VAR

The value at risk is the average minus (z x standard deviation), where z is the number of standard deviations from the normal distribution table. For a level of 95%, 50% will be above the average and 50% below. To have a 'cut-off' of 95%, then it means 50% above and 45% below. So we need a limit for the remaining 5%. So....you look in the tables for how many standard deviations give an answer of 5% (or 0.05). If you look, you will see that in fact it is somewhere between 1.64 and 1.65 std deviations. (It is difficult to explain in words - if you download the revision notes on here, then towards the end of them you will find a page on VaR where I have drawn a picture which should make sense of it) There is no formula for VaR (other that what I typed in the first line), and certainly no 'n' in it. I can only think that you are talking about the period for the standard deviation, but this depends on what period the question is asking for.

For VAR we first calculate. sd * square root of n ie the time period,do we take this time period in yrs or days?

That is not a VaR formula - it is the formula for converting the std devn for one time period to the std devn for another time period. (You may need to do this for VaR but only if the time period required is different than the time period given). n is not days or years! If you are converting a 6 month SD to a yearly SD you multiply by sq root of 2 (because there are 2 6-month periods in a year). If you are converting a 1 month SD to a yearly SD you multiply by sq root of 12 (because there are 12 1-month periods in a year) If you are converting a 2 month SD to a 6 month SD you multiply by sq root of 3 (because there are 3 2-month periods in 6 months) And so on.... :-)

Sir in the ot notes I went to the standard normal distribution table At 1.64 the value is 0.4495 And at 1.65 it is 0.4505 So how can i say its the value for a 5% level? Cz in the table the highest value is 0.4990 at 3.09 Pls help Thanks alot

Sorry - I wrote it wrongly. Because the cut-off is 5%, you are looking for 45% below the average. (Overall 50% is below the average, but with 5% cut-off that leaves 45%) So you are looking for an answer of 0.45.

Hello Tutor,

@johnmoffat said: If you are converting a 6 month SD to a yearly SD you multiply by sq root of 2 If you are converting a 1 month SD to a yearly SD you multiply by sq root of 12

I'm not clear on the above. Say for SD of 1.645: - converting a 6 month SD to a yearly SD = 1.645^(1/2) = 1.283 ? - converting a 1 month SD to a yearly SD = 1.645^(1/12) = 1.042 ? Thank you.

It is exactly as I wrote before, which is not what you have then written! To convert a six-month SD to a yearly SD: 1.645 x (sq root of 2) = 2.326 Converting 1 month to yearly: 1.645 x (sq root of 12) = 5.698

OIC, thanks for the clarification.

You are welcome :-)