Portfolio choice and asset pricing in incomplete markets

Chabakauri, Georgy (2009) Portfolio choice and asset pricing in incomplete markets. Doctoral thesis, University of London: London Business School.

Abstract

This Thesis studies the portfolio choice and asset pricing in economic settings with incomplete markets and is comprised of three chapters. Chapter 1 explores the formation of stock prices in a general equilibrium economy with heterogeneous investors facing portfolio constraints. We compute the equilibrium when both investors have (identical for simplicity) CRRA preferences, one of them is unconstrained while the other faces an upper bound constraint on the proportion of wealth invested in stocks. We demonstrate that under certain parameters the model can generate countercyclical stock return volatilities, procyclical price-dividend ratios, excess volatility and other patterns observed in the data. Our baseline analysis is also extended to models with heterogeneous beliefs. Chapter 2 studies the portfolio choice in economies with incomplete markets with investors guided by mean-variance criteria. Mean-variance criteria remain prevalent in multiperiod problems, and yet not much is known about their dynamically optimal policies. In this chapter we provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the total risky asset demand. Chapter 3 provides a simple solution to the hedging problem in a general incomplete-market economy in which a hedger, guided by the minimum-variance criterion, aims at reducing the risk of a non-tradable asset. We derive fully analytical optimal time-consistent hedges and demonstrate that they can easily be computed in various stochastic environments. Our dynamic hedges preserve the simple structure of complete-market perfect hedges and are in terms of generalized "Greeks" familiar in risk management applications. We demonstrate that our optimal hedges typically outperform their static and myopic counterparts under plausible economic environments.