Risk-adjusted exponential gradient strategies for online portfolio selection

This paper concerns online portfolio selection problem whose main feature is with no any statistical assumption on future asset prices. Since online portfolio selection aims to maximize the cumulative wealth, most existing online portfolio strategies do not consider risk factors into the model. To enrich the research on online portfolio selection, we introduce the risk factors into the model and propose two novel risk-adjusted online portfolio strategies. More specifically, we first choose several exponential gradient (\(\text {EG}(\eta )\)) with different values of parameter \(\eta \) to build an expert pool. Later, we construct two risk methods to measure performance of each expert. Finally, we calculate the portfolio by the weighted average over all expert advice. We present theoretical and experimental results respectively to analyze the performance of the proposed strategies. Theoretical results show that the proposed strategies not only track the expert with the lowest risk, but also are universal, i.e., they exhibit the same asymptotic average logarithmic growth rate as best constant rebalanced portfolio (BCRP) determined in hindsight. We conduct extensive experiments by using daily stock data collected from the American and Chinese stock markets. Experimental results show the proposed strategies outperform existing online portfolio in terms of the return and risk metrics in most cases.