# Daily VAR

Simple question but im struggling to get a handle on this:

A single government bond has a current market value of \$1,000 and duration of 0.62. The daily standard deviation associated with such bods is 0.32% and the current yield is 13%. The time until the risk associated with the bond is eliminated is 25 days. The standardized value from a normal distribution associated with the target probability is 1.65. What is the Var?

What’s the answer? I calculated 13 cents.

I’m curious how you got your answer of 13 cents. The amount seems too small relative to the SD given. the SD for your yield is at .32%, meaning that if you move down only 1SD from the current yield of 13%, you will earn a return of about 12.68% and this will impact the price of the bond by more than 13cents given the duration of .62.

I honestly don’t really know what would be a correct solution to this question, but here is my try:

Daily SD=.32%. SD for the 25 day period of risk exposure=.32*sqrt(25)=1.6%

VAR=change in the current yield. VAR=1.65*1.75=2.64. Basically, over the next 25 days we have a 5% chance of a yield decrease of 2.64.

Now we use effective duration formula

%PriceChange=Effective Duraiton * %Yield Differential (ie. VAR)

%PriceChange=.62*2.64%=1.643%

So over the next 25 days, our 5% VAR in dollars is 1000*(.01643)=16.43 dollars

I found this question to be tough, since it puts together some of FI material and my frame when approaching its solution was to ignore duration value initially. Where did you find it?

^i’m actually not sure where I calculated the .13, feel like I wrote the 13% current yield rather than what I had calculated.

I calculated \$1.13 by using the coupon as the return in question (13%/360*25) = (.009028 - 2.64%) * \$65 = ~\$1.13

I was thinking that the return would be from the next coupon due (\$65)- seeing now the next coupon is about 45 days away based on the duration of 62 which is out of the range of ‘risk’ the question provides.

VAR = 1.65 * 0.32% * 1000 * 13% = 0.69

Galli, I understand your approach, but I think that yield changes impact not only the value of your coupon but your overall bond value.

cpk, why do you multiply by 13%? also yield changes affect the value of your bond relative to the duration of your bond. It seem to me that duration should play a role in the calculation of a bond’s market value.

not sure if the VAR was for Bond Market value or for the Daily Yield of bond…

Not sure really if anything I wrote is even relevant. But I think the OP’s question is poorly worded.

Im not sure where I got the question – I think is one of the old past mock or exam. And I don’t think this is relevant to thecurrent curriculum anymore.

Anyway the answer says you can calculate VAR from duration and the workings are:

Daily VAR = Market value x Duration x % change in yields

Worst change in yields = 1.65 x 13% x 0.32% = 0.000686

25 day VAR = 1,000 x 0.62 x 0.000686 x 25^0.5 x 25^0.5 = \$2.13

damn, this solution makes no sense

i applied the same formula and approach from the link you provided and it still doesn’t make sense. I even tried using just a straight up daily VAR calculation and ignored the 25 period, just to see if I would get matching solutions, and nothing came out of it. notice how you divide by 1.13 using the approach from the link, while in broadex’s solution there is nothing of this sort. i keep getting different solutions using these two approaches.

can you solve it?