Risk Economics and Multi-Agent CCAPM

Abstract

Utility models to price risk assets have been used following the seminal contribution of Markowitz, Sharpe, Lintner and a legion of economist and financial engineers. Models such as CAPM (Capital Assets Pricing Model) are for example linear risk models, implying a quadratic utility function which is used profusely in the financial industry. Generalization to the CCAPM (The Consumption Capital Assets Pricing Model) has further extended the theoretical and practical usefulness of such models, as well as provide an apparent relationship (in some cases) with pricing models based on Arrow-Debreu state preference theory. In this chapter this economic framework is extended, in the sense that the CCAPM may account for some endogenous factors embedded in economic aggregates (such as aggregate consumption rather than just an individual’s consumer). Such an extension has not been subjected to an empirical analysis but provides a theoretical framework for assessing a number of additional factors that affect the pricing of risk. In particular, it provides an economic and financial framework to value and price assets in situations that depart from the complete market hypothesis such as debt, consumers wealth etc. Applications are considered in both this chapter and the next.

References and Additional Reading

The Walras, Arrow and Debreu, have set the foundations for pricing in an equilibrium (complete) competitive market (Arrow 1951a, b, 1963a, 1982; Arrow et al. 1996; Debreu 1959) while Keynes (1935), Cochrane (2005), Campbell and Cochrane (1999) have set up the elements of the CCAPM approach based on te utility approach to decision making under uncertainty (for example, Borch 1968; Dreze and Modigliani 1972; Epstein and Zin 1989, 1991, Sharpe on the CAPM, Adler and Dumas 1980, Losq and Chateau 1982.

Applications are numerous. For example, Esscher (1932) on the Probability Function of Collective Risk which leads to a transformation to a risk neutral probability measure (a result used by actuaries for example). Gollier (2000), Gollier and Pratt (1996), provide a study of utility and risk aversion. Duffie and Garleanu (2001), on CDO, Sen (1973) on economic inequality, Ljungqvist and Sargent (2000) on a Recurive macroeconomic Theory. Miyahara (2012) book on pricing options in incomplete markets, Culp (2006) on Structure Finance in Insurance

Pricing IPO has similarly attracted both theoretical and empirical research (Alexander 1993 on Law and avoidance in IPO, Beatty and Ritter 1986; Benveniste and Spindt 1989)

The CCAPM has provided an extensive list of publications, both on the validity of such models and based on empirical research. Some essential references include Breeden (1979), Campbell (1999, 2000, 2003), Campbell and Cochrane (1999), Cochrane (1991, 2007), Cochrane’s book on Assets pricing (2005). Other papers include Fama and French (1997), on the equity premium, Mimeo, Fama (1970a, b), on a review efficient capital markets and Fama’s (1970), multiperiod consumption-investment decisions model, Almeida and Garcia (2008), on the empirical likelihood estimators for stochastic discount factors and Savov (2010). On Asset Pricing with Garbage

Numerous papers have also been published by Merton including his book in 1990 on Continuous Time Finance, 1969 on Lifetime portfolio selection under uncertainty, 1973 on Merton R.C., 1990, Continuous Time Finance book, 1973 seminal paper on the theory of rational option pricing, 1977, Optimum consumption and portfolio rules in a continuous time model and many others listed on Merton’s website.

Other references on the CCAPM include, Chapman (1997), Approximating the asset pricing kernel, Dittmar (2002), Nonlinear pricing kernels, kurtosis preference and evidence from the cross section equity returns, Duffie and Zame (1989), The consumption based capital asset pricing model, Duffie’s books, (1988) on Security Markets and (1992), on Dynamic Asset Pricing Theory.

Environmental applications are numerous, including Granovskii et al. (2006), on environmental and economic aspects of hydrogen production and utilization in fuel cell vehicles, Greaker (2003a), on Strategic environmental policy when the governments are threatened by relocation, as well as Greaker (2003b), on Strategic environmental policy; eco-dumping or a green strategy. Brannlund et al. (2006), on the effects on consumption and emissions, Greening et al. (2000), on a survey of energy efficiency and consumption