Optimal portfolios of variance swaps are constructed taking account of both autocorrelation and cross asset dependencies. Market prices of variance swaps are extracted from option surface calibrations. The methods developed permit simulation of cash flows to arbitrary portfolios of variance swaps. The optimal design maximizes the index of acceptability introduced in (Cherny and Madan, Review of Financial Studies, 2009). Full nonlinear optimization is contrasted with Simultaneous Perturbation Stochastic Approximation (SPSA). Preliminary out of sample results favor the use of SPSA.