# Controlling for factors that influence minimum variance optimization

I am trying to compare the performance of two minimum variance optimization (mvpo) methods applied on stocks Hierarchical risk parity (HRP) vs the analytical global minimum variance formula.

I feel like using naively chosen empirical data simulated data will affect the results in an unpredictable way. One of those factors is the magnitude of the covariance between assets, another is shocks to the stocks.

My question is if there is an accepted way of varying parameters like this in a simulation study where the covariance and mean matrix are manipulated. I am new to this field, so any specific research or part in a book would be appreciated.

• Hi and welcome. What do you mean with "performance"? Is that some in-sample / out-of-sample measure? Of what? If you want to run a 'clinical' study, you could indeed use simulated data and see how the parameters affect the optimal weights under both methods. If you want to test empirical performance, then you could separate your data in training and test data sets, and compare performance on both, no? – Kermittfrog Feb 12 at 12:00
• Thank you! I measure the out of sample variance (oov) for performance. I am using simulated data with a training and validation sample, the problem is that I want to change some characteristics in the sample to know what influences the oov. The reason for this is that I want to increase the validity of my study. Otherwise the results depends to much on my dataset. One example is that my covariance matrix has values that favour one method, while another covariance structure favours another. Hence I want to systematically increase/decrease the covariance and shocks to understand such effects – Lollorn Feb 13 at 15:40
• Then i would recommend using purely simulated data sets,no? – Kermittfrog Feb 13 at 17:10
• In the empirical case I would find datasets with the following qualities: High/low correlations/shocks. I wanna do this using a simulation, as I believe that it would be hard to interpret the data using empirical sets. For example, risk parity is said to work well during the 2008 crash/shock, but fail during the covid one. Hence I wanna create simulated data where I can vary the amount of shocks and correlations. My problem is that I don't know how to vary simulated data to reflect that properly. It is the implementation of shocks and dependence changes I don't know how to implement well. – Lollorn Feb 13 at 18:56