Optimal Risk-Averse Timing of an Asset Sale: Trending vs Mean-Reverting Price Dynamics

TL;DR

This paper analyzes the optimal timing for risk-averse investors to sell assets under trending and mean-reverting price models, deriving thresholds and comparing strategies across different utilities and dynamics.

Contribution

It introduces a comprehensive framework for optimal asset sale timing considering various utility functions and stochastic price models, including explicit threshold derivations.

Findings

Optimal thresholds depend on asset price, risk aversion, and quantity.

Timing options can cause non-concavity in the value function.

Numerical results illustrate strategies and timing premiums.

Abstract

This paper studies the optimal risk-averse timing to sell a risky asset. The investor's risk preference is described by the exponential, power, or log utility. Two stochastic models are considered for the asset price -- the geometric Brownian motion and exponential Ornstein-Uhlenbeck models -- to account for, respectively, the trending and mean-reverting price dynamics. In all cases, we derive the optimal thresholds and certainty equivalents to sell the asset, and compare them across models and utilities, with emphasis on their dependence on asset price, risk aversion, and quantity. We find that the timing option may render the investor's value function and certainty equivalent non-concave in price. Numerical results are provided to illustrate the investor's strategies and the premium associated with optimally timing to sell.