Generalization Bounds for Regularized Portfolio Selection with Market Side Information

Drawing on statistical learning theory, we derive out-of-sample and suboptimal guarantees about the investment strategy obtained from a regularized portfolio optimization model which attempts to exploit side information about the financial market in order to reach an optimal risk-return tradeoff. This side information might include for instance recent stock returns, volatility indexes, financial news indicators, etc. In particular, we demonstrate that an investment policy that linearly combines this side information in a way that is optimal from the perspective of a random sample set is guaranteed to perform also relatively well (\ie, within a perturbing factor of $O(1/\sqrt{n})$) with respect to the unknown distribution that generated this sample set. Finally, we evaluate the sensitivity of these results in a high dimensional regime where the size of the side information vector is of an order that is comparable to the sample size.