Duration of assets and liabilities- Reading 14

[johntavv]

For reading 14, practice problem 8A, we have:

4yrs ago last year
Duration of assets 6yrs 6yrs
Estimated duration of liabilities 5.5yrs 4yrs
CFO says: the rapidly increasing popularity of our 2-year fixed rate product has increased our asset base substantially. we should take advantage by investing in higher yielding, investment-grade, longer duration bonds in order to maximise our spread and maintain a constant duration of the assets.
Answer says: as the duration of assets is held steady through the CFO’s urging to invest in higher-yielding, longer duration bonds, the duration of the liabilities will shrink.
With the duration of assets being held steady, why does the duration of liabilities shrink? Is it because adding a 2 year fixed rate product to a 4 year liability reduces overall duration of liabilities?

 

[S2000magician]

It’s a poorly worded answer, in my opinion: the answer makes it sound as though the steady duration of the assets is somehow causing the decrease in the liabilities’ duration, which isn’t the case.
As they sell more 2-year, fixed-rate bonds (whose duration is less than 2 years), the duration of their liabilities will get closer to that of the 2-year bonds; it’s higher than 2 years now, so it will decrease.

 

[johntavv]

With a 2-year, fixed rate bond, why is its duration less than 2 years?

 

[S2000magician]

The Macaulay duration of a 2-year zero-coupon bond is 2 years.
The higher the coupon, the shorter the duration, so a 2-year fixed-rate bond will have a Macaulay duration slightly less than 2 years.
And the modified duration of a bond is the Macaulay duration divided by (1 + r) where r is the YTM per coupon period; this will make the modified duration smaller still.
Here’s an article I wrote on this stuff: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-...