Direct versus iterated multiperiod Value‐at‐Risk forecasts

Abstract

Since the late nineties, the Basel Accords require financial institutions to measure their financial risk by reporting daily predictions of Value at Risk (VaR) based on 10‐day returns. However, a vast part of the related literature deals with VaR predictions based on one‐period returns. Given its relevance for practitioners, in this paper, we survey the literature on available procedures to estimate VaR over an h‐period. First, to convert 1 day into 10‐day VaR, it is popular to use the square‐root‐of‐time (SRoT) rule, which is only satisfied under very restrictive and unrealistic properties of returns. Alternatively, direct (based on h‐period returns) and iterated (based on one‐period returns) two‐step procedures can be implemented to obtain 10‐period VaR. We also illustrate and compare the performance of these procedures in the context of popular conditionally heteroscedastic models for returns using both simulated and real data. We show that, under realistic assumptions on the distribution of returns, multiperiod VaR predictions based on iterating an asymmetric GJR model with normal or bootstrapped errors are usually preferred. We also show that, in general, direct methods could be not only biased but also inefficient.