Combining Alpha Streams with Costs

TL;DR

This paper analyzes how to optimally allocate investments across multiple alpha streams traded on the same platform with trade crossing, considering costs and turnover reduction effects, and introduces algorithms for efficient allocation.

Contribution

It presents a novel algorithm for allocation with crossing and costs, including an approximation for nonlinear costs, and defines 'regression with costs' for singular covariance matrices.

Findings

Turnover reduction depends on the universe of alpha streams.

Allocation weights can be negative when crossing is allowed.

The proposed methods improve allocation efficiency under costs.

Abstract

We discuss investment allocation to multiple alpha streams traded on the same execution platform with internal crossing of trades and point out differences with allocating investment when alpha streams are traded on separate execution platforms with no crossing. First, in the latter case allocation weights are non-negative, while in the former case they can be negative. Second, the effects of both linear and nonlinear (impact) costs are different in these two cases due to turnover reduction when the trades are crossed. Third, the turnover reduction depends on the universe of traded alpha streams, so if some alpha streams have zero allocations, turnover reduction needs to be recomputed, hence an iterative procedure. We discuss an algorithm for finding allocation weights with crossing and linear costs. We also discuss a simple approximation when nonlinear costs are added, making the allocation problem tractable while still capturing nonlinear portfolio capacity bound effects. We also define "regression with costs" as a limit of optimization with costs, useful in often-occurring cases with singular alpha covariance matrix.