. The sample kurtosis is almost always greater than, the value expected for a normal distribution and the distributions are commonly characterized as fat-tailed and peaked. The theory "stable paretian hypothesis" states that price changes measured over calendar time intervals conform most closely to symmetric stable laws with characteristic exponent. Some recent empirical evidence casts doubt upon the stable paretian hypothesis. Another but less widely known hypothesis that purports to explain the high kurtosis values for common stock returns uses the theory of subordinated stochastic processes. Subordinated models of security returns can frequently be described as mixtures of normal distributions. The hetereoscedasticity associated with such mixtures of normals will cause the sample kurtosis to have large values.

The article presents an analysis of stock purchase warrant hedging within stable Paretian market scenarios. An overview of the development of warrant hedge procedures and their investment analysis foundations are given and extensions are offered through probabilistic modeling. The author utilizes logarithmic price relatives through asymmetric stable Paretian distributions to formulate an optimized decision theory. Connections between warrant hedging and other valuation models are also made and discussed.

The article discusses the probability distribution of stock market returns in a capital market and the fluctuations of asset supply and demand. It is noted that there is a problem with dynamic equilibrium theory, which is that the distribution of returns is static and that causes capitalists to not diversify their investments. The article concludes that diversifying the investment portfolio in partnership with the stationary-distribution-of-returns theory means that the stockholders wealth will remain constant.

The article reports on the effect of information on the investment behavior of a decision maker. The information on the probability distribution of returns on a risky asset like a portfolio or mutual fund can bring a decision maker to a risk aversion decision. The utility functions with convex segments imply similar investment behaviors. The opportunity to access information results in the acceptance of a single-period actuarially unfair gamble with respect to future wealth levels.

Ex ante predictions of the riskiness of returns on common stocks — or, in more general terms, predictions of the probability distribution of returns — can be based on fundamental (accounting) data for the firm and also on the previous history of stock prices. In this article, we attempt to combine both sources of information to provide efficient predictions of the probability distribution of returns. We predict two parameters of the distribution of returns for each security in each year: the response to the overall market return (β), and the variance of the part of risk, specific to the security, that is uncorrelated with the market return. A cross section of time series data on returns and accounting variables, taken primarily from the Compustat tape, is used. Several recent developments in statistical methodology are applied. [ABSTRACT FROM AUTHOR]

This article provides the specifications of the market's composite parameters and probability assessments when investors differ in their investment decisions as well as in their risk-aversion, when there is no riskless asset available for holding or borrowing, and when short sales are limited and when most investors are unaware about the prospects of most available securities. Throughout each section of the article formulae for the Pareto-optimal distribution of the holding of any risk asset among investors will be analysed in terms of each investor's parameters and assessments relative to those of the market.

This article presents several algorithms for improving computational efficiency based on the report from Porter, Wart, and Ferguson. Particular attention is given to the logical inconsistency of any attempt to compare and contrast stochastic dominance (SD) and efficiency relative to Markowitz (EV) efficiency criteria on empirical grounds.