Review of Dynamic Allocation Strategies: Utility Maximization, Option Replication, Insurance, Drawdown Control, Convex/Concave Management

Abstract:     
We review the main approaches to dynamically reallocate capital between a risky portfolio and a risk-free account: expected utility maximization; option-based portfolio insurance (OBPI); and drawdown control, closely related to constant proportion portfolio insurance (CPPI). We present a refresher of the theory under general assumptions. We discuss the connections among the different approaches, as well as their relationship with convex and concave strategies. We provide explicit, practicable solutions with all the computations as well as numerical examples. Fully documented code for all the strategies is also provided.

Number of Pages in PDF File: 24

Keywords: CPPI, OBPI, drawdown control, option replication, dynamic programming, Hamilton-Jacobi-Bellman equation, Pontryagin principle, geometric Brownian motion, power utility, constant exposure portfolio, buy-and-hold

JEL Classification: C1, G11

working papers series