Relationship between interest rates and annuity rates

[Harashima Senju]

Hi

I'm struggling to understand the relationship between interest rates and annuity rates. In the online classroom, a question on why new business for annuity products has decreased.

The solution mentions that

• low interest rates would correspond to lower bond yields (bond yield = coupons/bond price)
• lower bond yields result in less attractive annuity rates

I can't quite understand the link between bond yields and annuity rates.

 

[Carmen]

Hi

I would think that usually the annuity payment is backed with bonds of similar duration (good match in timing as annuity payments and bond coupons are regularly paid out). Hence, the coupons from the bonds can be used to cover the annuity payments. This is where the link between bond yields and annuity rates comes into play, i.e. whatever the bond yield is would determine the annuity rates.

If interest rates drop, it would mean that there is lower discounting on the coupons, leading to higher present value of those coupons. Higher present value then corresponds to higher price of the bonds. This would lead to the yield of the bonds to drop as you've mentioned "bond yield = coupons/bond price".

Considering that the annuity is supported by bonds, since lower interest rates leads to lower bond yields, this would mean the annuity rates would be lower. A potential customer would then view the annuity product as undesirable and look for other options instead.

Hope my understanding is correct and help clarifies, else would appreciate any feedback if the above is not how there is a link between bond yields and annuity rates.

 

[Harashima Senju]

Hi

I would think that usually the annuity payment is backed with bonds of similar duration (good match in timing as annuity payments and bond coupons are regularly paid out). Hence, the coupons from the bonds can be used to cover the annuity payments. This is where the link between bond yields and annuity rates comes into play, i.e. whatever the bond yield is would determine the annuity rates.

If interest rates drop, it would mean that there is lower discounting on the coupons, leading to higher present value of those coupons. Higher present value then corresponds to higher price of the bonds. This would lead to the yield of the bonds to drop as you've mentioned "bond yield = coupons/bond price".

Considering that the annuity is supported by bonds, since lower interest rates leads to lower bond yields, this would mean the annuity rates would be lower. A potential customer would then view the annuity product as undesirable and look for other options instead.

Hope my understanding is correct and help clarifies, else would appreciate any feedback if the above is not how there is a link between bond yields and annuity rates.

thanks that makes sense

 

[James Nunn]

Hi

Thanks for your question Harashima and thanks for your answer Carmen. Carmen wanted confirmation that the stated bond yield / annuity rate linkage argument was correct and it is. To summarise:

1. Bonds are a good match for annuities so annuity providers will hold these to back annuity liabilities
2. Any decrease to bond yields would therefore reduce money available to annuity providers to pay annuities and higher premiums (or lower annuity rates) would be needed to cover the difference.

The second point is a slightly different way of looking at it but the argument that discount rates will follow bond yield movements is also correct.

I think the link between interest rates and bond yields is understood but this can be explained by the Expectations Theory as covered in Chapter 11 (Behaviour of the markets).