Intertemporal Asset Pricing Model Research Articles

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

AbstractDiscounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.

Intertemporal asset pricing and the marginal utility of wealth

We consider the general class of discrete-time, finite-horizon intertemporal asset pricing models in which preferences for consumption at the intermediate dates are allowed to be state-dependent, satiated, non-convex and discontinuous, and the information structure is not required to be generated by a Markov process of state variables. We supply a generalized de finition of marginal utility of wealth based on the Frechet differential of the value operator that maps time t wealth into maximum conditional remaining utility. We show that in this general case all state-price densities/stochastic discount factors are fully characterized by the marginal utility of wealth of optimizing agents even if their preferences for intermediate consumption are highly irregular. Our result requires only the strict monotonicity of preferences for terminal wealth and the existence of a portfolio with positive and bounded gross returns. We also relate our generalized notion of marginal utility of wealth to the equivalent martingale measures/risk-neutral probabilities commonly employed in derivative asset pricing theory. We supply an example in which our characterization holds while the standard representation of state-price densities in terms of marginal utilities of optimal consumption fails.

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

ABSTRACTWe derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.

Improving the Asset Pricing Ability of the Consumption-Capital Asset Pricing Model?

This paper compares the asset pricing ability of the traditional consumption-based capital asset pricing model to models from two strands of literature attempting to improve on the poor empirical results of the C-CAPM. One strand is based on the intertemporal asset pricing model of Campbell (1993, 1996) and Campbell and Vuolteenaho (2004). The model takes the traditional C-CAPM as its starting point, but substitutes all references to consumption out, as empirical consumption data is assumed to be error ridden. The other strand to be investigated is based on the premise that the C-CAPM is only able to price assets conditionally as suggested by Cochrane (1996) and Lettau and Ludvigson (2001b). The unconditional C-CAPM is rewritten as a scaled factor model using the approximate log consumptionwealth ratio cay, developed by Lettau and Ludvigson (2001a), as scaling variable. The models are estimated on US data and the resulting pricing errors are compared using average pricing errors and a number of composite pricing error measures. The conditional C-CAPM and the two beta I-CAPM of Campbell and Vuolteenaho (2004) result in pricing errors of approximately the same size, both average and composite. Thus, there is no unambiguous solution to the pricing ability problems of the C-CAPM. Models from both the alternative literature strands are found to outperform the traditional C-CAPM on average pricing errors. However, when weighting pricing errors by the full variance-covariance matrix of returns or the moment matrix of returns, the traditional C-CAPM actually outperforms the models from both the two new litterature strands.

House prices and rents: An equilibrium asset pricing approach

Abstract We use a relatively general intertemporal asset pricing model where housing services and consumption are non-separable to measure overvaluation of housing in relation to rents in Spain, the UK and the US. Part of the increase in real house prices during the late nineties can be seen as a return to equilibrium following some undershooting after previous price peaks. However, marked increases in house prices led to price-to-rent ratios above equilibrium by mid-2003 (around 30% above equilibrium in the UK, 20% in Spain and 10% in the US). Part of that overvaluation — particularly in Spain and the UK — may be attributable to the sluggishness of supply in the presence of large demand shocks in this market and/or the slow adjustment of observed rents.

Financial Integration: A New Methodology And An Illustration

This paper develops a simple new methodology to test for asset integration and applies it within and between American stock markets. Our technique is tightly based on a general intertemporal asset-pricing model, and relies on estimating and comparing expected risk-free rates across assets. Expected risk-free rates are allowed to vary freely over time, constrained only by the fact that they are equal across (risk-adjusted) assets. Assets are allowed to have general risk characteristics, and are constrained only by a factor model of covariances over short time periods. The technique is undemanding in terms of both data and estimation. We find that expected risk-free rates vary dramatically over time, unlike short interest rates. Further, the S&P 500 market seems to be well integrated, and the NASDAQ is generally (but not always) integrated. However, the NASDAQ is poorly integrated with the S&P 500.

A NEW APPROACH TO ASSET INTEGRATION: METHODOLOGY AND MYSTERY

Abstract. This paper develops a new methodology to test financial market integration. Our technique is based on an intertemporal asset‐pricing model, and relies on estimating and comparing expected discount rates across asset markets. Expected discount rates are allowed to vary freely over time, constrained only by the fact that they are equal across assets. Assets are allowed to have very general risk characteristics, and are constrained only by a linear factor model of covariances with the discount rate over short time periods. We provide a variety of domestic and international empirical illustrations of our technique, and find surprisingly little evidence of integration.

Financial Integration: A New Methodology and an Illustration

This Paper develops a simple new methodology to test for asset integration and applies it within and between American stock markets. Our technique is tightly based on a general intertemporal asset-pricing model, and relies on estimating and comparing expected risk-free rates across assets. Expected risk-free rates are allowed to vary freely over time, constrained only by the fact that they are equal across (risk-adjusted) assets. Assets are allowed to have general risk characteristics, and are constrained only by a factor model of covariances over short time periods. The technique is undemanding in terms of both data and estimation. We find that expected risk-free rates vary dramatically over time, unlike short interest rates. Further, the S&P 500 market seems to be well integrated, and the NASDAQ is generally (but not always) integrated. The NASDAQ, however, is poorly integrated with the S&P 500.

Asset Pricing Redux: Methodology and Mystery

This paper develops a simple new methodology to test financial market integration. Our technique is tightly based on a general intertemporal asset-pricing model, and relies on estimating and comparing expected discount rates across asset markets. The technique is undemanding in terms of both data and estimation. We provide a variety of domestic and international empirical illustrations of our technique, and find surprisingly little evidence of integration. While the S&P 500 market seems typically to be integrated, others are not, including: the NASDAQ, the Toronto Stock Exchange, and three different classes of American bonds. Further, there is little evidence of integration between these apparently deep frictionless financial markets.

Human-Capital-Adjusted Capital Asset Pricing Model

While multi-beta models are found to be good approximations for the cross-sectional behaviour of stock prices, theyfail to explain whythat part of an asset’s risk related to human capital is not captured bythe asset’s market beta. The empirical evidence also provides little justification for the linear relationship between expected returns and human capital betas. This paper addresses these issues with a theoretical examination of the effect of human capital on securityprices. An intertemporal asset pricing model is derived in which expected returns are linearlyand positivelyrelated to market betas and human capital betas.

Hedging Against Liquidity Risk and Short Sale Constraints

This paper exploits the intuition of the ICAPM to propose a measure that formally compares the empirical performance of competing asset pricing models in the presence of short selling constraints. In a multifactor context, portfolios are said to be efficient if they yield the highest expected return for a given variance and for a given degree of sensitivity to state variables that capture future investment-consumption risks. The measure of model misspecification is the maximal expected return loss caused by holding the market portfolio instead of the multifactor efficient portfolio. Including a proxy for liquidity in intertemporal pricing models takes the market portfolio closer to multifactor efficiency relative to scenarios that discard liquidity. Indeed, when no short positions are allowed, including a liquidity proxy in an intertemporal asset pricing model results in near exact multifactor efficiency of the market portfolio. Our empirical results can be explained by noting that liquidity risk is typically of major concern whenever the market declines. Investors who take short positions implicitly hedge against liquidity risk, thus a proxy for liquidity plays only a secondary role when such positions are allowed. In contrast, the liquidity proxy plays a major role when short selling is precluded.

An International Asset Pricing Model with Time-Varying Hedging Risk

This paper employs a two-factor international equilibrium asset pricing model to examine the pricing relationships among the world's five largest equity markets. In addition to the traditional market factor premium, a hedging factor premium is included as the second factor to explain the relationship between risks and returns in the international stock markets. Moreover, a GARCH parameterization is adopted to characterize the general dynamics of the conditional second moments. The results suggest that the additional hedging risk premium is needed to explain rates of return on international equities. Furthermore, the restriction that the coefficient on the hedge-portfolio covariance is one smaller than the coefficient on the market-portfolio covariance can not be rejected. This suggests that the intertemporal asset pricing model proposed by Campbell (1993) can be used to explain the returns on the five largest stock market indices.

An empirical analysis of intertemporal asset pricing models with transaction costs and habit persistence

In intertemporal asset pricing models, transaction costs are usually neglected. In this paper we explicitly incorporate transaction costs in these models and analyze to what extent this extension is helpful in explaining the cross-section of expected returns. An empirical analysis using CRSP data on size-based portfolios examines the role of the transaction costs and shows that incorporating such costs in the consumption-based model with power utility does not yield very satisfactory results. However, the introduction of habit persistence substantially improves the model. We find rather strong evidence of habit persistence in monthly consumption data. The plots of the models' pricing errors indicate that an intertemporal asset pricing model with transaction costs and habit persistence explains the cross-sectional variation in the portfolio returns quite accurately.

Intertemporal Risk in the Foreign Currency Futures Basis

AbstractWe investigate covariation of payoffs from spot and futures positions in foreign currency markets. The weights in a hedged position are determined by the prices of futures and spot contracts and by foreign and domestic interest rates. Evaluating this hedged position using an intertemporal asset‐pricing model leads to a testable equilibrium model for the time series evolution of the futures basis. Systematic intertemporal risk will be proportional to the conditional covariance of the basis with a generalized discount factor. Empirical implementation uses a conditional capital‐asset‐pricing model (CAPM) in which both the quantity and the price of covariance risk are free to vary over time. However, for this application, the estimated intertemporal risk is insignificantly different from zero, the risk in the futures position offsets that in the spot, providing an effective hedge.RésuméLa covariance des recettes découlant des positions à terme et au comptant prises sur les marchés des devises constitue l'objet principal de cette étude. Les pondéra‐tions utilisées pour la position couverte sont fixées à partir des prix des contrats à terme et des contrats au comptant d'une part et à partir des taux d'intérět étranger et national de l'autre. La position couverte ainsi définie peut alors ětre évaluée à l'aide d'un modèle temporel d'évaluation des actifs financiers. Ceci rend possible la formualtion d'un modèle d'équilibre de l'évolution de la série temporelle de la «base» (basis) sur le marché à terme vérifiable empiriquement. Dans cette formulation, le risque systématique temporel est proportionnel à la covariance conditionnelle de la base ajustée à l'aide d'un facteur d'actualisation généralisé. La vérification empirique de ce modèle utilise un modèle conditionnel d'évaluation des actifs financiers dans lequel le prix ainsi que l'amplitude du risque de covariance peuvent varier librement sur le temps. Cependant, dans cette application, le risque temporel estimé n'est pas significativement différent de zéro, le risque de la position à terme étant contrebalancé par celui de la position au comptant dans le contexte d'une couverture parfaite.

Can Fundamentals Explain Cross-Country Correlations of Asset Returns?

Previous studies show that existing correlations between national returns are higher than correlations between the national growth rates of fundamental variables. This paper examines the ability of intertemporal asset pricing models to explain cross-country correlations of national returns. We find that when capital markets are assumed to be fully integrated, a simple intertemporal general equilibrium model is able to explain the observed co-variability of domestic asset returns but generates too little variability in those returns. Results improve considerably if a less restrictive version is employed. In that setting, both domestic variability and cross-country co-variability of returns are consistent with capital market integration.

Rethinking Deviations From Uncovered Interest Parity: the Role of Covariance Risk and Noise

We examine the ability of the standard intertemporal asset pricing model and a model of noise trading to explain why the forward foreign exchange premium predicts the future currency depreciation with the 'wrong' sign. We find that the intertemporal asset pricing model is unable to predict risk premia with the correct sign to be consistent with the data. The noisetrader model, while highly stylised, receives fragmentary support from empirical research on survey expectations. This paper investigates the theoretical basis of an asset pricing anomaly in international finance known as the forward premium bias. That is, the empirical finding that the forward premium helps to predict the future percentage rate of currency depreciation but not with the sign implied by uncovered interest parity.' As a corollary to the forward premium bias, Fama (1984) demonstrates that the deviation from uncovered interest parity, which we denote by pt, is negatively correlated with and is more volatile than the rationally expected rate of depreciation. These empirical findings have long posed a challenge to international economic theory. In this paper, we explore two very different approaches to explaining this puzzle: the standard representative-agent intertemporal asset pricing model and a model of noise trading. Our analysis of the intertemporal asset pricing model employs quarterly data for the United States, Great Britain, Germany, and Japan extending from

A Discrete‐Time Intertemporal Asset Pricing Model: GE Approach with Recursive Utility

This paper studies the equilibrium characterization of asset pricing in a discrete‐time Lucas exchange economy (Lucas 1978) with the intertemporal recursive utility function of Epstein and Zin (1989). A general formulation of equilibrium asset pricing is presented. It is shown that risk aversion of a certainty equivalent corresponds to risk aversion in the intertemporal asset pricing model. The discrete‐time analogue of Ma's (1993) option pricing formula is derived in an i.i.d. environment, with which we prove an observational nonequivalence theorem in distinguishing the differences of the betweenness recursive utility functions and the expected utility functions. Additionally, when the consumption growth rate follows a first‐order Markov process, it is shown that the observational nonequivalence result holds for Kreps–Porteus expected utility. Finally, as by‐products, this paper also contains derivations of closed‐form formulas for the aggregate equity (with endogenously determined yields), the term structure of interest rates, and European call options on the aggregate equity in a Markov setting.

Regime Shifts and Changing Volatility in Stock Returns: A Rational Expectations Equilibrium Model

I present an intertemporal asset pricing model of learning to explain the GARCH behavior of stock returns and the intertemporal variation of expected returns. I assume that dividends follow a diffusion process whose drift rate shifts between two unobservable states at random times. I first show that the asset price is increasing and convex in investors' posterior probability of the good state. I then characterize the changes in asset price sensitivity to news, return volatility and expected returns as function of investors' level of uncertainty over the state of the economy.

Central bank intervention and risk in the forward market

A two country inter-temporal asset pricing model is developed which implies that central bank foreign exchange intervention affects the forward exchange risk premium. The model is estimated from daily foreign exchange intervention data for the US, German and Japanese central banks. Considerable empirical support is found for the theoretical model with intervention influencing the risk premium in the forward market. Purchases of dollars by the Federal Reserve Bank are found to be associated with excess $ denominated returns. There is evidence that intervention has increased rather than reduced exchange rate volatility.

The term structure of interest rates and economic activity: An empirical critique

Intertemporal asset pricing models, relating macroeconomic variables to asset returns and the term structure of interest rates, suggest that the term structure (yield curve) contains forecast-enhancing information about the future growth rate of real economic activity. Empirical evidence that the term structure contains information regarding a variety of macroeconomic variables has been presented in the literature over the last two decades. Recent empirical studies on the information content of the yield spread have been conducted using simple linear univariate forecasting models. U.S. and G7 data have been found to support a leading association between the term structure of interest rates and changes in the level of future real economic activity. However, many of the econometric models presented in the literature are far from adequate; in particular, several empirical studies of the term structure have not adequately accounted for important explanatory variables. The purpose of the paper is to evaluate the significance of these empirical models.