Replication of an actively-managed mutual fund using a small set of ETFs

Six ETFs (SPY, XLF, XLP, XLE, LQD, SHY) replicating the return distribution of Vanguard Asset Allocation (VAAPX). Replication of the daily return based on the immediately preceding 500-day data, i.e. 2 years. The out-of-sample backtest covers from 01 Jan 03 to 05 Apr 08. The lower holding limits for the replicating assets were 0,0,0,0,0,-1,-1 (i.e. long only equities, but short/borrow possible for fixed-income assets) and the upper holding limits at 1,1,1,1,1,1,1. Each optimised basket is self-financing, i.e. the weights add up to 1. We see the Asset Replicator captures the distribution pretty well.

------------ BACKTEST SUMMARY STATISTICS START ------------
Benchmark
Mean: 2.4006013509941815E-4
Var : 6.536813587536973E-5
Skew: -2.6322070042219065E-8
Kurt: 2.4578023774739083E-8
Asset_Replicator_0
Mean: 3.91485413068411E-4
Var : 6.299331467871073E-5
Skew: -7.904698545549026E-8
Kurt: 2.4889273783143836E-8
------------ BACKTEST SUMMARY STATISTICS END --------------

If we were to optimise the basket to replicate the return distribution of VAAPX over the backtest period, then the basket would look like:

giving the historic performance against the replicated asset of: