Performance analysis of the optimal strategy under partial information

TL;DR

This paper analyzes how partial information affects the performance of the optimal investment strategy in a stochastic asset model with an unobservable trend, providing asymptotic metrics and comparing Sharpe ratios.

Contribution

It offers a detailed asymptotic analysis of the optimal strategy's performance under partial information in a stochastic trend model, including explicit formulas and performance comparison.

Findings

Asymptotic expectation and variance of logarithmic returns are derived.

Partial information leads to a quantifiable loss in Sharpe ratio.

Performance metrics depend on signal-to-noise ratio and trend reversion speed.

Abstract

The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.