Optimal Investment Strategy for Risky Assets

TL;DR

This paper develops an optimal investment strategy for portfolios with risky assets modeled by multiplicative Brownian motion, focusing on maximizing long-term growth and accounting for both return and volatility, especially for highly risky assets.

Contribution

It introduces a new approach to portfolio optimization that considers both return and volatility for risky assets modeled by multiplicative Brownian motion, applicable to highly risky assets.

Findings

Optimal fraction of capital in risky assets identified

Weights of assets depend on both return and volatility

Strategy maximizes long-term growth rate

Abstract

We design an optimal strategy for investment in a portfolio of assets subject to a multiplicative Brownian motion. The strategy provides the maximal typical long-term growth rate of investor's capital. We determine the optimal fraction of capital that an investor should keep in risky assets as well as weights of different assets in an optimal portfolio. In this approach both average return and volatility of an asset are relevant indicators determining its optimal weight. Our results are particularly relevant for very risky assets when traditional continuous-time Gaussian portfolio theories are no longer applicable.