This study pertains to forecasting portfolio risk using a GARCH (Generalized Autoregressive Conditional Heteroscedasticity) approach. Three models are compared to the GARCH model (1,1) i.e., random walk (RW), historical mean (HMM) and J.P. Morgans exponentially weighted moving average (EWMA). In recent years, many volatility forecasting models have been presented in the financial literature. Using the historical average of stock returns to determine the optimal portfolio is current practice in academic circles. However, we doubt the ability of this method to provide the best estimated portfolio variance. Moreover, an error in the estimated covariance matrix could result in a completely different portfolio mix. Consequently, we believe it would be relevant to examine the volatility forecasting model proposed in different studies to estimate the standard deviation of an efficient portfolio. With a view to building an efficient portfolio in an international context, we will analyze the forecasting models mentioned above. The purpose of this research is to determine whether a GARCH approach to forecasting the covariance matrix makes it possible to obtain a risk that most resembles the actual observed risk for a given return than the model traditionally used by practitioners and academic researchers. To this end, we selected six international stock indices. The study was conducted in a Canadian context and consequently, each stock index is converted into Canadian dollars. Initially, we estimate the covariance matrix for each forecasting model mentioned above. Then, we determine the proportions to invest in the portfolio and calculate the standard deviation of a minimum variance portfolio. Finally, the best model is selected based on the variances between estimated and actual risk by minimizing the root mean squared error (RMSE) for each forecasting model. Our results show that the GARCH (1,1) model is good for estimating risk in a minimum variance portfolio. As well, we find that it is statistically impossible to make a distinction between the accuracy of this model and the RW model. Lastly, our results show that based on the four statistical error measures used, the HMM is the least accurate for estimating portfolio risk. We therefore decided not to use this model and to rely instead on the GARCH approach or the RW, the simplest of all the models.
Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review
