Allan Borodin, Ran El-Yaniv, Vincent Gogan
A novel algorithm for actively trading stocks is presented. While tradi- tional universal algorithms (and technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of techni- cal trading can “beat the market” and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning.
1 Introduction: The Portfolio Selection Problem
The portfolio selection (PS) problem is a challenging problem for machine learning, online algorithms and, of course, computational ﬁnance. As is well known (e.g. see Lugosi ) sequence prediction under the log loss measure can be viewed as a special case of portfo- lio selection, and perhaps more surprisingly, from a certain worst case minimax criterion, portfolio selection is not essentially any harder (than prediction) as shown in  (see also , Thm. 20 & 21). But there seems to be a qualitative difference between the practical utility of “universal” sequence prediction and universal portfolio selection. Simply stated, universal sequence prediction algorithms under various probabilistic and worst-case mod- els work very well in practice whereas the known universal portfolio selection algorithms do not seem to provide any substantial beneﬁt over a naive investment strategy (see Sec. 4).
A major pragmatic question is whether or not a computer program can consistently out- perform the market. A closer inspection of the interesting ideas developed in information theory and online learning suggests that a promising approach is to exploit the natural volatility in the market and in particular to beneﬁt from simple and rather persistent statis- tical relations between stocks rather than to try to predict stock prices or “winners”. We present a non-universal portfolio selection algorithm1, which does not try to predict win- ners. The motivation behind our algorithm is the rationale behind constant rebalancing algorithms and the worst case study of universal trading introduced by Cover . Not only does our proposed algorithm substantially “beat the market” on historical markets, it also beats the best stock. So why are we presenting this algorithm and not just simply making money? There are, of course some caveats and obstacles to utilizing the algorithm. But for large investors the possibility of a goose laying silver (if not golden) eggs is not impossible.
1Any PS algorithm can be modiﬁed to be universal by investing any ﬁxed fraction of the initial
wealth in a universal algorithm.