Identifying small mean-reverting portfolios

Abstract

Given multivariate time series, we study the problem of forming portfolios with maximum mean reversion while constraining the number of assets in these portfolios. We show that it can be formulated as a sparse canonical correlation analysis and study various algorithms to solve the corresponding sparse generalized eigenvalue problems. After discussing penalized parameter estimation procedures, we study the sparsity versus predictability tradeoff and the impact of predictability in various markets.

An inexact interior point method for L 1-regularized sparse covariance selection

“…They are often the ideal choice for solving small to medium size generic SDP problems. It is not difficult to see that (6) can be cast as a standard log-det SDP problem with p(p + 1)/2 linear constraints. In [44], Yuan and Lin actually applied a standard primal-dual interior-point method to solve (6).…”

“…It is not difficult to see that (6) can be cast as a standard log-det SDP problem with p(p + 1)/2 linear constraints. In [44], Yuan and Lin actually applied a standard primal-dual interior-point method to solve (6). However, as we have pointed out earlier, a standard IPM solver would encounter a severe computational bottleneck or even become impractical when p is large since its computational cost per iteration is at least O(p 6 ).…”

“…For the problems in [36], X is extremely sparse and well structured, and the authors were able to solve problems with p up to 34, 000 and |Ω c | up to 100, 000 although the computer architecture used and times taken were not mentioned. More recently, Wang, Sun and Toh [38] applied a Newton-CG primal proximal-point (PPA) method to solve (6). In the algorithm, each subproblem is solved by a semismooth Newton-CG method for which they used a preconditioned conjugate gradient (PCG) solver to compute an inexact Newton direction from the semismooth Newton equation in each inner iteration for the subproblem.…”

“…Second-order information is involved in their predictor step. Note that among the methods just described, the ANS method in [21] is the only one that is designed for the problem (6).…”

“…In financial portfolio management, sparse portfolios with fewer assets incur less transaction costs and are more tractable. In [6], the covariance selection model is applied to find a sparse portfolio for mean-reversion trading strategies. In the research of dependency networks of genome data, a gene may play a role in many biological pathways and be associated with many other genes, though all these effects may be transmitted through direct associations of only a few genes in the neighborhood.…”