A New Approach to International Arbitrage Pricing

This paper uses a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage-pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts, and other derivative securities. Only the nonlinear arbitrage-pricing model does an adequate job of explaining the time series behavior of a cross section of international returns.     

Some Results in the Theory of Arbitrage Pricing

This paper derives a stronger version of Huberman's recent “preference free” pricing theorem. This pricing result relates the expected return on an asset to its factor responses and the covariance structure of the residuals from a linear factor model. It must characterize any infinite asset economy in which no arbitrage opportunities are present whether or not the factor model has uncorrelated residuals. This result provides the intuition for the role of residual risk in the pricing model and eliminates some classes of arbitrage opportunities still present under Huberman's bound. Some applications to empirical tests and performance measurement are also discussed.     

Joint Estimation of Factor Sensitivities and Risk Premia for the Arbitrage Pricing Theory

The APT is represented as a multivariate regression model with across-equations restrictions. Both observed and unobserved (latent) macroeconomic factors are included, thus generalizing and unifying two previous strands of literature. Large portfolios representing unobserved factors are treated as endogenous, and nonlinear 3SLS estimates are shown to differ sharply from estimates that ignore this endogeneity. Using monthly stock returns and six factors, we cannot reject January effects. The following results are invariant with respect to the inclusion of January effects: we reject the CAPM in favor of the APT; however, we cannot reject the APT restrictions on the linear factor model.     

Simulating and Forecasting Utility Stock Returns: Arbitrage Pricing Theory vs. Capital Asset Pricing Model

Just when the capital asset pricing model (CAPM) has become accepted by public utility regulators as a method for estimating a utility's screening rate, academic criticism of the model's theoretical and empirical shortcomings has led to empirical testing of the alternative arbitrage pricing theory (APT). This paper expands on recent APT-CAPM performance comparisons by simulating returns of public utility stocks using versions of both models, as was done by Bower, Bower, and Logue in a 1984 paper. In addition, the models are used for ex-post forecasting of returns in a subsequent time period. The Litzenberger-Ramaswamy method is used to correct for errors-in-variables in the CAPM cross-sectional equation. This allows for estimating the security market line using firm betas. The same methodology is used in the APT stages. Three different criteria—the Theil inequality, the sources of mean square error, and Chen's estimated weights of expected return-are used to compare CAPM and APT simulation and forecasting of the equity screening rates. Tested on a sample of 128 public utility companies, results show that neither model is clearly dominant. There is a tendency for reversal of performance. The model that is superior for simulating returns tends to be inferior for forecasting them, and vice-versa.     

Mimicking Portfolios and Exact Arbitrage Pricing

We characterize the sets of mimicking positions with returns that can serve in place of factors in an exact K-factor arbitrage-pricing relation for a set of N assets. All of the sets are K-dimensional nonsingular linear transformations of each other. We interpret three examples of such transformations and discuss empirical considerations. We provide conditions under which the mimicking positions can be expressed as portfolios, and we characterize the relation between mimicking portfolios and the minimum-variance frontier.     

Arbitrage Asset Pricing under Exchange Risk

This paper extends the APT to an international setting. Specifying a linear factor return-generating model in local currency terms, we show that the usual risk-diversification rule in the APT does not yield a riskless portfolio unless currency fluctuations obey the same factor model as asset returns. We then consider an arbitrage portfolio whose exchange risk is hedged by foreign riskless bonds. Under the resulting no-arbitrage conditions, the expected returns are not on the same hyperplane, unlike the closed-economy APT, unless they are adjusted by the cost of exchange risk hedging.     

A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: C16, G10, G13     

An Empirical Test of the Arbitrage Pricing Theory on Australian Stock Returns 1974-85

This paper examines empirically, issues concerning the Arbitrage Pricing Theory (APT). Firstly, in the spirit of Chamberlain and Rothschild [1983], the existence of an approximate factor structure is explored. Secondly, following Beggs [1986] and employing a principal components approach, a test of arbitrage pricing and the importance of the error of approximation, is conducted. Finally, using a non nested framework, the APT and CAPM are tested against each other. The results show mixed support for the APT having up to 3 priced factors.     

On the Number of Factors in the Arbitrage Pricing Model

Recent theory has demonstrated that the Arbitrage Pricing Model with K factors critically depends on whether K eigenvalues dominate the covariance matrix of returns as the number of securities grows large. The purpose of this paper is to test whether sample covariance matrices can be characterized as having K large eigenvalues. Using all available data on the 1983 CRSP tapes, we compute sample covariance matrices of returns in sequentially larger portfolios of securities. Analyzing their eigenvalues, we find evidence that one eigenvalue dominates the covariance matrix indicating that a one-factor model may describe security pricing. We also find that, for values of K larger than one, there is no obvious way to choose the number of factors. Nevertheless, we find that while only the first eigenvalue dominates the matrix, the first five eigenvalues are growing more distinct.     

Arbitrage With Holding Costs: A Utility-Based Approach

Unit time costs, or holding costs, are incurred in many arbitrage contexts. Examples include losing the use of short sale proceeds and lending funds at below market rates in reverse repurchase agreements. This paper analyzes the investment problem of a risk averse arbitrageur who faces holding costs. The model allows prices to deviate from “fundamental” values without allowing for riskless arbitrage opportunities. After characterizing an arbitrageur's optimal strategy, the model is examined in the context of the Treasury market. The analysis reveals that holding costs are an important friction in this market and that they can significantly affect arbitrageur behavior.     

Overconfidence, Arbitrage, and Equilibrium Asset Pricing

This paper offers a model in which asset prices reflect both covariance risk and misperceptions of firms' prospects, and in which arbitrageurs trade against mispricing. In equilibrium, expected returns are linearly related to both risk and mispricing measures (e.g., fundamental/price ratios). With many securities, mispricing of idiosyncratic value components diminishes but systematic mispricing does not. The theory offers untested empirical implications about volume, volatility, fundamental/price ratios, and mean returns, and is consistent with several empirical findings. These include the ability of fundamental/price ratios and market value to forecast returns, and the domination of beta by these variables in some studies.     

Pricing Weather Derivatives Using the Indifference Pricing Approach

Abstract

This paper adopts an incomplete market pricing model–the indifference pricing approach–to analyze valuation of weather derivatives and the viability of the weather derivatives market in a hedging context. It incorporates price risk, weather/quantity risk, and other risks in the financial market. In a mean-variance framework, the relationship between the actuarial price and the indifference price of weather derivatives is analyzed, and conditions are obtained concerning when the actuarial price does not provide an appropriate valuation for weather derivatives. Conditions for the viability of the weather derivatives market are examined. This paper also analyzes the effects of partial hedging, natural hedges, basis risk, quantity risk, and price risk on investors’ indifference prices by examining the distributional impacts of the stochastic variables involved.     

Liquidity and Arbitrage in Options Markets: A Survival Analysis Approach

This paper examines the determinants of the time it takes foran index options market to return to no arbitrage values afterput-call parity deviations, using intraday transactions datafrom the French index options market. We employ survival analysisto characterize how limits to arbitrage influence the expectedduration of arbitrage deviations. After controlling for conventionallimits to arbitrage, we show that liquidity-linked variablesare associated with a faster reversion of arbitrage profits.The introduction of an Exchange Traded Fund also affects thesurvival rates of deviations, but this impact essentially stemsfrom the reduction in the level of potential arbitrage profits.     

Pricing Interest Rate Derivatives: A General Approach

The relationship between affine stochastic processes and bondpricing equations in exponential term structure models has beenwell established. We connect this result to the pricing of interestrate derivatives. If the term structure model is exponentialaffine, then there is a linkage between the bond pricing solutionand the prices of many widely traded interest rate derivativesecurities. Our results apply to m-factor processes with n diffusionsand l jump processes. The pricing solutions require at mosta single numerical integral, making the model easy to implement.We discuss many options that yield solutions using the methodsof the article.     

A New Approach to Testing Asset Pricing Models: The Bilinear Paradigm

We propose a new approach to estimating and testing asset pricing models in the context of a bilinear paradigm introduced by Kruskal 18 . This approach is both simple and at the same time quite general. As an illustration we apply it to the special case of the arbitrage pricing model where the number of factors is pre-specified. The data appear to be generally in conflict with a five or seven factor representation of the model used by Roll and Ross 30 . When we consider the number of replications of our test and the large number of observations on which it is performed, the frequency with which we reject the three factor APM does not lead us to conclude that this model is unrepresentative of security returns. Further, the rejection of the five and seven factor versions is to be expected if the three factor version is correct. The paradigm gives insight into the appropriate specification of the model and suggests that there may be a small number of economy wide factors that affect security returns.     

Information Flow and Pricing Errors: A Unified Approach to Estimation and Testing

This study examines whether rates of information flow differbetween trading and nontrading periods, and whether the variancesof pricing errors differ at the open and close of trading. Theapproach improves on existing methods by allowing for correlationbetween pricing errors and information flow, and by conductinginferences at the individual security level. The daytime rateof information flow is about seven times the overnight rate,and the variances of pricing errors at the open are not differentfrom those at the close of trading. This evidence differs fromexisting results based on return variance ratios.