Asset allocation: A multivariate GARCH approach

Michael Hartung Mortensen

Student thesis: Master thesis


The purpose of this thesis is to investigate if a proactive portfolio strategy, whose asset weights depend on a covariance matrix forecasted by a multivariate generalized autoregressive conditional heteroscedasticity (M-GARCH) model, outperform a simple portfolio strategy, whose asset weights depend on a covariance matrix forecasted by a simple moving average model. The estimated covariance matrixes will be the starting point when designing the global minimum variance portfolio (GMVP). This specific portfolio will be the basic point for the comparison between the two portfolio strategies. As a standard procedure the two portfolios will be compared relative to a benchmark index. The two portfolio strategies are illustrated using the assets: MSCI Europe Index, MSCI Americas Index, and MSCI Pacific Index. MSCI World Index represents the benchmark index. In this thesis the diagonal BEKK model (DBEKK), will represents the multivariate approach, which is a restricted version of the full BEKK model. The simple moving average model is a simple average of the last 60 observations. The study concludes that the proactive portfolio strategy performs better than the simple portfolio strategy and also outperforms the benchmark index on the risk measures: standard deviation, value at risk, and expected shortfall. The proactive portfolio strategy also performs better in terms of pure return and the return-risk measures: treynor ratio, sharpe ratio, and information ratio. This leads to the unambiguous conclusion that the proactive portfolio strategy in all measures outperforms the simple portfolio strategy. A major weakness of the D-BEKK model is that the number of parameters to be estimated rise sharply as the dimensions of the model increases, which is often referred to as “the curse of dimensionality”, causing the model to be used only in a limited universe. This undoubtedly narrows the field of potential users. However, portfolio mangers who only care about a few asset classes or who is responsible for the overall strategic asset allocation may benefit from the obtained results. The D-BEKK model is a restrictive version of the full BEKK model, and as a consequence fails to recognize and include the volatility spillover from other asset classes. The D-BEKK model is only able to model the elements in the covariance matrix based on it´s own lags. This can be critical because many studies seem to agree that there is significant volatility spillover between asset classes. This indicates that there may be more to be gained by using a MGARCH model that also takes this phenomenon into account

EducationsMSc in Finance and Accounting, (Graduate Programme) Final Thesis
Publication date2011
Number of pages90