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XYZ Bank Balance Sheet (in AUD millions) (as of June 30, 2022) Assets: 1. Cash ...

May 18, 2024

Solution by Steps

step 1

To determine the bank's exposure to rising interest rates, we need to analyze the duration of its assets and liabilities. Duration measures the sensitivity of the price of a bond to changes in interest rates

step 2

Calculate the weighted average duration of the bank's assets. The formula for the weighted average duration is:

\text{Weighted Average Duration} = \frac{\sum (\text{Duration} \times \text{Value})}{\text{Total Value}}

Using the provided data:

\text{Total Assets} = \$1,190

\text{Weighted Average Duration of Assets} = \frac{(0.3 \times 80) + (0.7 \times 40) + (1.5 \times 25) + (6 \times 25) + (2 \times 50) + (5.5 \times 20) + (4 \times 400) + (1.2 \times 200) + (5.2 \times 100) + (1.1 \times 150)}{1,190}

= \frac{24 + 28 + 37.5 + 150 + 100 + 110 + 1600 + 240 + 520 + 165}{1,190}

= \frac{2974.5}{1,190}

\approx 2.5 \text{ years}

step 3

Calculate the weighted average duration of the bank's liabilities. Using the provided data:

\text{Total Liabilities} = \$1,120

\text{Weighted Average Duration of Liabilities} = \frac{(0.2 \times 350) + (1.2 \times 400) + (1.8 \times 100) + (4.5 \times 100) + (0.75 \times 100) + (12 \times 50) + (10 \times 20)}{1,120}

= \frac{70 + 480 + 180 + 450 + 75 + 600 + 200}{1,120}

= \frac{2055}{1,120}

\approx 1.8 \text{ years}

step 4

Compare the weighted average durations of assets and liabilities. The bank's assets have a higher duration (2.5 years) compared to its liabilities (1.8 years). This means that the value of the bank's assets is more sensitive to changes in interest rates than its liabilities

step 5

Recommendation: To mitigate the exposure to rising interest rates, the bank should consider strategies such as: 1. Reducing the duration of its assets by investing in shorter-term securities. 2. Increasing the duration of its liabilities by issuing longer-term debt. 3. Using interest rate swaps or other hedging instruments to manage interest rate risk

Answer

The bank's assets have a higher duration (2.5 years) compared to its liabilities (1.8 years), indicating greater sensitivity to interest rate changes. To mitigate this risk, the bank should consider reducing asset duration, increasing liability duration, or using hedging strategies.

Key Concept

Duration and Interest Rate Sensitivity

Explanation

Duration measures the sensitivity of a bond's price to interest rate changes. A higher duration means greater sensitivity. By comparing the durations of assets and liabilities, we can assess the bank's exposure to interest rate risk.