# VAR

CFAI book 5 page 278 question # 9. I do not understand this problem at all. Looked at the solution-does not make any sense.

A: 1% yearly VaR is -40%. Since the loss greater than 50% has a probability of .005%, and -50% to -40% has a probability of 0.005%, to get the loss at the 0.01% level, start at the top of the table and add up the probabilities in order until you get 0.01. This is -40%. The rest should be straightforward (multiply portfolio value by -40%) For the 5% loss, do the same. Start at the first point, 0.005% probability of more than 50% loss. Add the probabilities until you hit 5%. This would be .005+.005+.01+.015 + .015 = .05. Now look to the left and read off the return which is -20% to -10%. Choose the higher of these (why: because the probability is 0.035 you’d have a -20% or greater loss, and .05% you’d have a loss greater than 10%). 10% of the portfolio is 0.1*\$10,000,000 If you want to test yourself, what is the 6.65% VaR? (I know it’s a weird number, but I have to work with the table given!) Then, what is the 11.65% VaR?

DoubleDip Wrote: ------------------------------------------------------- > A: 1% yearly VaR is -40%. Since the loss greater > than 50% has a probability of .005%, and -50% to > -40% has a probability of 0.005%, to get the loss > at the 0.01% level, start at the top of the table > and add up the probabilities in order until you > get 0.01. This is -40%. That’s the step I do not understand. In the table, third row from the top shows probability pf .01 and corresponding return is -40 to -30%- what does that mean? I’m lost there. The rest should be > straightforward (multiply portfolio value by > -40%) > > For the 5% loss, do the same. Start at the first > point, 0.005% probability of more than 50% loss. > Add the probabilities until you hit 5%. This > would be .005+.005+.01+.015 + .015 = .05. Now > look to the left and read off the return which is > -20% to -10%. Choose the higher of these (why: > because the probability is 0.035 you’d have a -20% > or greater loss, and .05% you’d have a loss > greater than 10%). 10% of the portfolio is > 0.1*\$10,000,000 > > If you want to test yourself, what is the 6.65% > VaR? (I know it’s a weird number, but I have to > work with the table given!) Then, what is the > 11.65% VaR?

It means that there is a 1% chance that the loss will be between -40 and -30%. But this is not the same as a 1% VaR. You have to look at cumulative probability. So, there is an 0.5% chance the loss will be more than 50%; a 1% chance the loss will be more than 40% (this is the 0.5% probability that the loss will be between 40% and 50%, PLUS the 0.5% probability that the loss will be greater than 50%); a 2% chance the loss will be more than 30% (this is the 1% chance the loss is between 30% and 40% PLUS the just-calculated 1% chance the loss is at greater than 40%); a 3.5% chance the loss will be more than 20%; (…) a 5% chance the loss will exceed 10%; … see what I am doing, just adding the probabilities.