m Cost Minimization and Asset Pricing

A cost-based approach to asset-pricing equilibrium relationships is developed. A cost function induces a stochastic discount factor (pricing kernel) that is a function of random output, prices, and capital stockt. By eliminating opportunities for arbitrage between financial markets and the production technology, firms minimize the current cost of future consumption. The first-order conditions for this cost minimization problem generate the stochastic discount factor. The cost-based approach is dual in nature and determines state-claim prices as the current-period marginal cost of increasing future stochastic output. A costbased pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data. Asset pricing theory requires that an asset’s price equals the inner product of a stochastic discount factor (or pricing kernel) and the asset’s stochastic payout (Ross, 1978; Harrison and Kreps, 1979; Hansen and Singleton, 1982; Clark, 1993; Cochrane, 2001; Campbell, 2003; Du¢ e, 2003; and many, many others). The stochastic discount factor can be rationalized as subjective Arrow "state-claim prices". If the stochastic return on an asset is denoted by ~ R and the stochastic discount factor is represented by ~ m; the equilibrium implication is that E h ~ m ~ R i = 1; (1) where E represents the expectation operator. The consumption-based approach identi…es ~ m with the consumer’s intertemporal marginal rate of substitution between nonstochastic current period consumption and stochastic future consumption. An important, and apparently unresolved, empirical challenge to the consumption-based approach is that the resulting models do not appear to …t market data particularly well (Hansen and Singleton, 1982; Hansen and Jagannathan, 1991, 1997; Campbell, Lo, and MacKinlay, 1997; Cochrane, 2001; Campbell, 2003). Perhaps the most famous manifestation of this lack of …t is the equity-premium puzzle introduced by Shiller (1982) and Mehra and Prescott (1985). As is well-known, for the most popular speci…cation of the consumption-based discount factor, the consumption-based model can be reconciled with observed low volatility of aggregate consumption growth only if risk aversion is much larger than is commonly believed. Our intent is not to resolve the equity-premium puzzle or to explain the perceived poor performance of the consumption-based model. Instead, our focus is on enlarging the range of economic models available for asset pricing analysis. We consider a representation of the stochastic discount factor that arises not from consumers optimally smoothing stochastic consumption across time but from the intertemporal optimization behavior of producing …rms that have access to …nancial markets. The associated asset pricing rule emerges from the rational need to exploit any opportunities for risklessly raising intertemporal returns or lowering current period costs. Even though many presentations of …nancial market equilibrium quite consciously ignore producers, there are a number of reasons to take their perspective in looking at asset-market