The Market Model and Capital Asset Pricing Theory: A Note

This note shows that a linear market model is sufficient to derive a linear relationship between beta and expected return. Furthermore, the slope of the relationship will be identical with that of the Capital Asset Pricing Model if the return on the market portfolio is normally distributed. However, results from characterization theory suggest that the linear market model assumption is close to that of multivariate normality.     

Investment Policy Implications of the Capital Asset Pricing Model

The results of previous generalized Security Market Line (SML) tests of the Mean Variance (MV) and Linear Risk Tolerance (LRT) Capital Asset Pricing Models indicate that the models are empirically identical. A very widely accepted, but technically incorrect, explanation for the results is that with normal return distributions all expected utility maximizing riskaverse investors will pick MV portfolios. The paper shows that the generalized SML tests cannot distinguish between the MV model and a much wider variety of power utility LRT models than has previously been entertained. On the other hand, with approximately normal, or real world, return distributions the investment policies of the various models are shown to be different from each other, and from the MV policy in particular. To the extent the results of the portfolio selection calculations are robust, the results of, and implications drawn from, the tests of the macro pricing relations are not based on firm micro foundations.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital AssetPricing Model (CCAPM), Pareto optimal consumption allocationsare characterized by each agent's consumption process beingadapted to the filtration generated by the aggregate consumptionprocess of the economy. The wealth processes of the agents,however, are adapted to the finer filtration generated by aggregateconsumption and the conditional distribution of future aggregateconsumption. Therefore, in order to achieve pareto optimal consumptionallocations, a sufficiently varied set of assets must existsuch that any wealth process adapted to this finer filtrationcan be implemented by dynamically trading in that set of assets.We provide sufficient conditions for the existence of such aset of assets based on dynamically trading contingent claimson aggregate consumption. In addition, we give sufficient conditionsfor the existence of equilibria in a dynamically effectivelycomplete market in which agents are only able to trade in contingentclaims on aggregate consumption, the market portfolio of firms,and a (numeraire) zero-coupon bond. We demonstrate the roleof short- and long-term contingent claims on aggregate consumptionfor the implementation of Pareto optimal allocations inthe presenceof short- and long-term risks. In addition, in the presenceof personal risks, we demonstrate the role of insurance contracts.JEL Classification: G13.     

Dynamic Spanning in the Consumption-Based Capital Asset Pricing Model

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve Pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations in the presence of short- andlong-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.     

Temporal Aggregation and the Continuous-Time Capital Asset Pricing Model

We examine how the empirical implications of the Capital Asset Pricing Model (CAPM) are affected by the length of the period over which returns are measured. We show that the continuous-time CAPM becomes a multifactor model when the asset pricing relation is aggregated temporally. We use Hansen's Generalized Method of Moments (GMM) approach to test the continuous-time CAPM at an unconditional level using size portfolio returns. The results indicate that the continuous-time CAPM cannot be rejected. In contrast, the discrete-time CAPM is easily rejected by the tests. These results have a number of important implications for the interpretation of tests of the CAPM which have appeared in the literature.     

Co-Kurtosis and Capital Asset Pricing

This paper examines the impact of co-kurtosis on asset pricing using a four-moment capital asset pricing model. It is shown that, in the presence of skewness and kurtosis in asset return distribution, the expected excess rate of return is related not only to the systematic variance but also to the systematic skewness and systematic kurtosis. Investors are compensated in higher expected return for bearing the systematic variance and the systematic kurtosis risks. Investors also forego the expected excess return for taking the benefit of increasing the systematic skewness.     

Application of the Capital Asset Pricing Model to Multi-period Investments

This paper presents a method for evaluating a multi-period asset that is consistent with the valuations implied by the capital asset pricing model, and shows how the results of the valuation processes can be expressed in terms of a number of commonly used valuation formulas.
Ce papier expose tout d'abord une méthode permettant d'estimer une valeur immobilisée à multiples périodes qui soit compatible avec les évaluations fournies par le modéle d'bvaluation de l'actif immobilisé. II montre ensuite comment les résultats des opérations d'haluation peuvent être exprimés au moyen d'un nombre de formules d'estimation couramment utilisées.
Dieser Beitrag stellt eine Methode für die Bewertung einer mehrperiodischen Investition dar, die mit den Bewertungen, die das 'Capital Asset Pricing' Modell impliziert, übereinstimmt. Er zeigt, wie die Ergebnisse des Bewertungsprozesses mittels einer Anzahl gebrluchlicher Formeln ausgedruckt werden konnen.     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

Adjustment Costs and Capital Asset Pricing

Discrete-time models of asset pricing have hitherto generally avoided studying the relationship between the underlying technology inherent in the economy and the determinants of the price of capital. A fully articulated economy is constructed in which there is a nontrivial technology for producing capital. The existence of adjustment costs in augmenting the quantity of capital has interesting implications for the stochastic properties of asset prices, as well as other macroeconomic variables. Examples of such economies are used to illustrate this point.     

Option Coskewness and Capital Asset Pricing

This article shows how the market coskewness model of Rubinstein(1973) and Kraus and Litzenberger (1976) is altered when a nonredundantcall option is optimally traded. Owing to the option’snonredundancy, the economy’s stochastic discount factor(SDF) depends not only on the market return and the square ofthe market return but also on the option return, the squareof the option return, and the product of the market and optionreturns. This leads to an asset pricing model in which the expectedreturn on any risky asset depends explicitly on the asset’scoskewness with option returns. The empirical results show thatthe option coskewness model outperforms several competing benchmarkmodels. Furthermore, option coskewness captures some of thesame risks as the Fama–French factors small minus big(SMB) and high minus low (HML). These results suggest that thefactors that drive the pricing of nonredundant options are alsoimportant for pricing risky equities.(JEL G11, G12, D61)     

Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model

We 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.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting 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.     

Labor Mobility: Implications for Asset Pricing

Labor mobility is the flexibility of workers to walk away from an industry in response to better opportunities. I develop a model in which labor flows make bad times worse for shareholders who are left with capital that is less productive. The model shows that firms face greater operating leverage by providing flexibility to mobile workers. I construct an empirical measure of labor mobility consistent with the model and document an economically significant cross‐sectional relation between mobility, operating leverage, and stock returns. I find that firms in mobile industries earn returns over 5% higher than those in less mobile industries.     

LAPM: A Liquidity-Based Asset Pricing Model

The intertemporal CAPM predicts that an asset's price is equal to the expectation of the product of the asset's payoff and a representative consumer's intertemporal marginal rate of substitution. This paper develops an alternative approach to asset pricing based on corporations' desire to hoard liquidity. Our corporate finance approach suggests new determinants of asset prices such as the distribution of wealth within the corporate sector and between the corporate sector and the consumers. Also, leverage ratios, capital adequacy requirements, and the composition of savings affect the corporate demand for liquid assets and, thereby, interest rates.     

Estimation and Test of a Simple Model of Intertemporal Capital Asset Pricing

A simple valuation model with time‐varying investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by the real interest rate and the maximum Sharpe ratio, which follow correlated Ornstein–Uhlenbeck processes. The model parameters and time series of the state variables are estimated using U.S. Treasury bond yields and expected inflation from January 1952 to December 2000, and as predicted, the estimated maximum Sharpe ratio is related to the equity premium. In cross‐sectional asset‐pricing tests, both state variables have significant risk premia, which is consistent with Merton's ICAPM.