Portfolio Management and Asset Pricing

Suppose that a group of agents having divergent expectations can share risks efficiently by trading on financial markets and by purchasing insurance. The objective of this research is to examine how the divergence of opinions on the profitability of firms affects

• The investors’ portfolio management and the consumers’ insurance demand;
• The equilibrium asset and insurance prices;
• The optimal investment strategy by firms.

We will consider an Arrow-Debreu economy which is classical in all directions, except that investors diverge on their subjective probability distribution of the various states of nature. This does not come from any asymmetric information, but rather from a deeper divergence of opinion about how to interpret various signals of the economy. We conjecture the following properties of the competitive equilibrium:

1. As in the standard model, there exists a representative agent, but his beliefs is a complex combination of the different investors’ beliefs. At the aggregate level, the standard CAPM formula applies, but with a distribution of returns that takes into account of the investors’ disagreement.
2. The collective probability distribution is biased in favor of the beliefs of the more risk tolerant agents in the group. Intuitively, if an agent does not participate to the collective investment, either because of his high risk aversion or because of his pessimism, his beliefs will not matter for pricing.
3. From this central result, we want to show how increasing disagreement on the individual subjective state probability affects the state probability of the representative agent. We want to show that the collective state probability is decreased by the heterogeneity of beliefs, at least when relative risk aversion is larger than unity. When there are only two states of nature, we want to show that the representative agent has a bias towards certainty. This latter result may be useful to understand the insurability problem of catastrophic risks.
4. Moreover, we want to prove that the divergence of opinions about the probability of occurrence of a boom may help solving the equity premium puzzle.

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