Question

Assume a bank has $100 million of assets with a duration of 2.7, and $95 million of liabilities with a duration of 1.03. If interest rates increase from 10 percent to 11 percent, how does the net worth of the bank change? (increase or decrease by how much)

Answer 1

ANSWER:

Total asset value = $100 million

duration = 2.7

delta i = change in rates = 11% - 10% = 1% = 0.01

interest = 10% = 0.1

% delta p = - dur * ( delta i / (1 + interest))

% delta p = -2.7 * ( .01 / ( 1 + .1) )

% delta p = -2.7 * ( .01 / 1.1) = -2.7 * .009 = -0.025 = -2.5%

total liabilities = $95 million

duration = 1.03

delta i = change in rates = 11% - 10% = 1% = 0.01

interest = 10% = 0.1

% delta p = - dur * ( delta i / (1 + interest))

% delta p = -1.03 * ( .01 / ( 1 + .1) )

% delta p = -1.03 * ( .01 / 1.1) = -1.03 * .009 = -0.009 = -0.9%

difference between asset and liability % change = -2.5% - (-0.9%) = -1.6%

total assets = $100 million

change in assets = $100 million * -1.6% = -$1.6 million.

so, the net worth of the bank would decline by $1.6 million.