AbstractsBusiness Management & Administration

Modeling risk of the multi-period market portfolio: an equilibrium-based approach

by Xin Xu




Institution: University of New South Wales
Department: Banking & Finance
Year: 2013
Keywords: Mean-Variance Efficiency; Multi-period Market Portfolio; Portfolio Optimization; Dynamic Programming; Volatility; Market Risk; GARCH; Equilibrium; Market Security Economy; Merton's Problem
Record ID: 1042130
Full text PDF: http://handle.unsw.edu.au/1959.4/53009


Abstract

This thesis studies risk of the multi-period market portfolio, both instantaneously and over time, using an equilibrium-based approach. For instantaneous properties, we first show that the representative investor���s problem of maximizing the expected utility of lifetime consumption, aka Merton���s problem, is equivalent to a generalized mean-variance optimization problem, which has both expected return and ���covariance��� constraints, where ���covariance��� is that of the optimal portfolio���s return with changes in future investment opportunities. As the solution to this problem, the market portfolio is characterized by a multi-dimensional ���mean-covariance surface���, which generalizes the classic, single-period, two-dimensional ���mean-variance efficient frontier���. In addition to well-known preference-dependent (e.g. logarithmic preferences) conditions, we identify preference-independent conditions that are necessary and sufficient for the market portfolio to be mean-variance efficient. We also demonstrate that these conditions are unlikely to be satisfied in reality. We further explore a number of insightful decompositions of the market portfolio. For time series properties, we study equilibrium-consistent return processes of the market portfolio, both theoretically and empirically. Theoretically, Bick (1990), and He & Leland (1993) (HL) provided necessary and sufficient conditions for the market portfolio���s diffusion return processes to be consistent with preference-driven equilibria. We consider a similar problem but allow endogenous, market-clearing, instantaneously riskless interest rates. We are thus able to support a larger family of equilibrium consistent specifications of mean and volatility structures of the market portfolio���s rates of return. When interest rates are deterministic, our conditions become those of HL. We also discuss how to implement these conditions in practical applications. Empirically, we introduce an implementation method of the equilibrium conditions, and implement them by modeling the market portfolio���s return volatility, which is central to financial risk management. We analyze two families of equilibrium-based volatility structures, one represented by current popular models, and another in which we propose new models. In an empirical study, our proposed models, while as easy to implement, outperform the popular ones, in three out-of-sample forecast evaluations of different time periods, by standard predictability criteria. This is true especially during high-volatility periods, whether markets rise or fall.