## Swap

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

### Swap

Pls explain

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?

sreeram.jyothi
Posts: 6
Joined: Sat Apr 14, 2012 10:00 am

### Re: Swap

Hi Suresh,

First of all, this question seems to have a typo. Rather than 'swap', the question should say 'bond'.
To tackle this question, you just need to use the "classical" VaR formula
As you know, duration would be the best way to measure the risk of a bond.
The approximate duration for a 10 year bond, taking many assumptions about coupon and interest rates, would be approximately 7.0 years.
The volatility of the swap value over 10 years is calculated as follows:
(V)(99%) = Z* [market_value * duration * yield volatility *(10)^ 0.5 ]
= 2.33 * 10,000,000 * 7.0 * 0.00074 * 3.16
= approx 380,000

Hope this helps

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

### Re: Swap

Dear jyothi,

can you pls explain how have you calculated the approximate duration of the 10 year bond? Is there any shortcut to calculate the approximate duration of a bond?

sreeram.jyothi
Posts: 6
Joined: Sat Apr 14, 2012 10:00 am

### Re: Swap

Hi Suresh,

To find the exact duration of a bond, you can use the excel functions, DURATION and MDURATION. Duration depends mostly on maturity, but also depends on coupon and the current interest rate and coupon frequency. The higher the coupon, the more the frequency, the lower the duration.
If the coupon is high, say 12% per annum, we can see that duration is 6 years, and of course a zero coupon bond has a duration of 10 years

Hope this helps

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

### Re: Swap

Dear Jyothi,

Sorry but its not helping me. What you are telling that I know. I know if coupon, frequency, and no of years is given how to calculate duration.

M asking for the above question where only no of years is given and we have to calculate VaR using delta normal method. Here u know that approximate duration of 10 yr bond is 7 years cuz of experience. But lets say no of years is 20, 25 or 17 years and no coupon is given then how will I approximate?

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

### Re: Swap

Suresh,

If nothing is given, take the duration as 70%-80% of the maturity. The 4 solution options should be relatively far so you don't need to worry. But just ensure you dont take it as 100% of the maturity for a coupon bond

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

### Re: Swap

Dear Content pristine,

Thanks a lot for your revert. I was expecting this type of ans only so that in exam I can calculate the duration approximately.