Robust Portfolios and Weak Incentives in Long-Run Investments

TL;DR

This paper demonstrates that in long-term, frictionless markets, isoelastic portfolios are nearly optimal for a broad class of investors, and that long horizons weaken the impact of incentive schemes based on options.

Contribution

The paper proves the near-optimality of isoelastic portfolios in long-term models and analyzes the robustness of investment incentives to preference perturbations.

Findings

Isoelastic portfolios are nearly optimal for long horizons.

Long-term horizons weaken the effectiveness of option-based incentives.

Robust option incentives require many large exercise prices and are not always convex.

Abstract

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage-free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.