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Introductory Mathematics and Statistics for Islamic Finance, + Website by Noureddine Krichene, Abbas Mirakhor

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Chapter 21The Consumption-Based Pricing Model

The purpose of this chapter is to analyze capital asset pricing using the intertemporal-consumption model. This approach aims to determine the price of a capital asset in terms of an investor's intertemporal choice of his future consumption as in the case of retirement planning and social security contributions. Consumption-based pricing model is called equilibrium pricing model because it applies the standard consumer utility maximization model under budget constraint and derives first-order conditions for equilibrium. From the first-order optimization conditions, the model shows the price of an asset to be equal to its expected discounted future payoffs; the stochastic discount factor is the marginal rate of substitution between present and future stochastic consumption. The consumption-based model shows the equivalence of pricing payoffs and returns, and enables us to derive the capital asset pricing model (CAPM), portfolio theory, mean-variance efficiency frontier, and risk-neutral pricing. The chapter stresses equivalence of asset pricing methods under uncertainty; each method implies the others. For instance, risk-neutral pricing should be free of arbitrage and should satisfy the optimality conditions of investors' choices.

The merit of the consumption-based asset pricing is to relate asset pricing to economic growth and capital theory. Consumption is the ultimate objective of investment. Growth theory has been concerned with ...

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