Periodic Value at Risk

Abstract

Many practitioners annualize VaR just like the standard deviation. We show that this approach is incorrect, and a more sophisticated formula should be used for deriving a periodic VaR from parameters of the daily returns distribution. Another problem addressed here is the distribution of daily and periodic returns and its effect on VaR. While a fat-tailed distribution is more appropriate for modeling daily returns, we show that using the log-normal distribution is still a reasonable choice for modeling periodic returns and calculating a periodic VaR for holding periods of one month and longer.