Question

The Raymond Burr National Bank has $1,000 in assets with an average duration of 5 years. This bank has $800 in liabilities with an average duration of 6.25 years. Market interest rates start at 6 percent and fall by 1 percent. What is the change in net worth of this bank?

Please show the steps to solve this without using Excel.

Answer 1

increase in asset = -asset duration*change in yield*asset value

=-5*(-0.01)*1000=50

increase in liabilities = =6.25*(-0.01)*800=50

change in networth = increase in asset-increase in liabilities = 50-50 = 0

Answer 2

Calculating the Change in Net Worth of the Bank

Given:

• Assets:

• Value = $1,000

• Duration ($D_A$) = 5 years

• Liabilities:

• Value = $800

• Duration ($D_L$) = 6.25 years

• Interest Rate Change ($\mathrm{\Delta }r$): Decrease of 1% (from 6% to 5%).

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Step 1: Understand the Duration Gap Formula

The change in net worth ($\mathrm{\Delta }NW$) due to interest rate changes is calculated using:

$$\mathrm{\Delta }NW\approx -(D_A-D_L\times \frac{L}{A})\times A\times \frac{\mathrm{\Delta }r}{1+r}$$

Where:

• $A$ = Assets ($1,000)

• $L$ = Liabilities ($800)

• $r$ = Initial interest rate (6% or 0.06)

• $\mathrm{\Delta }r$ = Interest rate change (-1% or -0.01).

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Step 2: Plug in the Values

1. Calculate the Duration Gap:

   $$D_{\text{gap}}=D_A-D_L\times \frac{L}{A}=5-6.25\times \frac{800}{1000}=5-5=0$$

   (The duration gap is zero, meaning the bank is initially immunized against interest rate changes.)

2. Compute Change in Net Worth:

   $$\mathrm{\Delta }NW\approx -0\times 1000\times \frac{-0.01}{1.06}=0$$

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Answer:

The change in net worth is $0.