Beating the Best Constant Rebalancing Portfolio in Long-Term Investment: A Generalization of the Kelly Criterion and Universal Learning Algorithm for Markets with Serial Dependence

Abstract: In the online portfolio optimization framework, existing learning algorithms generate strategies that yield significantly poorer cumulative wealth compared to the best constant rebalancing portfolio in hindsight, despite being consistent in asymptotic growth rate. While this unappealing performance can be improved by incorporating more side information, it raises difficulties in feature selection and high-dimensional settings. Instead, the inherent serial dependence of assets' returns, such as day-of-the-week and other calendar effects, can be leveraged. Although latent serial dependence patterns are commonly detected using large training datasets, this paper proposes an algorithm that learns such dependence using only gradually revealed data, without any assumption on their distribution, to form a strategy that eventually exceeds the cumulative wealth of the best constant rebalancing portfolio. Moreover, the classical Kelly criterion, which requires independent assets' returns, is generalized to accommodate serial dependence in a market modeled as an independent and identically distributed process of random matrices. In such a stochastic market, where existing learning algorithms designed for stationary processes fail to apply, the proposed learning algorithm still generates a strategy that asymptotically grows to the highest rate among all strategies, matching that of the optimal strategy constructed under the generalized Kelly criterion. The experimental results with real market data demonstrate the theoretical guarantees of the algorithm and its performance as expected, as long as serial dependence is significant, regardless of the validity of the generalized Kelly criterion in the experimental market. This further affirms the broad applicability of the algorithm in general contexts.