# Value at Risk

I just want to check whether: (a) the CBOK requires; and (b) the curriculum provides the method and assumptions for; the calculation of 10 per cent yearly VAR of a particular risk exposure given data on 1 per cent daily VAR of that risk exposure. I am unable to find anything in the curriculum so far.

Yes, it does. Take the daily data and turn that into annual, bing bang boom. Daily st dev x sqrt 250

Buddy, I wish it was that easy – the level of significance is changing.

level of significance only affects the number used - 1.645 vs. 1.96 vs. 2.33 an assumption they mention in the curriculum is that if expected return had a mean reverting value of 0 - you could just do it with the std. deviation. daily return std deviation = x annual return std deviation = x*sqrt(250). as blanders above has stated.

cpk123 Wrote: ------------------------------------------------------- > level of significance only affects the number used > - 1.645 vs. 1.96 vs. 2.33 > > an assumption they mention in the curriculum is > that if expected return had a mean reverting value > of 0 - you could just do it with the std. > deviation. > > daily return std deviation = x > annual return std deviation = x*sqrt(250). > > as blanders above has stated. +1.

I dont think they had any example similar to this…i would say this is pretty tricky

kh.asif Wrote: ------------------------------------------------------- > I dont think they had any example similar to > this…i would say this is pretty tricky Exactly – although I get the logic, I don’t think its intuitive. And where does it say about the mean reverting value? The curriculum has no examples or sample questions or blue box examples on anything similar. Quite tricky.

cpk123 Wrote: ------------------------------------------------------- > level of significance only affects the number used > - 1.645 vs. 1.96 vs. 2.33 > > an assumption they mention in the curriculum is > that if expected return had a mean reverting value > of 0 - you could just do it with the std. > deviation. > > daily return std deviation = x > annual return std deviation = x*sqrt(250). > > as blanders above has stated. +2 Not tricky.

Ok. My question to you guys saying its not tricky is – are you’ll drawing from you from the CBOK or practical experience or elsewhere? I studied the curriculum, did samples, mocks and what not – but haven’t come across a question like this at all.

CBOK…its actually in the Schweser stuff pretty explicitly. Z score doesnt change due to annual vs daily, it only changes due to significance. Just make sure your return is annual (or whatever youre looking for) and your st dev is annual (or whatever youre looking for) and the formula is the same.

it is a read between the lines thing in the curriculum on a particular left hand side page… that is all I remember … can look it up later when I have the textbook to provide with the reference. where it talks about the mean reverting value of 0, and also goes on to state in no uncertain terms that using a mean value of 0 - is a more CONSERVATIVE VAR estimate – since when you use a non-zero value - your VAR value will be a lower number. e.g. say mean = 10, stddev = 10, and 1% var 10 - 10(2.33) = -13.33 --> VAR of 13.33 if mean = 0 --> VAR = 23.33 – so you are more conservative

Well! If its in the schweser I should go bury myself.

cpk123 Wrote: ------------------------------------------------------- > level of significance only affects the number used > - 1.645 vs. 1.96 vs. 2.33 > > an assumption they mention in the curriculum is > that if expected return had a mean reverting value > of 0 - you could just do it with the std. > deviation. > > daily return std deviation = x > annual return std deviation = x*sqrt(250). > > as blanders above has stated. Thats what we do exactly for calculating VaR for our FX portfolio. We calculate the daily Std Dev, then multiply by 1.65 and 2.33 for 5% and 1 % daily VaR. For weekly VaR, multiply the prev result by sqrt 5.

L3 Book 5 (2011), pages 236-237

good thing that my common sense clicked worked in the exam…i guess all those school years where I checked the answer first and calculated backwards to do the math did help after all…

Thanks people, much appreciated. I hope there aren’t many more suprises that I’m in for.

don’t forget to multiply by the value of the portfolio in your VaR calculation.

The Z-score doesn’t change depending on timing of returns (e.g. annual, monthly, daily, etc…) because the z-score is a standardized number that tells the number of standard deviations away from the mean you would expect to go given a specific confidence level. Remeber the z-score assumes a normal distribution which means it assumes that regardless of what information you are evaluating that it can be described by the normal curve. Changing a z-score would mean you are no longer consistent with a normal distribution.

Straight from the CFAI book: With an expected return of 0.135, we move 1.65 stan- dard deviations along the x-axis in the direction of lower returns. Each stan- dard deviation is 0.244. Thus we would obtain 0.135 - 1.65(0.244) =-0.268.36 At this point, VAR could be expressed as a loss of 26.8 percent. We could say that there is a 5 percent chance that the portfolio will lose at least 26.8 percent in a year. It is also customary to express VAR in terms of the portfolio’s currency unit. Therefore, if the portfolio is worth \$50 million, we can express VAR as \$50,000,000(0.26= \$13.4 million. This figure is an annual VAR. If we prefer a daily VAR, we can adjust the expected return to its daily average of approximately 0.135/250 = 0.00054 and the standard deviation to its daily value of 0.244/(250)^.5= 0.01543, (Level III Volume 5 Alternative Investments, Risk Management, and the Application of Derivatives , 4th Edition. Pearson Learning Solutions p. 235). The book talks about a 2 week VAR, for that would you: divide by 26 and 26^.5 or figure 10 trading days in 2 weeks and divide by 25 and 25^.5 ?

250 trading days in a year, 10 days in two weeks so the latter if you are computing 2 week VaR from one year VaR.