What is the duration GAP of a bank whose assets and liabilities are as follows? Assets:...

What is the duration GAP of a bank whose assets and liabilities are as follows?

Assets:
Cash $52 million
Short-term Investments (D=0.4) $153 million
Short-term Loans (D=0.8) $201 million
Long-term Investments (D=3.8) $247 million
Long-term Loans (D=5.2) $400 million

Liabilities:
Demand Deposits $46 million
Short-term Interest-bearing Deposits (D=0.3) $592 million
CDs (D=2.8) $148 million
Borrowed funds (D=0.1) $151 million

Round to three decimals.

Solutions

Expert Solution

duration Gap = weighted average asset duration - weighted average liability duration

Weighted average asset duration = duration of asset*(market value of asset/market value of total asset)

Weighted average liability duration = duration of liability*(market value of liability/market value of total liability)

Total asset = $52 million + $153 million + $201 million + $247 million + $400 million = $1,053 million

Total liabilities = $46 million + $592 million + $148 million + $151 million = $937‬ million

Weighted average asset duration = 0.4*($153/$1,053) + 0.8*($201/$1,053) + 3.8*($247/$1,053) + 5.2*($400/$1,053) = 0.4*0.1452991452991453‬ + 0.8*0.1908831908831909‬ + 3.8*0.2345679012345679‬ + 5.2*0.3798670465337132‬ = 0.0581196581196581 + 0.1527065527065527 + 0.891358024691358‬ + 1.975308641975309 = 3.077492877492877‬ Years

Weighted average liability duration = 0.3*($592/$937) + 2.8*($148/$937) + 0.1*(151/937) = 0.3*0.631803628601921‬ + 2.8*0.1579509071504803‬ + 0.1*0.1611526147278549‬ = 0.1895410885805763‬ + 0.4422625400213448‬ + 0.0161152614727855‬ = 0.6479188900747066‬ Years

duration Gap = 3.077492877492877 - 0.6479188900747066‬ = 2.430 Years

jeff jeffy answered 1 year ago

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