Forecasting Value-at-Risk under Temporal and Portfolio Aggregation

We examine the impact of temporal and portfolio aggregation on the quality of Value-at-Risk (VaR) forecasts over a horizon of ten trading days for a well-diversified portfolio of stocks, bonds and alternative investments. The VaR forecasts are constructed based on daily, weekly or biweekly returns of all constituent assets separately, gathered into portfolios based on asset class, or into a single portfolio. We compare the impact of aggregation to that of choosing a model for the conditional volatilities and correlations, the distribution for the innovations and the method of forecast construction. We find that the degree of temporal aggregation is most important. Daily returns form the best basis for VaR forecasts. Modelling the portfolio at the asset or asset class level works better than complete portfolio aggregation, but differences are smaller. The differences from the model, distribution and forecast choices are also smaller compared to temporal aggregation.