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date: 22 February 2020

Abstract and Keywords

This article investigates the determination of the optimal active risk policy as a function of time and relative performance (state variables) using stochastic programming techniques. The multi-period model assumes there is a minimum performance knockout barrier for the investor, in order to consider the investor's performance tolerance in a dynamic investment environment, and he can then observe the performance of the fund dynamically. A more formal specification of the model is such that the investor turns over a sum of money to the fund manager and delegates fund investment decisions to him over a certain length of time. The relationship between active risk and active return is specified by an active efficient frontier. A multinomial scenario tree is generated to represent the possible realization of the managed portfolio's relative performance at the end of each stage, and then the backward induction method is used to find the optimal solution. The scenario-tree generated is a lattice approximation of the state space of relative returns. There are two sources of inaccuracy in using a lattice that include the quantization error and specification error. The quantization error is incurred by approximating a continuous distribution with discrete outcomes while mismatching between the barrier level and the available lattice points causing a specification error.

Keywords: dynamic programming, optimal active risk policy, stochastic programming techniques, multi-period model, quantization error, specification error

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