Subject ST1, April 2014, Q5

[Shandz]

In the answer to this question one of the bullet points is:-

• Matching will be important if yields are expected to increase. If the duration of assets is greater than liabilities this would lead to a loss.

Why is would this lead to a loss?

Is this because for a bond, the price of the bond is inversely proportional to the yield? If the yield goes up the price will go down, because the price can be thought as the present value of all the future cashflows added together.

So for longer duration bonds the cashflows will go further into the future and so an increase the discount rate has a larger impact on the present value of the cashflows and therfore the price. Am I think along the right lines here?

 

[Robert Chadburn]

Yes, that's exactly right. You can also think of it in this way, using a simple example. Suppose we have a liability due in 1 year for 100. If current yields are, say 2%, then we could cover that with an asset worth 100/1.02 = 98.04 today.

Suppose the asset we use is a zero coupon bond maturing in 2 years time. To have the same PV as the liability that bond would pay 98.04 x 1.02^2 = 102 in 2 years time. So at current yields, the PV of the assets = PV liabilities, so all seems to be well.

Now suppose after 1 year, bond yields have increased to 3% pa. The insurer now has to pay the liability, which will cost it 100. To pay for it, it will have to sell the asset. The sale price of the asset will then be 102/1.03 = 99.03. And so the insurer makes a loss of 0.97 as a result.

Robert