NON-LINEAR SHRINKAGE AND MULTIVARIATE GARCH: AN EMPIRICAL ASSESSMENT OF CRYPTOCURRENCY'S POSITION IN PORTFOLIO OPTIMIZATION

Abstract

This paper considers the cryptocurrency market and evaluates whether the inclusion of cryptocurrencies improves the performance of portfolios containing S&P100 and S&P500 stocks. This paper differentiates itself from existing literature on portfolio allocation with cryptocurrency because it is the first, to my knowledge, to apply modern methods for high dimensional covariance matrix estimation in this context. This study applies non-linear shrinkage and composite likelihood to enable estimation of high imensional conditional covariance matrices via popular DCC and BEKK models for portfolio weight construction. These methods address issues such as invertibility under high concentration ratios with the sample covariance matrix estimator and improve on existing multivariate GARCH models. An additional contribution of this study involves analysing the performance of scalar BEKK with non-linear shrinkage, which has only been suggested, but not yet applied in existing literature. The findings suggest that the inclusion of cryptocurrencies and use of non-linear shrinkage improves portfolio performance.