Intertemporal Capital Asset Pricing Model With Time Varying Parameters

A simple valuation model that allows for time variation in investment opportunities is developed and estimated. The model assumes that the investment opportunity set is completely described by two state variables, 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 data on US Treasury bond yields and inflation for the period January 1952 to December 2000. The estimated state variables are shown to be related to the equity premium and to the level of stock prices as measured by the dividend yield. Innovations in the estimated state variables are shown to be related to the returns on the Fama-French arbitrage portfolios, HML and SMB, providing a possible explanation for the risk premia on these portfolios. When tracking portfolios for the state variable innovations are constructed using returns on 6 size and book-to market equity sorted portfolios, the tracking portfolios explain the risk premia on HML and SMB, and these state variable tracking portfolios perform about as well as HML and SMB in explaining the cross-section of returns on the 25 size and book-to market equity sorted value weighted portfolios. An additional test of the ICAPM using returns on 30 industrial portfolios does not reject the model while the CAPM and the Fama-French 3 factor model are rejected using the same data.

Characterizing the instantaneous investment opportunity set by the real interest rate and the maximum Sharpe ratio, a simple model of time varying investment opportunities is posited in which these two variables follow correlated Ornstein-Uhlenbeck processes, and the implications for stock and bond valuation are developed. The model suggests that the prices of certain portfolios that are related to the Fama-French HML and SMB hedge portfolio returns will carry information about investment opportunities. This provides a justification for the risk premia that have been found to be associated with these hedge portfolio returns. Evidence that the FF portfolios are in fact associated with variation in the investment opportunity set is found from an analysis of stock returns. Further evidence of time variation in the real investment opportunity set is found by analyzing bond yields, and the time variation in investment opportunities that is identified from bond yields is shown to be associated both with the time-variation in investment opportunities that is identified from stock returns and with the returns on the Fama-French hedge portfolios. Finally, it is shown that the estimated parameters imply substantial variation in stock prices that is not associated with cash flow expectations.

Seminar paper from the year 2018 in the subject Economics - Finance, grade: 1.7, University of Duisburg-Essen (Faculty of Business and Economics), language: English, abstract: The Capital Asset Pricing Model (CAPM), which is developed by Harry Markowitz, lacks on empirical validation and is not economically fully plausible. By only considering a single period within the CAPM, Merton tried to improve the model by implementing different intertemporal assumptions. This paper focuses on the analysis, if the lack of the CAPM can be improved by using the assumptions of the ICAPM and if the eight investigated models are in the sense of Merton's assumptions. The first chapter reviews a short explanation of the classical CAPM and his critics, followed by Merton's intertemporal CAPM and his assumptions in the next chapter. Additionally, there were models developed, trying to be economically plausible by considering the ICAPM main assumptions, which are presented in the second chapter. A different way to develop an empirical better fitting CAPM is by using empirical motivated state variables. Fama & French started to take this approach by developing the three-factor-model (FF3). A lot of researchers were influenced by the FF3 and made their own version of a multifactor model by implementing variables. Even Fama & French enhanced their three-factor-model by adding further variables. In the third section there is the forecasting power of the four ICAPM models and the four empirical motivated multifactor models on the US market data and on the European market data compared. Then follows an examination if these models can be determined in the sense of the ICAPM restrictions. The last chapter concludes the results.

While mainstream financial theories and applications assume that asset returns are normally distributed and individual preferences are quadratic, the overwhelming empirical evidence shows otherwise. Indeed, most of the asset returns exhibit “fat-tails” distributions and investors exhibit asymmetric preferences. These empirical findings lead to the development of a new area of research dedicated to the introduction of higher order moments in portfolio theory and asset pricing models. Multi-moment asset pricing is a revolutionary new way of modeling time series in finance which allows various degrees of long-term memory to be generated. It allows risk and prices of risk to vary through time enabling the accurate valuation of long-lived assets. This book presents the state-of-the art in multi-moment asset allocation and pricing models and provides many new developments in a single volume, collecting in a unified framework theoretical results and applications previously scattered throughout the financial literature. The topics covered in this comprehensive volume include: four-moment individual risk preferences, mathematics of the multi-moment efficient frontier, coherent asymmetric risks measures, hedge funds asset allocation under higher moments, time-varying specifications of (co)moments and multi-moment asset pricing models with homogeneous and heterogeneous agents. Written by leading academics, Multi-moment Asset Allocation and Pricing Models offers a unique opportunity to explore the latest findings in this new field of research.

The main message of this paper is that it is Elasticity of Intertemporal Substitution, which is at the heart of the asset pricing puzzles, not Risk Aversion. We illustrate that point, by first showing that under certainty a model, which allows for a separation of the two characteristics of preferences - the one in Epstein and Zin (1991), leads to a specification of the main pricing equation, which involves a measure of Elasticity of Intertemporal Substitution only and not a measure of Risk Aversion. We then resort to an approximation of the main asset pricing equation under uncertainty, to demonstrate the central role played by Elasticity of Intertemporal Substitution and to emphasize the importance of its variability. We illustrate that importance by showing that the model in Campbell and Cochrane (1999) is in fact based on time-varying Elasticity of Intertemporal Substitution rather then on time-varying Risk Aversion.The main contribution of the paper is to develop a discrete-time alternative to the two most popular recursive utility based asset pricing models. The model proposed in the paper, directly nests the standard one, while replicating and improving upon the two frequently cited advantages of the Epstein-Zin model. It allows for time-varying risk premia, associated with the two most popular asset pricing factors and it achieves separation of risk attitudes from attitudes towards time via constant relative risk aversion (CRRA) and time-varying Elasticity of Intertemporal Substitution.

Asset Pricing Theory is an advanced textbook for doctoral students and researchers that offers a modern introduction to the theoretical and methodological foundations of competitive asset pricing. Costis Skiadas develops in depth the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, but with emphasis on geometric and martingale methods that facilitate an effortless transition to the more advanced continuous-time theory. Among the book's many innovations are its use of recursive utility as the benchmark representation of dynamic preferences, and an associated theory of equilibrium pricing and optimal portfolio choice that goes beyond the existing literature. Asset Pricing Theory is complete with extensive exercises at the end of every chapter and comprehensive mathematical appendixes, making this book a self-contained resource for graduate students and academic researchers, as well as mathematically sophisticated practitioners seeking a deeper understanding of concepts and methods on which practical models are built. Covers in depth the modern theoretical foundations of competitive asset pricing and consumption/portfolio choice Uses recursive utility as the benchmark preference representation in dynamic settings Sets the foundations for advanced modeling using geometric arguments and martingale methodology Features self-contained mathematical appendixes Includes extensive end-of-chapter exercises

Financial Markets and the Real Economy reviews the current academic literature on the macroeconomics of finance.

Winner of the prestigious Paul A. Samuelson Award for scholarly writing on lifelong financial security, John Cochrane's Asset Pricing now appears in a revised edition that unifies and brings the science of asset pricing up to date for advanced students and professionals. Cochrane traces the pricing of all assets back to a single idea--price equals expected discounted payoff--that captures the macro-economic risks underlying each security's value. By using a single, stochastic discount factor rather than a separate set of tricks for each asset class, Cochrane builds a unified account of modern asset pricing. He presents applications to stocks, bonds, and options. Each model--consumption based, CAPM, multifactor, term structure, and option pricing--is derived as a different specification of the discounted factor. The discount factor framework also leads to a state-space geometry for mean-variance frontiers and asset pricing models. It puts payoffs in different states of nature on the axes rather than mean and variance of return, leading to a new and conveniently linear geometrical representation of asset pricing ideas. Cochrane approaches empirical work with the Generalized Method of Moments, which studies sample average prices and discounted payoffs to determine whether price does equal expected discounted payoff. He translates between the discount factor, GMM, and state-space language and the beta, mean-variance, and regression language common in empirical work and earlier theory. The book also includes a review of recent empirical work on return predictability, value and other puzzles in the cross section, and equity premium puzzles and their resolution. Written to be a summary for academics and professionals as well as a textbook, this book condenses and advances recent scholarship in financial economics.