# Full Scale Optimization

Consider the returns to the S&P500 and the Barclay's Agg bond index.

The distributions are quite different. A simple histogram shows that the two are quite different in shape. The differences become more dramatic if we consider the two dimensional histograms for the actual returns and then under the assumption of normality - where the covariance is all the information we use.

Most of the time the two are closely clustered, the differences are in the tails and both are far from normal.

Full scale optimization allows us to explore the space of solutions without parametrizing the distribution of the returns. It just lets the returns themselves drive what part of the space we explore given the utility generated by a particular portfolio.

Quite understandably this is of interest to asset allocators and fund of funds as the returns to their real world problems are far from normal. Unfortunately you cannot brute force your way into solving this problem for more than two or three assets – the size of the solution space just blows up. It is too big to solve.