Question

1. A savings bank’s weighted average asset duration is 7 years. Its total liabilities amount to $900 million, while its assets total $1 billion.
   1. What is the dollar-weighted duration of the bank’s liability portfolio if it has zero leverage adjusted duration gap?  
   2. Does zero duration gap mean the bank has hedged the interest rate risk perfectly? Comment on it by referring to the problems with duration.

Answer 1

a. Given:

Duration of assets(Da) = 7 years

Total Assets = $1billion = $1000million

Total Liabilities = $900 million

Duration gap = 0years

Now, Weighted average of liabilities(WL)= Total LIabilities/Total Assets= 900/1000= 0.9

By using the formula,we get:

Duration Gap = Da - (DL*WL)

0= 7 - (DL*0.9)

DL*0.9=7

DL= 7/0.9 = 7.8

So. the dollar weighted duration of bank's liability is 7.8 years.

b. No, zero duration gap doesn't mean that  the bank had hedged the interest rate risk. In the given context it means that there is a perfect balance between total assets and total liabilities for a given maturity .