Single equivalent discount rates

[almost_actuary]

Hello! I have probably a silly question but I haven't done this for a while...! I was wondering if someone could walk me through how to calculate a single equivalent discount rate by hand?

For example, if we take the first 5 years of the gilt curve as at 28 Feb 2019 (just for ease, but hoping this method extrapolates out for the whole curve!) how I would I calculate the single equivalent?

Year Gilt
1 0.771001
2 0.802474
3 0.856910
4 0.917013
5 0.974830


Thanks in advance!

 

[Hemant Rupani]

Just calculate value present value at start point and end point

Say duration is t

Single rate (end value/start value) ^(1/t)

 

[mugono]

Hello! I have probably a silly question but I haven't done this for a while...! I was wondering if someone could walk me through how to calculate a single equivalent discount rate by hand?

For example, if we take the first 5 years of the gilt curve as at 28 Feb 2019 (just for ease, but hoping this method extrapolates out for the whole curve!) how I would I calculate the single equivalent?

Year Gilt
1 0.771001
2 0.802474
3 0.856910
4 0.917013
5 0.974830


Thanks in advance!

You will need the cash flow amount and information on the coupon frequency.

To calculate the GRY, you will need to replace the gilt yield implied by the gilt curve you’ve provided with a constant interest rate.

The GRY is the yield that gets you back to the market value (the PV) of the 5 year gilt. This will need to be solved by trial and error.

Eg, PV = 130, and assuming annual coupon frequency.

GRY is the yield that satisfies:

130 = CF1 / (1+i) + ... + CF5 / (1+i)^5.

Any elementary book on bond valuation can give further details if required.

Hope that helps.

 

[almost_actuary]

Thanks both!