Forecasting Value-at-Risk for equity returns with regime switching models

We use an univariate and multivariate Markov-Switching model to capture regime structures of three different equity returns. Besides a Markov-Switching approach, we use an endogenous regime switching model to capture the regime dynamics of equity returns. For each equity return we forecast the Value-at-Risk with a horizon of one month. We find that both Markov-Switching and endogenous regime switching models identify states with high volatility and a low intercept, and states with low volatility and a high intercept, except for the emerging market equity where no significant lower intercept is present in the high volatility state. Endogenous regime switching is present in developed market equity and private equity, indicating leverage effects in developed market equity and both leverage and trend following effects in private equity. Only the forecasts obtained from the multivariate Markov-Switching model pass the calibration backtests for all equities.