# Calculating IR sensitivity

I'm trying to figure out how to find IR sensitivity of a bond whose time to maturity of a bond is 2 years. Bond pays 10.875 percent coupons yearly. Duration is 1.8 years.

How do you find the interest rate elasticity of the bond price?

• Do you mean that you want to find the change in price for a 1bp move in interest rates? – JoshK May 23 '16 at 13:45
• @JoshK: the price elasticity with respect to changes in 1 + YTM – user20847 May 23 '16 at 17:49
• Please let your accounts be merged. – Bob Jansen May 23 '16 at 18:45
• I believe you mean convexity of the bond? – Dendi Suhubdy May 23 '16 at 20:26

Ok, so I think you are just asking what is the dv01 of the bond. So if the yield goes up one bp what's the new price? And if it goes down, what's the new price? That's the simple way that people look at it. For a bond that can't be called or converted in any way it's pretty easy. Let's assume that's what you have.

Here's the process:

1. So first you need to find out what is the current price of that bond. You need to get that from somewhere this is based on a certain settlement date, so make sure you get that as well or your price is not too meaningful.
2. Decide what yield convention you want to use. ACT/ACT? Yields only mean something in contex of a convention. If I tell you that you are going 55 on the freeway you need to know if we are talking kph/mph/knotts, etc.
3. Figure out the yield that is implied at the current price.
4. Add a bp to the yield and compute what the new price would be.
5. Take off a bp from the yield and compute the new price.

Do you know how to calculate the yield from price and price from yield? You can do it in Excel or Bloomberg or program it yourself. I'm sure there are lots of posts here explaining how to do a Newtonian expansion if you really want to code it up yourself. I have some old code I could post if you really can't find that.

Good luck.

Adding a few notes to answer the follow up question. When you are being asked about sensitivity to "1+YTM" they mean what is what is the "dv01", or the dollar value of a .01 move in rates.

The idea of convexity just means that a .01 bp change in rate might change your price .10 cents at yield X and a .01 bp change in rate might change your price .20 cents and yield Y. The change in price is not a linear response to change in rate.

You have to know your settlement date and the current price to determine a yield. Then once you know the yield you can bump it up and down and see the price impact. I think you can see this intuitively in the extremes. Imagine if a $10 coupon note with$100 par can be bot for \$100 for settle the day before it matures. That would be a very high yield (by any convention). Then imagine if you change the price slightly you would greatly change the yield.