Please note: This master’s research paper presentation will take place in DC 2310.
Sadman Samin Khan, Master’s candidate
David R. Cheriton School of Computer Science
Supervisors: Professors Yuying Li, Peter Forsyth
This research project studies benchmark-relative portfolio allocation under asymmetric reward-risk objectives in a discrete-time setting with infrequent rebalancing. The investor allocates wealth dynamically so as to outperform a passive benchmark portfolio over a fixed investment horizon, with performance measured through the terminal relative wealth ratio. The motivation is that conventional variance-based portfolio criteria do not adequately capture the skewness, heavy tails, and downside asymmetry observed in financial returns.
We develop a simulation-based neural-network framework that learns state-dependent allocation policies directly from sampled return paths. In the two-asset setting, stock and bond returns are generated from a calibrated double-exponential jump-diffusion model. In the multi-asset setting, synthetic return paths are produced using a stationary block bootstrap applied to historical data, allowing the simulation environment to preserve important empirical dependence structures without imposing a restrictive parametric specification.
Two Omega ratio-inspired optimization formulations are considered. The first maximizes expected benchmark-relative return subject to a penalty on expected shortfall below the benchmark, yielding a stable and economically interpretable efficient frontier. The second combines expected benchmark-relative return with the Omega ratio itself, thereby incorporating asymmetric upside-downside trade-offs directly into the learning objective. Numerical experiments show that, for moderate trade-off parameters, the two formulations generate very similar terminal wealth distributions and state-dependent allocation policies. However, direct optimization of the Omega ratio is prone to degeneracy and numerical instability when the downside term becomes very small, since large Omega values can then be achieved without economically meaningful improvements in expected terminal wealth.
The results therefore support a benchmark-relative formulation based on fixing a downside risk budget and maximizing expected relative return within that constraint. More broadly, the study shows that simulation-based neural-network methods can learn economically meaningful dynamic allocation policies under realistic market dynamics, and that the framework remains effective when the asset universe is expanded beyond the two-asset case.