Hello

Is Beta of an Asset Class used during reverse-optimization process ?

According to curriculum:

“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.” and then

“…uses the weights associated with the asset classes to form a working version of the global market portfolio, and then uses the beta of each asset relative to our working version of the global market portfolio to infer what expected returns would be if all assets were priced by the CAPM according to their market beta”

If asset betas, risk-free rate and market risk premium are given then we can calculate E(Returns) using CAPM for each asset class, why would we need optimization process for solving for expected returns ?!

This statement may be a possible explanation but it is not clear for me:

“By using reverse optimization, we are consistently relating assets’ expected returns to their systematic risk. If there isn’t a consistent relationship between the expected return and systematic risk, the optimizer will see this inconsistency as an opportunity and seek to take advantage of the more attractive attributes.”

Please explain!

TIA