Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability
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Christian Gollier
We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. 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 uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly 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.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
- Advances Article
- Policy Advice with Imperfectly Informed Experts
- Backward Induction and Model Deterioration
- Contributions Article
- Search and Bargaining in Large Markets With Homogeneous Traders
- To Make or Buy: An Allocation of Attention
- A Simple Inducement Scheme to Overcome Adoption Externalities
- Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability
- Uniform Proofs of Order Independence for Various Strategy Elimination Procedures
- Players With Limited Memory
- Precedents and Timing: A Strategic Analysis of Multi-Plaintiff Litigation
- Optimal Auctions with Endogenous Entry
- Topics Article
- Multiple-Object Auctions Around a Circle
- Market Size and Vertical Equilibrium in the Context of Successive Cournot Oligopolies
- Trade and Linked Exchange; Price Discrimination Through Transaction Bundling
- A Sequential Signaling Model of the Sale of an Invention to an Oligopolist
- Vertical Differentiation, Asymmetric Information and Endogenous Bank Screening
- Patent Renewal Fees and Self-Funding Patent Offices
- Imitation and Long Run Outcomes
- Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games
- Unraveling of Information: Competition and Uncertainty
- A Theory of Vague Expected Utility
- Sequential Decision-Making and Asymmetric Equilibria: An Application to Takeovers
