Roland Portait

Dynamic asset allocation with mean variance preferences and a solvency constraint

Abstract The aim of this article is to analyze the portfolio strategies that are mean-variance efficient when continuous rebalancing is allowed and a solvency constraint (wealth positiveness) is imposed at each point in time. Under very general assumptions (Ito processes for the security price dynamics) those efficient strategies are identified as synthetic put options on the particular inefficient portfolio yielding the return with minimal second moment. This general characterization allows us to derive a closed-form formula for the optimal portfolio weights when the investment opportunity set is constant (the optimal weights are explicit functions of the current market index). The formula is then used to simulate dynamically efficient strategies for different horizons and targets, and to describe the time pattern of the allocation to stocks versus bonds.

Investment and hedging under a stochastic yield curve: A two-state-variable, multi-factor model

Abstract This paper examines portfolio decisions involving both fixed and non-fixed income securities. Two state variables, the short-term and the long-term interest rates, fully determine the bonds prices and partly influence the other assets prices. We propose first a methodology for determining optimal portfolios in such a context and then use that methodology to solve the portfolio problem of investors whose long-term bond holdings are constrained, which generates undesirable interest rate risk that are hedged with futures contracts. The individual futures positions, which involve several hedging components and the futures market equilibrium open interest are derived and analysed.

Pricing stock and bond derivatives with a multi-factor Gaussian model

The martingale approach to pricing contingent claims can be applied in a multiple state variable model. The idea is used to derive the prices of derivative securities (futures on stock and bond futures, options on stocks, bonds and futures) given a continuous time Gaussian multi-factor model of the returns of stocks and bonds. The bond market is similar to Langetiegs multi-factor model, which has closed-form solutions. This model is a generalization of Vasiceks model, where the term structure depends on state variables following correlated mean reverting processes. The stock market is affected by systematic and unsystematic risk.

Optimal portfolio allocations with tracking error volatility and stochastic hedging constraints

The performance of mutual fund or pension fund managers is often evaluated by comparing the returns of managed portfolios with those of a benchmark. As most portfolio managers use dynamic rules for rebalancing their portfolios, we use a dynamic framework to study the optimization of the tracking error–return trade-off. Following these observations, we assume that the manager minimizes the tracking error under an expected return goal (or, equivalently, maximizes the information ratio). Moreover, we assume that he/she complies with a stochastic hedging constraint whereby the terminal value of the portfolio is (almost surely) higher than a given stochastic payoff. This general setting includes the case of a minimum wealth level at the horizon date and the case of a performance constraint on terminal wealth as measured by the benchmark (i.e. terminal portfolio wealth should be at least equal to a given proportion of the index). When the manager cares about absolute returns and relative returns as well, the risk–return trade-off acquires an extra dimension since risk comprises two components. This extra risk dimension substantially modifies the characteristics of portfolio strategies. The optimal solutions involve pricing and duplication of spread options. Optimal terminal wealth profiles are derived in a general setting, and optimal strategies are determined when security prices follow geometric Brownian motions and interest rates remain constant. A numerical example illustrates the type of strategies generated by the model.