Question

Could you please explain this step by step? I do not understand how to calculate long end duration with the different prices?

What is long end duration? Calculate the long end duration for a bond with a current price of £109.5, if its price drops to £108.5 when the yield curve steepens at the long end by 50bps; and if its price increases to £112.2 when the yield curve flattens at the long end by 50bps. Interpret the value of the long-end duration obtained.

Answer 1

Long end duration is also termed as long duration which explains that bonds with higher duration are more sensitive to change in price in respect to change in interest rate. That means short duration bonds are less sensitive in comparison to bond with long duration.

In the given scenario we have given with two situation one is when the bond price decreases and yield curve rises, another is where bond price increases yield curve falls.

Bond Price and Interest Rate relation is explain

1. If bond price drop to 108.5 from 109.5, yield rises by 50 bps
2. If bond price increases to 112.2 from 109.5 , yield decline by 50 bps

This also explains that there is negative relationship between yield and bond price.

Bond Long Duration

(P_- - P₊) / 2P_{0 *} (change in i)

Where

P₊ = Bond Price when Yield Up = 108.5

P_- = Bond Price when Yield Down = 112.2

P₀ = Bond Price = 109.50

change in i = 50 bps =0.005

= 112.2 - 108.5 /(2* 109.5* 0.005) = 3.3790 or 3.38 (rounded off to 2)

Interpretation - There is difference between Bond duration and Bond Maturity. Bond maturity represents when bond will get mature but bond duration represents that how much it will take for an investor to get the return on investment. Bond duration represents the sensitivity to interest rate changes to the prices of bond and in given example it says bond is 3.38% sensitive to change in the interest rate.

I hope this helps, please let me know in case of any confusion. Thanks and have a good day.