Intertemporal arbitrage pricing theory

It is shown that the arbitrage pricing theory holds in eachinfinitesimal period of a continuous trading model under theassumption that dividend payoffs are functionals of factor andidiosyncratic uncertainty. This generalizes the one- periodmodel's result that the arbitrage pricing theory holds underthe assumption that price changes in a given period satisfya factor structure. Since instantaneous returns in a multiperiodmodel are endogenously determined, the theory is derived underassumptions that may be viewed as restricting more primitivecharacteristics of the economy than the assumptions made forthe one-period model.     

Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

Preferences, continuity, and the arbitrage pricing theory

This article investigates the structure on preferences requiredto derive Ross's arbitrage pricing theory (APT). It is shownthat only ordinal preferences are required. In particular, theAPT does not require that agents possess preferences representableas risk-averse expected utility functions. This characteristicof the APT is not shared by the standard equilibrium-based capitalasset pricing models.     

Exchange risk and universal returns: A test of international arbitrage pricing theory

According to the international arbitrage pricing theory (IAPT) posited by Solnik (1983), currency movements affect assets' factor loadings and associated risk premiums. Based on a novel universal return decomposition, we propose an empirical model to test this proposition and perform tests using U.S. stock returns in the period 1975–2008. Our results confirm that currency movements significantly affect the market betas of a large proportion of stocks. Further cross-sectional tests indicate that currency movements affecting the market factor are significantly priced in stock returns. Based on these and other findings, we conclude that Solnik's IAPT is supported. An important implication of our findings is that exchange rate risk can broadly affect stock returns through both factor loading and residual factor channels.     

Exchange risk and universal returns: A test of international arbitrage pricing theory

According to the international arbitrage pricing theory (IAPT) posited by Solnik (1983), currency movements affect assets' factor loadings and associated risk premiums. Based on a novel universal return decomposition, we propose an empirical model to test this proposition and perform tests using U.S. stock returns in the period 1975–2008. Our results confirm that currency movements significantly affect the market betas of a large proportion of stocks. Further cross-sectional tests indicate that currency movements affecting the market factor are significantly priced in stock returns. Based on these and other findings, we conclude that Solnik's IAPT is supported. An important implication of our findings is that exchange rate risk can broadly affect stock returns through both factor loading and residual factor channels.     

An empirical examination of the implications of arbitrage pricing theory

This paper presents a comprehensive set of tests of the implications of the Arbitrage Pricing Theory. We find, unlike previously reported results, a very limited relationship between the expected returns and the covariance (factor loadings) measures of risk. Furthermore, unique variance measures of risk, while generally making only small contributions to the explanation of asset returns, turn out to be significant about as frequently as the coveriance measures of risk — which is inconsistent with the Arbitrage Pricing Theory model. The intercept tests are more mixed but provide only limited support to the model.     

A note on sufficient conditions for no arbitrage

It is shown that the absence of call spread, butterfly spread and calendar spread arbitrages is sufficient to exclude all static arbitrages from a set of option price quotes across strikes and maturities on a single underlier.     

Multivariate regression tests of the arbitrage pricing theory: The instrumental-variables approach

This article expands the theoretical basis upon which empirical testing of the arbitrage pricing theory (APT) rests. Specifically, it specifies linear restrictions for worlds in which the APT holds. These restrictions may, in principle, be tested. Since the regressors in the model are only “noisy” proxies for a specific linear transformation of the factors or mimicking portfolios, testing regressions suffer from an errors-in-variables problem. The standard econometric treatment for this problem is the instrumental-variables approach. A size-based example is employed to compare the test results derived from the instrumental-variables approach to those obtained via the ordinary least squares (OLS) method. The results from both methods cannot reject a two-factor APT for the size-sorted portfolio sample. The authors appreciate the helpful comments of Edwin Burmeister, Raymond Chiang, Steve Pruitt, participant at the 1989 Western Finance Association annual meetings, Indiana University, and University of Miami, and especially Shmuel Kandel.     

Deriving the arbitrage pricing theory when the number of factors is unknown

This paper examines the use of proxies (or reference variables) for the true factors in the arbitrage pricing theory (APT). It generalizes other authors' existing work and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll (Ingersoll J 1984 J. Finance 39 1021-39), and our propositions can be thought of as specializations of his theorems. Similar to Nawalkha (Nawalkha S 1997 J. Financial Economics 46 357-81), our work does not use the mathematics of Hilbert and Banach spaces and, thus, is open to a much wider audience. The practical implication of our results is that model builders should be generous with the number of factors they use, as excessively parsimonious models suffer from inaccuracy.     

A note on the no arbitrage condition for international financial markets

We consider an international financial market model that consists ofN currencies. The purpose is to derive a no arbitrage condition which is not affected by the choice of numéraire between theN currencies. As a result, we show that a finiteness condition for an arbitrary chosen currency and the no arbitrage condition for the basket currency are necessary and sufficient for the no arbitrage property of all theN currencies. Research supported in part by Nomura Foundation for Social Science and by the European Community Stimulation Plan for Economic Science contract Number SPES-CT91-0089. The authors thank an anonymous FEJM referee for helpful comments.     

A note on capital asset pricing and heterogeneous taxes

In this paper, we present a stylized model where we show how asset prices, i.e., required expected rates of returns, may be characterized in a world with heterogeneous asset taxes. Within a simple CAPM-like framework, we derive an after-tax beta equal to the pre-tax beta multiplied by a (non-obvious) asset specific tax adjustment. We further show in what sense the Security Market Line here can be replaced by a Security Market Fan. Well-known CAPM relations are obtained as special cases, and policy implications are analyzed.     

Irreversible investment and discounting: an arbitrage pricing approach

This paper presents a unified approach to valuing investment projects under uncertainty, based on stochastic discount factors, by linking optimal stopping theory to the no-arbitrage principle in asset pricing. An investment threshold for the case where the discount factor and the project’s cash-flow both follow a geometric Brownian motion is derived. Comparative statics of the investment trigger are obtained adding to and clarifying on the uncertainty–investment debate. Finally, two different ways to obtain discount factors are illustrated: spanning assets and representative agent analysis. The link between the characteristics of these different approaches and the optimal investment policy is clarified.     

A note on the efficiency of the binomial option pricing model

We discuss the efficiency of the binomial option pricing model for single and multivariate American style options. We demonstrate how the efficiency of lattice techniques such as the binomial model can be analysed in terms of their computational cost. For the case of a single underlying asset the most efficient implementation is the extrapolated jump-back method: that is, to value a series of options with nested discrete sets of early exercise opportunities by jumping across the lattice between the early exercise times and then extrapolating from these values to the limit of a continuous exercise opportunity set. For the multivariate case, the most efficient method depends on the computational cost of the early exercise test. However, for typical problems, the most efficient method is the standard step-back method: that is, performing the early exercise test at each time step.     

日元套利交易的影响及未来走势分析

日元套利交易是利用日元与其他高息货币间利率差来获得利润的交易方式,一般表现为投资者从金融机构借入日元,并在外汇市场中卖出,同时买入高利率货币,从中赚取利率差。一旦这一交易被大多数市场参与者认同,外汇市场将会出现日元被抛出、高息货币被抢购的局面,最终导致日元不断贬值,而高息货币则持续升值,这使投资者获取了日元与高息货币间利差和持有高息货币升值两方面的收益。     

The consumption based asset pricing model: A note on potential tests and applications

Breeden's demonstration that Merton's multi-beta capital asset pricing model can be collapsed into a single-beta model where betas are computed with respect to aggregate consumption is an important theoretical advance. Nonetheless, Breeden's model retains many of the empirical problems that beset Merton's earlier version. In general the consumption betas will be nonstationary, so that the state variables must be observable for the model to be estimated.     

Index arbitrage and the pricing relationship between Australian stock index futures and their underlying shares

This paper examines the mispricing of Australian stock index futures. Exogenous and endogenous price volatility is confirmed to have a positive impact on the mispricing spread, after filtering out predictable time series components. More accurate pricing associated with surprise trading volume in the underlying stocks is consistent with arbitrageurs acting to narrow price disparities relative to the futures market. Ex‐ante interest rate volatility is the primary source of risk faced by arbitrageurs and fluctuations in the transaction cost of opening index arbitrage positions influence the extent to which they drive prices towards theoretical fair values.     

A note on pricing interest rate derivatives when forward LIBOR rates are lognormal

We derive the closed form pricing formulae for contracts written on zero coupon bonds for the lognormal forward LIBOR rates. The method is purely probabilistic in contrast with the earlier results obtained by Miltersen et al. (1997).     

Notes on dynamic factor pricing models

These notes discuss three aspects of dynamic factor pricing (i.e., APT) models. First, the diversifiable component of returns is unpredictable in a no-arbitrage world. Second, conditional factor loadings or betas have an unconditional factor structure when returns follow an unconditional factor structure, which provides a link between conditional and unconditional factor pricing models. Third, the estimation of dynamic factor pricing models is easily simplified in large cross sections when returns follow an unconditional factor structure. These results aid in the interpretation of existing applications and identify some of the issues in the formulation and estimation of dynamic factor pricing models.     

Structural asset pricing theory with wavelets

We apply Fourier and wavelet decompositions to structural asset pricing models with time non-separable utility. Through simulations, we show how Fourier decompositions of the utility function, coupled with isolating certain frequencies of the stochastic consumption process, reveal a preference for temporal allocations. We demonstrate the usefulness of wavelets by highlighting their ability to isolate frequency and time, simultaneously. While much work has been devoted to wavelet applications of financial data, we are unaware of papers that use wavelets to analyze structural aspects of asset pricing models.     

Index arbitrage with heterogeneous investors: A smooth transition error correction analysis

The traditional index arbitrage model assumes a constant threshold mispricing between the futures and cash prices for all investors. Allowing for heterogeneity in investors' transaction costs, objectives, and capital constraints, we model the intraday mispricing of DJIA futures as a smooth transition autoregressive (STAR) process with the speed of adjustment toward equilibrium varying directly with the mispricing. We show that the observed mean reversion in mispricing changes is induced by heterogeneous arbitrageurs, instead of a statistical illusion-infrequent trading of index portfolio stocks. We further use a STAR error correction model to describe the nonlinear dynamics between the DJIA futures and index. This model describes not only which market is more informationally efficient than the other, but also the legging process – the nonsimultaneous establishing of cash and futures positions.