Suppose A Bank’s Assets And Liabilities Have Been Classified ✓ Solved

Suppose a bank’s assets and liabilities have been classified

1. Suppose a bank’s assets and liabilities have been classified into assets and liabilities that are rate sensitive and those that are not.

a) Calculate the effect of a decline of interest rates by 3% on bank income.

b) Calculate the effect of a decline of interest rates by 3% on interest margin.

c) Fill in the balance sheet to achieve such profit.

2. XYZ Bank has total asset value of $200 million, and total liability value of $200 million where $20 million is the equity capital. The average duration of the assets is calculated to be 2.5, and the average duration of liabilities is 1.1.

a. What is the duration gap for XYZ bank?

b. What is the change in the market value of net worth as a percentage of assets (ΔNW/A) if interest rates fall from 6% to 5%?

c. What is the percentage change in the market value of assets (%ΔA)?

d. What is the percentage change in the market value of liabilities (%ΔA)?

e. What is the dollar change in the net worth?

3. One of the ways the Bank of Canada exercises control over the monetary base is through its purchases and sales of government securities in the open market.

a) How will a Bank of Canada purchase of $100 of government bonds from banks affect the monetary base?

b) How will a Bank of Canada sale of $100 of government bonds to the nonbank public affect the monetary base?

c) How will a Bank of Canada purchase of $100 of government bonds from the nonbank public affect the monetary base?

4. Suppose the desired reserve ratio is set at 10% in the banking system.

a. What would be the total change in the deposits in the banking system if the central bank sells $2 million government bonds to bank A?

b. What would be the total change in the deposits in the banking system if the central bank buys $1 million government bonds from bank A given that an additional 10% of any deposits are held as excess reserves?

5. Suppose the central bank’s goal for inflation is 2%, and the equilibrium real overnight rate is 2%. Assume that real GDP is currently 1% above potential, and current inflation is 3%. Use the Taylor Rule to calculate the target overnight rate AND the value of the real overnight rate that is implied by that target rate.

6. How would paying off Bank of Canada’s advances of $100 by the banking system affect MS if desired reserve ratio is 10% and the desired currency holding ratio is 25%?

SECTION II: ESSAY 1. Suppose Canadian economy is facing economic slowdown, and you are in charge of implementing necessary monetary policy to revive things. What is the policy you would implement? Describe 3 monetary transmission mechanisms that would lead to economic recovery.

Paper For Above Instructions

The banking sector plays a critical role in economic stability and growth by managing interest rates and facilitating monetary policy. This essay examines several aspects related to bank asset and liability management, focusing on the impact of interest rate fluctuations, duration gaps, and monetary policy's efficacy in promoting economic recovery.

Impact of Interest Rate Decline on Bank Income

Declining interest rates predominantly affect banks' income by reducing the yield on rate-sensitive assets. Suppose the bank in question has rate-sensitive assets worth $85 million and liabilities worth $95 million. A 3% decline in interest rates can significantly decrease interest income for both assets and liabilities.

To illustrate:

Calculation of Income Effect:

• Rate-Sensitive Assets: $35 million (short-term securities) + $50 million (variable mortgage) = $85 million
• Reduction in Income: $85 million * 0.03 = $2.55 million decrease in bank income.

The sign of change is negative, indicating a decrease in income.

Effect on Interest Margin

The interest margin is calculated as the difference between interest income and interest interest expense. A decline in interest rates can compress this margin, particularly when liabilities reprice faster than assets.

Calculation of Interest Margin Effect:

• Interest Income = ($85 million 3%) - ($95 million 3%) = -$0.3 million

This implies a negative shift in interest margin by $0.3 million.

Filling the Balance Sheet for Desired Income

Suppose bank management wants to achieve an interest income of $1.35 million even after a 3% decline in rates. They might restructure liabilities to enhance interest income. A proposed balance sheet might look as follows:

Calculating Duration Gap for XYZ Bank

The duration gap is a metric used to assess the interest rate risk exposure of a bank. It can be calculated using the weights of assets and liabilities along with their respective durations:

Formula:

Duration Gap = (Duration of Assets - Duration of Liabilities) / Total Assets

• Duration of Assets: 2.5, Total Assets: $200 million
• Duration of Liabilities: 1.1, Total Liabilities: $200 million
• Duration Gap = (2.5 - 1.1)/200 = 0.007

Changes in Market Value and Net Worth

As interest rates fluctuate, so does the market value of assets and liabilities:

• Change in Net Worth (%ΔNW/A): A 1% decrease in interest rates will increase the market value of net worth due to the duration effect.
• Percentage Change in Market Value of Assets: Calculated similarly based on the asset duration will yield a specific result rounded to one decimal place.
• Dollar Changes in Market Value are directly related to the percentage changes derived from the mentioned calculations.

Monetary Policy Implementation for Economic Recovery

In response to an economic slowdown, implementing an expansionary monetary policy is essential. The target should include three primary monetary transmission mechanisms:

1. Interest Rate Channel: Reduction of interest rates lowers borrowing costs, prompting investment in low-interest environments.
2. Wealth Effect: Lower rates increase asset prices leading to greater household equity and consumption.
3. Exchange Rate Channel: Currency depreciation enhances export competitiveness while increasing import costs.

Conclusion

Through managing assets and liabilities and responding appropriately to interest rate changes, banks can stabilize and steer economies towards recovery during downturns. By understanding these financial metrics, banks enhance their operational efficiency, ensuring financial stability.

References

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