Abstract
We consider the problem of portfolio optimization with a correlation constraint. The framework is the multi-period stochastic financial market setting with one tradable stock, stochastic income, and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable index at some benchmark time horizon. The goal is to maximize a portofolio’s expected exponential utility subject to the correlation constraint. Two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones. We find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies. Both these portfolio strategies yield significantly lower risk when compared to the unconstrained setting, at the cost of a small utility loss. The performance of the CSGP and CPC portfolio strategies is similar.
Highlights
Mean variance optimization introduced by Markowitz (1952) changed the pathway of how fund managers look at optimal investments
Portfolio optimization under correlation constraints is of particular interest to hedge funds which implement market defensive strategies with higher returns during down markets than up-markets, and this makes our research interesting from a practical standpoint
We study the impact of correlation constraint on a portfolio optimization problem of one stock and stochastic income stream in a discrete multi-period setting
Summary
Mean variance optimization introduced by Markowitz (1952) changed the pathway of how fund managers look at optimal investments. The paper Landsman et al (2018) finds explicit solutions for optimizing a generalized measure applied to constrained and unconstrained portfolios All these works consider a static framework; the optimization is performed at time zero and the optimal strategies are implemented. To the best of our knowledge, we are not aware of other studies that consider time inconsistency arising due to the correlation constraint in the context of portfolio optimization in a multi-period setting. The rest of the paper is organized as follows—Section 2 describes the model, the stock price process, benchmark index, and stochastic income stream, the trading strategies, risk preference, and the objective. The benchmark index B := { Bt : t = 0, h, ..., ( N − 1)h}, represents the performance of the economy and is correlated to the underlying stock and the income It is given by the following difference equation:. Drift μ3 and volatility σ3 are chosen so that the benchmark index is positive
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