“Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability” by Christian GOLLIER
University of Toulouse
We consider a two-period portfolio problem when asset returns are predictable. First-order (second-order) predictability means that an increase in the first period return yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices, with application in portfolios of bonds with different maturities. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is larger than unity. This implies that first-order predictability increases the initial optimal portfolio risk if this condition is satisfied. A similar result is obtained with second-order predictability (mean-reversion in stock returns, learning …) under the condition that absolute prudence be smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.