How do you compute the VaR for this problem:The position is you have 1/3 probability of gaining $1001/3 probability of gaining $201/3 probability of losing $30alpha is 1%my friend's answer is -$30, mine is $33 1/3...which is the correct answer?and if -30$ is correct, is it then always the smallest amount of gain (or largest amount of gain) among the choices regardless of probability?thanks. am kinda a newbie at this btw.

You want the 99% VaR (I take it the "alpha=1%", an expression I'm not familiar with, means the 99%)This means you'll lose less than this amount 99% of the time.In this example, the 99% falls in that bottom 1/3 so the answer is 30.

hey thanks for the help.yep, alpha = 1% means 99% VaRso I guess my friend is right then.What I want to understand is does that mean that the 99% VaR always coincide with the greatest amount of loss or least amount of gain, as long as the probability of that happening is greater than 1%?For example,I have probability of winning $1 ninety-eight percent of the time but losing $100 two percent of the time.so the 99% VaR is $100or another exampleI have probability of winning $100 ninety-nine percent of the time but winning $1 one percent of the time.so the 99% VaR is negative $1?Is my understanding correct?thanks again.

Sort of.The only problem with your examples is VaR is computed relative to your current mark-to-market. A position in which you can only make $100 or $1 implies that interest rates are at least 1% (and probably much higher) over the VaR period. VaR makes more sense computed over periods where the interest rate is negligible. VaR also makes more sense for continuous distributions. For example, if your gain will be selected from a uniform distribution from -$90 to +$110, the 1% point is -$88, so the 99% VaR is $88.

QuoteOriginally posted by: islandboyWhat I want to understand is does that mean that the 99% VaR always coincide with the greatest amount of loss or least amount of gain, as long as the probability of that happening is greater than 1%?yes

Aaron, ppauper,thanks for your help! cheers!