# Dynamic Index Tracking and Risk Exposure Control Using Derivatives

## TL;DR

This paper introduces a continuous-time, derivative-based methodology for index tracking and risk management, providing a general framework for constructing dynamic portfolios that achieve targeted exposures and analyze tracking errors.

## Contribution

It develops a novel pathwise approach for dynamic derivative portfolio construction and establishes a general tracking condition applicable under various models.

## Key findings

- Derives a tracking condition linking portfolio drift to exposure coefficients
- Introduces a slippage process quantifying deviation from targeted returns
- Demonstrates implementation and comparison of strategies using futures and options

## Abstract

We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In our multi-factor setting, the portfolio's realized slippage depends not only on the realized variance of the index, but also the realized covariance among the index and factors. We implement our trading strategies under a number of models, and compare the tracking strategies and performances when using different derivatives, such as futures and options.