This paper uses daily and weekly exchange rate data to test if there is significantly different in estimating the variances of exchange rates. This issue is important for computing the value at risk (VAR) because estimated variances are often the input for VAR computation. Under the assumption that the exchange rate follows geometric Brownian motion, that is, the exchange rate follows a lognormal distribution and there is no autocorrelation, the variances estimated from different data frequencies shouldn't be significantly different after adjusting the square root of time. However, this doesn't have to be true if the assumption violated. By examining daily and weekly Taiwan dollar-US dollar (NT/US) and daily Euro-US dollar (Euro/US) data from January 2003 to December 2008 by the variance ratio tests, the results show there is significantly different for daily NT/US exchange rates, but no significant difference for other exchange rate data. As the variance or standard deviation is often used for the estimation of value at risk, it implies the daily NT/US is not appropriate for the 10-day VAR calculation. However, such problem doesn't show up for the weekly NT/US exchange rates or daily Euro/US exchange rates.