Risk-Potential Framework for Dynamic Portfolio Selection

Description

The decision criterion plays a crucial role in selecting optimal portfolios that best fit investors’ investment expectation and risk attitudes. There are two main schools of such decision frameworks in the literature: the framework of expected utility maximization, based on Von Neumann-Morgenstern utility theorem that is derived from the assumed preferences of rational decision-makers, and the mean-risk framework pioneered by Markowitz, in which investors seek to strike a balance between risk and return. Despite its scientific rigour based on the justifiable axioms of rational behavior, the expected utility maximization framework is not widely adopted by practitioners due to its abstract nature and global assessment requirement. Mean-risk optimization on the other hand is popular in investment practice due to its clear intuition to practitioners, but suffers from several theoretical deficiencies, in particular the notorious time-inconsistency.In this project we propose a novel risk-potential portfolio selection framework which possesses both desirable theoretical features, including monotonicity and time-consistency, and straightforward financial intuition. We argue that investors should always set a target in investment and care about minimizing the possibility of falling short of the target and maximizing the possibility of exceeding the target simultaneously. We then define the two performance measures, i）Risk: lower partial moments below the target, and ii) Potential: upper partial moment above the target. Under a realistic premise that investors only need to provide their investment targets and the desired trade-offs between risk and potential, we can translate such investment parameters into a corresponding stochastic control formulation. In this research, we will proceed to show, building on our preliminary investigation, that our proposed risk-potential portfolio selection formulation is analytically solvable and computationally tractable, although the problem formulation is nonconvex in nature due to its inverse S-shape objective function. We will derive its wellposedness condition, and obtain its optimal investment strategy. We will then study the distinctive features and prominent properties of our framework, and compare it with various existing portfolio selection formulations, including the dynamic mean-variance formulation, dynamic mean-CVaR formulation, and dynamic behavioral portfolio selection under cumulative prospect theory.Our contributions in this research will advance the state-of-the-art and directly improve investment practice by i) connecting the objective function in investment models with the lower and upper partial moments associated with an investment target which are easily comprehensible by market practitioners, and ii) making the resulting investment models computationally tractable, thus offering investors more valuable guidance.