Portfolio Optimization through Data Conditioning and Aggregation

In this paper, we present a novel portfolio optimization method that aims to generalize the delta changes of future returns, based on historical delta changes of returns learned in a past window of time. Our method addresses two issues in portfolio optimization. First, we observe that daily returns of stock prices are very noisy and often non-stationary and dependent. In addition, they do not follow certain well-defined distribution functions, such as the Gaussian distribution. To address this issue, we first aggregate the return values over a multi-day period into an average return in order to reduce the noise of daily returns. We further propose a pre-selection scheme based on stationarity, normality and independence tests in order to select a subset of stocks that have promising statistical properties. Second, we have found that optimizing the average risk in a past window does not typically generalize to future returns with minimal risks. To this end, we develop a portfolio optimization method that uses the delta changes of aggregated returns in a past window to optimize the delta changes of future expected returns. Our experimental studies show that data conditioning and aggregation in our proposed method is an effective means of improving the generalizability while simultaneously minimizing the risk of the portfolio.