robust optimization as a result of the global financial crisis of 2008 asset managers have placed greater emphasis on managing portfolio uncertainty in extreme times. What many call tail risk tail risk arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution.

To build resilient portfolios Central return assumptions and other variables are not enough on their own. We need to assess an account for the uncertainty around these assumptions used in mean variants optimization after all every portfolio decision faces two sources of risk, not one the risks inherent in markets and securities and the risks of being wrong in our expectations.

So what is robust optimization given that mean variance optimization is highly sensitive to inputs. And the fact that those inputs are very difficult to estimate in many cases. It is easy to see how this would make it difficult to determine optimal portfolios, especially in times of stress like the financial crisis. In other words, the mvo model needs to be very accurately estimated to be effective. However, estimating is very difficult, like black litterman robust optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean variance framework that is prone to what we call estimation error recognizing this inherent uncertainty in the variable expectations allows investors to create portfolios that are more aware of the downside risks typically robust optimization focuses on the variations and estimation errors of covariance and correlations and expected returns of Assets in various.

Environments the goal is to produce stable asset allocation Solutions regardless of the market environment meaning portfolios with a lower turnover rate and suitable for long-term planning.

Mvo focuses on simple mean or average estimates that may not hold during Market stress or crisis like having one foot and freezing water and one foot in boiling water and on average feeling fine, but obviously there's a lot of pain overall similarly recessions and or Market crisis are binary not average outcomes. They will or will not happen.

Therefore the point estimates of traditional mvo overstate the confidence any investor can have in the outlook for asset returns.

Ro on the other hand is not a point estimate. It uses uncertainty tests for variables that try to contain all or most of their possible realizations.

It tries to offer in entire range of potential return paths across asset classes and factors allowing for a fuller picture of uncertainty inherent within those expectations.

Ro incorporates variable estimation risk into these uncertainty sets and improves on mean variance analysis by directly incorporating the uncertainty inherent in our estimates in other words the likelihood of estimates being wrong and by what degree the process in a fine-tuned way helps address tail Risk by attempting to determine the highest possible potential returns under negative scenarios. This Fuller array of information can help investors limit the impact of potential drawdowns in portfolios. It should be noted. However that there are interpretations of Ro that lead to different mathematical formulations and definitions of robustness in other contexts.

To summarize in Broad terms Ro effectively adds an additional step to traditional mvo by incorporating potential distributions of expectations or estimation error these ultimately dictate an efficient Frontier and optimal portfolio allowing for it to see improved performance in uncertain conditions dealing rigorously with that estimation error is a critical step in the use of robust portfolio optimization.