Creating Optimal Portfolios of Stocks with Time- Varying Risk: Using a Multivariate GARCH Approach

Jan Emil Weirum & Christopher Elgaard Jensen

Student thesis: Master thesis


In this thesis we analyze monthly historical stock returns data on 10 industries, to examine if the presence of time-varying risk is seen in real data and how it affects the construction of optimal portfolios, more specifically the calculations of asset-weights in optimal portfolios. We believe that taking this conditional asset-risk into consideration, we might be able to get better results with optimization methods that usually assumes constant correlation and uses a mean-variance approach. Through testing we find indications of an autoregressive conditional heteroskedastic process in all 10 series of returns. We construct a multivariate generalized autoregressive conditional heteroskedastic model, called multivariate GARCH, in order to model the time-varying risk of the assets as conditional covariance-matrices of our data-series. Over time there are significant variations in the conditional risks, meaning that using generalized historical means as a measure of today’s risk and/or expected returns is an over-simplified and possibly flawed approach. We find that our data can be modeled by a multivariate GARCH(1,1) model, and using statistical software packages we can compute and estimate the parameters of this model, in matrix-form which is necessary for the multivariate model. We will also be able to compute the conditional covariance-matrices and error-terms for every sample-period. Given the time-varying risk the GARCH model only allows us to do a single-period forecast into the future, so we will apply Monte Carlo Simulation in order to forecast multiple-periods ahead. We will then use the mean-variance optimization techniques from the Modern Portfolio Theory to compute Global Minimum Variance portfolios. We will present investment strategies that do monthly rebalancing of our portfolio, minimizing the conditional-risk in every month as found by Monte Carlo Simulations, and by applying the GARCH-model at ultimo a given month. We will suggest such an investment-strategy for periods of six consecutive months, and compare our results to portfolios constructed with simple mean-variance optimization. We will test the performance of these different types of strategies and find indications that the time-varying risk approach, seems to create better performing portfolios than the mean-variance optimization.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2013
Number of pages133