‘‘Reverse optimization takes as its inputs a set of asset allocation weights that are assumed to be optimal and, with the additional inputs of covariances and the risk aversion coefficient, solves for expected returns.’’

How does reverse optimization solve for expected returns? I mean, let’s assume that an 10% allocation to Emerging Market Equities (f.ex MSCI EMIM Index) is an ideal allocation. The index’s expected return is what it is, whether we use reverse optimization or not doesn’t really affect the expected return of the index?

The text says " It can be used to estimate expected returns for use in a forward-looking optimization. MVO solves for optimal asset weights based on expected returns, covariances, and a risk aversion coefficient. Based on predetermined inputs, an optimizer solves for the optimal asset allocation weights.As the name implies, reverse optimization works in the opposite direction. Reverse optimization takes as its inputs a set of asset allocation weights that are assumed to be optimal and, with the additional inputs of covariances and the risk aversion coefficient, solves for expected returns.".

I had a similar question and was at the same time tackling the problem set at the end of the chapter. I deem this part of a solution to be quite useful for the general understanding of the reverse optimization vs. MVO.