Risk-sensitive benchmarked asset management with expert forecasts

Abstract

We propose a continuous-time model in which investors use expert forecasts to construct a benchmark-outperforming portfolio in two steps. The estimation step takes the form of a Kalman filter. The control step derives the optimal investment policy in closed form and establishes that the value function is the unique classical solution to the Hamilton-Jacobi-Bellman partial differential equation. We show that the optimal investment policy generates a continuum of investment strategies, from passive benchmark replication to fully active bets in the Kelly portfolio. However, our model warns against over-betting on financial markets. Moreover, we find that the Kelly portfolio performs both security selection and factor tilt. A simulation study with market data confirms that factor choice is critical at every stage of the investment process. Finally, debiasing is equally crucial. Portfolios with debiased expert forecasts outperform portfolios with biased forecasts.