Katmai Co (12/09) – part (c) VAR

All you need to learn is that at 95% confidence level, it is 1.64 standard deviations ( because 1.64 in the tables gives an answer of 0.45 (which is 0.95 – 0.5)
At 99% confidence level it is 2.58 SD’s (because 0.99 – 0.5 = 0.49; 2.58 gives an answer of 0.49 from the tables)

Also, you cannot add SD’s – you add the squares of them and then take the square root.

So……if for example the monthly deviation is X and the yearly deviation is Y, then Y^2 = 12 x X^2

( for more explanation see the page in the revision notes on this website)

In theory it could be any confidence level, but the only ones we ever normally look at are 95% or 99%. (But once you understand you could do it for any confidence level, however unlikely).

First you subtract 50% from the confidence level. So at 95%, 95 – 50 = 45%
Then you restate as a decimal/ So 45% becomes 0.45
Then you look in the tables to see which number of standard deviations gives an answer of 0.45.

If you look in the tables, 1.64 gives an answer of 0.4495 and 1.65 gives an answer of 1.4505.
So the answer is actually somewhere between 1.64 and 1.65 std deviations. (1.64 is close enough for the exam)

150 basis points (or 1.5%) is not LIBOR but is the annual volatility of LIBOR and is therefore the annual standard deviation.
To arrive at the six-monthly standard deviation we multiply by the square root of 1/2 as explained in my free lectures on this.