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I am currently trying to carry out a mean variance optimisation, with the implementation of GARCH. I'm not sure if this is going to make complete sense as my understanding of GARCH is limited.

In the past whenever I have carried out mean variance optimisation (under Markowitz) I have calculated the expected returns, created a var-covar matrix and maximised the Sharpe Ratio [(Er-rf)/St.dev^2].

Currently, instead of carrying this out as usual, a friend who works in risk management suggested that I look at GARCH models to more accurate model volatility to account for clustering.

My question is what changes do I have to make to my mean variance optimisation for this to work? Can I take the variance outputs for each asset and run the var-covar matrix as normal and then maximise sharpe or do I have to continue to make further changes for the optimisation to actually make sense? I have read in some places that to create covariance matrix's for GARCH its best to run multivariate models.

Any help would be hugely appreciated:)

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  • $\begingroup$ What do you mean by take the variance outputs for each asset and run the var-covar matrix as normal? It could indeed make sense to use a multivariate version of GARCH such as DCC (but there are several alternatives). $\endgroup$
    – Richard Hardy
    Commented Apr 16 at 6:40
  • $\begingroup$ I guess my question is can I use the outputs produced from a GARCH model to create a covariance matrix that can be further used for portfolio optimisation. If I use a DCC, what would the steps be to get to a point where I can carry out mean variance optimisation? $\endgroup$
    – FraserM2000
    Commented Apr 16 at 13:18
  • $\begingroup$ DCC produces the variance matrix, so you can enter it directly as an argument into mean-variance optimization. Individual GARCH models do not produce the variance matrix; taken together, they only produce its diagonal. $\endgroup$
    – Richard Hardy
    Commented Apr 16 at 13:30

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