btw i believe CFAI 2005 exams thinks VAR is a probability too, with which i disagree 
VAR is a money amount (e.g. a dollar number) of percentage of portfolio associated with a probability and a specific time horizon. The dollar number is meaningless if the latter two are not specified. Definition 1: VAR is an estimate of the expected loss that would be exceeded with a given probability over a specified time period. Definition 2: VAR is an estimate of the maximum loss at a given confidence level over a specified time period. Thus a VAR of $1MM with probability of 5% over 1 year means that loss will exceed $1MM 5% of the time over one year. Or, alternatively, the maximum value of loss would be 1MM 95% of the time. The Variance-Covariance method of calculating VAR requires normality of returns distribution. The historical method and the Monte Carlo method do not. VAR for two portfolios are additive if the correlation between their return is one. For any other value, the combined VAR is less than the sum. I wrote all of the above to just make sure I remember it. I can see how one can twist the above definition to make VAR a probability, but then what is to prevent us from making VAR a time period! E.g. VAR is the time period over which the loss of 1MM is exceeded with a probability of 5%!@#%
Agree with strikershark and CFAAtlanta VAR is given as a dollar measure with a probaility associated with it; without assuming a probability and underlying distribution you won’t be able to calculate it if you are using variance/covariance method, normality has to be assumed, in this case X% VAR = mean§ - z-value * Std§ z-value is coming from standard normal distribution table (i.e., 1.65 for 5% level of significance, 2.33 for 1% level of significance) Lower lefel of significance (i.e., 0.01 vs. 0.05), means higher confidence level or probability that the loss won’t exceed VAR (99% vs 95%), means higher VAR in dollar terms, because z-value is higher when level of signifcance is lower You will say that there is a 1% chance that the loss will exceed $10M vs. a 5% chance that the loss will exceed $7M or 99% chance that the loss won’t exceed $10M and 95% chance that the loss won’t exceed $7M