Volatility Forecasting in Bull & Bear Markets

Abstract

This thesis considers the performance of variance forecasting in bull and bear markets. Three asset indices, the DAX, the Standard & Poor’s 500 and the CurrencyShares Euro Trust, are split into bull and bear periods whereby variance forecasting is evaluated in the two states. I employ a simple moving average, an EWMA, implied volatilities from official volatility indices and three GARCH specifications; a GARCH (1,1) and EGARCH(1,1) with Student’s t errors and a GARCH (1,1) with Hansen’s skewed t errors. I compute 30 days ahead variance forecasts using daily data and the true latent variance is approximated by the intra-month realized variance. Performance is measured by the R2 from regressing the realized variance on the estimated variance, the QLIKE statistic and the MSE. I find that implied volatilities forecast best in bull markets and that the GARCH and EGARCH forecast best in bear markets. In general, the predictions’ R2 and QLIKE statistics suffer 30 % - 50 % in bear markets and the MSE is as much as 15 times higher compared to bull markets.