Reverse Optimization and Beta of an Asset Class


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!


One is theoretical and another is market observed. What you conveniently missed out is the Bayesian Correction. The optimizer cannot work let alone exploit any arbitrage opportunity if the bayesian corrected inputs are not fed into the model.

TY, HerbsDelite, but still the process of reverse optimizationnot is not completely clear for me.

I am going to dive deeper into google at this moment to come back with right questions. Obviously CFAI material has no good explanation of this matter.

Just watched the videos about optimization and reverse optimization on youtube from Phil Davies. He used two methods to estimate expected returns: averaging historical returns and applying CAPM using regressed Beta. Then MVO delivered two optimal portfolios with each method of expected return calculation (historical and CAPM w Beta).

The reverse-optimizationis used to come with new set of expected returns using global market portfolio weights. Betas (CAPM) in reverse-optimization method are not used. In the video it is only mentioned that expected returns received from reverse-optimization are very close to the expected returns received using CAPM and Betas.

So I still cannot understand in what context Betas are mentioned in the curriculum in reverse-optimization section !?


I refer to the Reading 13. Section 2.4.1 and Exhibit 12