 # VAR definitions

Afternoon exam 1 Q17.2, Schweser: VAR: “a measure of maximum loss, in which (in your case) means we are 95% confident that the maximum 1-day loss is \$5m”. This answer says this is correct, but I think its wrong, or at least worded badly. To make my point, the statement above could be reworded equivolently: “95% of the time the maximum 1-day loss is \$5m”. But this assumes that there is a loss, ie the statement only seems to look at the lower half of the distribution of returns (the losses). It is (to me ) saying, “IF there is a 1-day loss, THEN it will not be worse than \$5m, 95% of the time”, which is of course wrong. I see VAR (in this case) as: 5% of the time we expect to lose at least \$5m, or 95% of the time we will do better than losing \$5m. Am I missing something here?

the wording is correct. watch how they show the percentages. in this case the MAX loss one can exect is \$5mln meaning hte loss will be SMALLER than \$5mln 95% of the time. (the right hand part of the normal curve) also a correct statement would have been the expected MINIMUM one day loss would be \$5mln 5% of the time (ie. the left hand part of the tail)

Check out bottom of page 25/ top of 26 on V5 CFAI readings… they have an example of this - CONFUSING and TRICKY…

this is how I remember these max/min things. ----- You have the bell shape distribution of your portfolio returns — r%, sigma%, right? Let’s say they are r=5%, sigma = (15/2.33)%, portfolio = \$100. That means if you go along x-axis to the left, you can reach returns as low as 4%, 3%, …0%, and most importantly, -1%, -2%, …, -10%, … negative infinity Those -ve returns on the far left part of the x-axis are what people concern, and what VAR wants to describe: How bad can your portfolio be? Now if r turns out to be -10%, then you LOSE \$100 x 10% = \$10. You say: How often can shxt like this happen? The answer is the area of the bell shape to the LEFT of x = -10%. Those are all having returns = or even worse than -10%. If that area is 0.01, you have 1% VAR of \$10, meaning you have 0.01 chance of MINIMUM LOSS of \$10 (since those returns in that little area are all worse than -10%). If you look at that the other way round, you can say hey I have 99% confidence that my return is on the RIGHT side of that bloody -10%, so I have 99% confidence that my MAXIMUM LOSS is just that \$10 in the far left. Making sense? My example is exactly the case when r=5%, sigma = (15/2.33)%, portfolio = \$100. Note that z = -2.33 for 1% significance Hope this helps. - sticky

I dont think you guys are getting what im saying. I’ve got a degree in mathematics, Im not confused by var itself. Just their wording. Put it this way, spot the difference below: a) “95% confident that the maximum one day loss is \$5m” b) “95% confident that the worst one day result is \$5m” Get it? (a) assumes that there IS a loss, (b) does not !!

when you calculate VaR, you get a number + if the number is 5, this means you will not lose more than 5 in 95% of the times + if the number is -5, this means you will earn 5 (negative VaR) in 95% of the times if, when calculating var, in this example, it comes out that VaR = 5, you know that in 5% of the times there will be a loss, and actually a loss equal to 5 (or a higher loss) I mean, forget about reasoning. you will get the number, which can be a loss (usually) or a minimum gain (in cases where VaR is negative, which I guess it is rare)

sorry that I did not read your post thoroughly. Stupid I wrote such a long post of crap elem100 Wrote: ------------------------------------------------------- > Afternoon exam 1 Q17.2, Schweser: > > VAR: “a measure of maximum loss, in which (in your > case) means we are 95% confident that the maximum > 1-day loss is \$5m”. > > This answer says this is correct, but I think its > wrong, or at least worded badly. > > To make my point, the statement above could be > reworded equivolently: > > “95% of the time the maximum 1-day loss is \$5m”. > > But this assumes that there is a loss, ie the > statement only seems to look at the lower half of > the distribution of returns (the losses). It is > (to me ) saying, “IF there is a 1-day loss, THEN > it will not be worse than \$5m, 95% of the time”, > which is of course wrong. I think the “commonly accepted” wording (like this from Schweser) is taking a loose interpretation instead of your detailed one. I don’t see any IF condition with the description of the loss. It’s just trying to describe how much you are expected to lose/gain, over an confidence level. > I see VAR (in this case) as: > > 5% of the time we expect to lose at least \$5m, or > 95% of the time we will do better than losing > \$5m. Doesn’t make much difference and looks equally correct to me. > Am I missing something here? no. I think you are just thinking too much, and too much logics in your mind - sticky

a) does not assume a LOSS…it says that the max loss is \$5mln. That can mean a gain of \$1, \$10, \$100 as well. Its simply saying that should a loss occur, the max loss is \$5mln. you’re reading too deep into VAR.