FMP - SWAPS

bks.gtb
Good Student
Posts: 13
Joined: Sat Apr 07, 2012 7:43 pm

FMP - SWAPS

In the below problem,i am not clear as to How duration has been arrived at as 7??

Hong Kong Shanghi Bank has entered into a repurchase agreement with a client where the client will sell a 10-year treasury bond to the bank and repurchase it in 10 days. The bond has a notional value of USD 10m, trades at par with the yield volatility for a 10- year treasury 0.074%. The swap’s maximum potential exposure at a 99% confidence level is closest to:
a. USD 1,200,000 Incorrect
b. USD 320,000 Incorrect
c. USD 380,000 Correct
d. USD 550,000 Incorrect
The correct answer is USD 380,000.

The approximate duration for a 10 year bond is 7.0. The volatility of the swap value over 10 years is calculated as follows: ? (V) = [market_value * duration * yield volatility *(10) 0.5 ] = 10,000,000 * 7.0 * 0.00074 * 3.16 = 163,806. To get the 99% confidence interval, we multiply ? (V) by 2.33, which gives approximately \$380,000.

Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

Re: FMP - SWAPS

Dear bks,

As written in qn, thsi is not swap, it is bond. In case of boond we calculate VaR in below fashion:

vaR = Market Value*Z*duration*bond yield volatility

The key thing in this qn is that duration in not given which we have to approximate. According to pristine approximate duration for coupon paying bond is 70% of term. But What I have seen is GARP old papers and bionic turtle i assuming it to be 80-90% of term.

So if you are solving it by taking duration as 70% (7) then the ans you will get is USD 380,000. But if you will take duration as 8 then it will be around 418,000. So in exam we have to calculate with both 70% and 80% to see what option is matching.

Hope it helps!

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

Re: FMP - SWAPS

Thats right Suresh.
Duration is inversely related to the interest rates. In countries where interest rates are very low (like 2-3%), you would take 80-90% of the maturity. Usually, I've seen most questions where yields are 5%-6% so 70% of maturity is a safe estimate.

Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

Re: FMP - SWAPS

Thanks Jyothi for throwing more light on that concept