Borrowing Constraints in Equilibrium
Ian Martin, Stanford University
This paper starts from the assumption that difficulties in borrowing against human capital impede young people from carrying out the investments prescribed by finance theory. According to the theory, for example, one should try to diversify both across assets and—the focus of this paper—across time, in the sense that sitting out of the market in one period and piling in the next is not an optimal strategy: better to be moderately exposed to the market in both periods.
This paper explores an overlapping-generations model with borrowing constraints. It presents the solution of a portfolio choice problem and investigates the equilibrium outcome. The framework is similar to that of Constantinides, Donaldson and Mehra (CDM, 2002), who argue convincingly that borrowing constraints on the young lower the riskless rate and raise the equity premium, and thereby contribute to explaining the associated puzzles. My model differs from CDM in that the assets which agents can choose to hold are not set down ex ante: in an attempt to adhere as closely as possible to the standard neoclassical framework, I allow the agents alive at any point in time to trade whatever assets they choose, subject to borrowing and budget constraints. I show that with this freedom, the borrowing-constrained young demand payoffs that look like call options on the market. These options are supplied, in equilibrium, by the middle-aged. To induce them to supply these options, implied volatility must be high; as an equilibrium consequence, realized volatility must be high. The model therefore provides a channel through which the presence of borrowing constraints can cause market volatility to increase—and thereby can potentially contribute to explaining the high volatility of real stock returns.