In the context of stochastic portfolio theory we introduce a novel class of portfolios which we call linear path-functional portfolios. These are portfolios which are determined by certain transformations of linear functions of a collections of feature maps that are non-anticipative path functionals of an underlying semimartingale. As main example for such feature maps we consider (random) signature of the (ranked) market weights. We prove that these portfolios are universal in the sense that every continuous (possibly path-dependent) portfolio function of the market weights can be uniformly approximated by signature portfolios. We also show that signature portfolios can approximate the log-optimal portfolio in several classes of non-Markovian models arbitrarily well and illustrate numerically that the trained signature portfolios are remarkably close to the theoretical log-optimal portfolios. This applicability to non-Markovian markets makes these portfolios much more general than classical functionally generated portfolios usually considered in stochastic portfolio theory.
Besides these universality features, the main numerical advantage lies in the fact that several optimization tasks like maximizing expected logarithmic utility or mean-variance optimization within the class of linear path-functional portfolios reduces to a convex quadratic optimization problem, thus making it computationally highly tractable.
We apply our method to real market data and show generic out-performance on out-of-sample data even under transaction costs.
The talk is based on joint work with Janka Möller.