**1. Introduction**

Over a series of two posts, we will discuss the consumption capital asset pricing model (CCAPM) and some of its results concerning expected asset price returns. In particular, we derive a range within which asset returns lie. The model we will be discussing describes the simplified behavior of a trader who chooses to consume a portion of his income and invest the rest in market assets over two time periods of any kind (i.e. days, months, etc.)

In this post, we describe a simplified setting of the model and derive a formula for prices arising from the marginal cost and marginal benefit of the trader’s investment decisions. This equation will then show us how prices are affected by preferences. Furthermore, the resultant equation turns out to be robust to the initial simple setting of the model. Our exposition of the model borrows from John Cochrane’s book, Asset Pricing.

**2. Investor Consumption Model**

We begin our discussion of the **Consumption Capital Asset Pricing Model (CCAPM)** by first modeling our trader with a **utility function** defined over current and future values of consumption:

To simplify our discussion, we assume that there exists only one consumption good, denoted by , and that all other asset values are quoted in terms of it. The utility function represents the “fundamental pleasure” that the investor derives from consuming the good in question. The period utility function is assumed to be increasing, concave, and continuously differentiable (i.e. smooth). That the function is increasing describes, somewhat expectedly, the desire for greater consumption rather than lesser consumption, while concavity is a result of the decling marginal value of greater consumption. In other words, our investors will be happy to consume more rather than less, but enjoy each additional unit at a decreasing rate.

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