Universal Portfolio Shrinkage

Abstract

We introduce a novel shrinkage methodology for building optimal portfolios in environments of high complexity where the number of assets is comparable to or larger than the number of observations. Our universal portfolio shrinkage approximator(UPSA) is derived in closed form, is easy to implement, and dominates other existing shrinkage methods. It exhibits an explicit two-fund separation, optimally combining Markowitz with a complexity correction. Instead of annihilating the low-variance principal components, UPSA weights them efficiently. Contrary to conventional wisdom, low in-sample variance principal components (PCs) are key to out-of-sample model performance. By optimally incorporating them into portfolio construction, UPSA produces a stochastic discount factor that significantly dominates its PC-sparse counterparts. Thus, PC-sparsity is just an artifact of inefficient shrinkage.