April 2010 Q1(iv)

[st2_taker]

Hi,

This question is regarding the impact of working capital that has reduced more than expected. Particularly due to the fact that Assets (backing the liabilities) and Liabilities that may not move exactly in line with each other.

One of the point stated that:

"risk free rates might have decreased, which is likely given the fall in
yields; this would also increase the value of the guarantees particularly
if the term of the liabilities is longer than the term of the assets"

May I know how to put this in the context of numerical examples?

Why would a decrease in risk free rates will cause the Liabilities > Assets , when the liab term is longer than asset term?

Thanks.

 

[Mark Willder]

This question is regarding the impact of working capital that has reduced more than expected. Particularly due to the fact that Assets (backing the liabilities) and Liabilities that may not move exactly in line with each other.

One of the point stated that:

"risk free rates might have decreased, which is likely given the fall in
yields; this would also increase the value of the guarantees particularly
if the term of the liabilities is longer than the term of the assets"

May I know how to put this in the context of numerical examples?

Why would a decrease in risk free rates will cause the Liabilities > Assets , when the liab term is longer than asset term?

A fall in the risk free rate will cause assets and liabities to rise in value. The liabilities are longer than the assets, so the impact of discounting is more pronounced, and the liabities rise faster than the assets.

Consider the following numerical example. An insurer has a liability of 100 in 10 years time. The risk free rate is 4%, so the value of liabilities is 67.56.

The insurer invests in a zero coupon bond paying 92.46 in 8 years time. This also has value of 67.56 at 4% interest.

Now the risk free rate decreases to 3.5%. The liabilities go up to 70.89, but the assets only go up to 70.22.

Best wishes

Mark