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The following balance sheet information is available for McCaslin State Bank (amounts in $ thousands and duration in years):

Assets Amount Duration

T-bills $180 0.50

Loans 4,548 7.00

Total Assets 4,728

Liabilities

Deposits 4,184 1.00

Total Liabilities 4,184

Equity 544

Total Lia & NW 4,728

a. What is the average duration of all the assets?

b. The average duration of all the liabilities is:

[4,184*1]/4184 = 1.00 years

c. What is the leverage-adjusted duration gap? Where, k = market value of liabilities/market value of assets

DG = DA - kDL =

Remember that a positive leverage-adjusted duration gap actually indicates that an increase in interest rates will lead to a decrease in net worth.

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., DR/(1+R) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * ΔR/(1 + R) = = $___________.

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Hubert Koch
Hubert KochLv2
28 Sep 2019

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Related questions

The following market value (mark-to-market) balance sheet information is available for Duguay State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam. What is the average duration of all the assets?

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = DA –kDL = 0

The choice is to make the duration of assets equal to:

DA =

or the duration of liabilities equal to:

DL =

Or some combination thereof.

The following market value (mark-to-market) balance sheet information is available for Delasho State Bank (amounts in $ thousands and duration in years):

Book Value Market Value

Assets Amount Amount Duration

T-bills $ 180 $ 180 0.50

Loans* 5,000 ______ _____

Total Assets 5,180 ______

Liabilities

Deposits 4,184 4,184 1.00

Total Liabilities 4,184 4,184

Equity 996 _______

Total Lia and NW 5,180 _______

*Since this is a simple bank, it has only one type of loan. The loan has a $5,000 book value (current outstanding principal), amortized loan with annual payments, an interest rate of 6 percent, and 20-years to maturity. Similar loans today would have an interest rate of 7 percent which is the market yield.

Using Excel, determine the market value and duration of the loan and fill in the blanks in the balance sheet above. Please include a copy of your Excel Spreadsheet with your completed exam. What is the average duration of all the assets?

Weighted Average Duration Assets:

b. What is the average duration of all the liabilities?

Weighted Average Duration Liabilities:

c. What is the leverage-adjusted duration gap? What is the interest rate risk exposure?

DG = DA - kDL =

d. What is the forecasted impact on the market value of equity caused by a relative upward shift in the entire yield curve of 1.5 percent [i.e., Dr/(1+r) = 0.0150]?

The market value of the equity will change by the following:

MVE = -DG * (A) * r/(1 + r) =

e. What variables are available to the financial institution to immunize the balance sheet? Taking one variable at a time, how much would each variable need to change to get DGAP equal to 0?

To immunize the institution for interest rate risk, the Leverage Adjusted DG needs to be zero:

DG = DA –kDL = 0

The choice is to make the duration of assets equal to:

DA =

or the duration of liabilities equal to:

DL =

Or some combination thereof.

1. The portfolio managers of a firm determined that over the next year interest-sensitive assets are in the amount of $1.5 billion while interest-sensitive liabilities are in the amount of $1.8 billion. Moreover, when considering all of the firm's assets and liabilities, they determined that the average duration of assets is 3.6 years while the average duration of liabilities is 4.0 years. The firm’s debt-to-equity ratio is 4-to-1.

1) Calculate GAP and Duration GAP (DGAP) for this situation.

2) What will happen to net interest income and relative asset prices (market values) as interest rates rise or fall?

(In other words, how are net income and overall market value impacted by changes in interest rates?)

3) What strategies could management employ to hedge against this risk?For instance should it buy or sell futures, call options or put options (i.e., for each derivative is it a buy or sell strategy?)?

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