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Solution 4 - FI lecture 5 2021-2022
Financial Institutions
Université de Lausanne
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Practice Problem on Interest Rate Risk
Chapter 9 23. Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9 years. The assets are financed with equity and a $900,000, two-year, 7 percent semiannual coupon capital note selling at par. a. What is the leverage-adjusted duration gap of Financial Institution XY? b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note: The relative change in interest rates is ΔR/(1 + R/2) = – 0. c. Using the information in parts (a) and (b), what can be said about the desired duration gap for the financial institution if interest rates are expected to increase or decrease? d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points. e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates?
Solution 23. Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9 years. The assets are financed with equity and a $900,000, two-year, 7 percent semiannual coupon capital note selling at par.
a. What is the leverage adjusted duration gap of Financial Institution XY?
Par value = $ Coupon rate = 7% R = 7% Semiannual payments Maturity = 2 years
t CFt DFt CFt x DFt CFt x DFt x t 0 32 0 31 15. 1 32 0 30 30. 1 32 0 29 43. 2 932 0 808 1,617. 900 1,707.
Duration = $1,707/$900 = 1. The leverage-adjusted duration gap can be found as follows: DA −DL k =9−1(900,000/1,000,000)=8
b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note: The relative change in interest rates is ΔR/(1 + R/2) = – 0.
The change in net worth using leverage adjusted duration gap is given by:
𝛥𝐸 = −[𝐷𝐴− 𝐷𝐿𝑘]∗ 𝐴 ∗
∆𝑅
1 +𝑅 2
= −[9. 94 − 1. 8975∗
9
10 ]∗ 1, 000,000 ∗(−0. 002)= 16,
c. Using the information in parts (a) and (b), what can be said about the desired duration gap for the financial institution if interest rates are expected to increase or decrease?
If the FI wishes to be immune from the effects of interest rate risk (either positive or negative changes in interest rates), a desirable leverage-adjusted duration gap (DGAP) is zero. If the FI is confident that interest rates will fall, a positive DGAP will provide the greatest benefit. If the FI is confident that rates will increase, then negative DGAP would be beneficial.
d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points.
𝛥𝐸 = −[𝐷𝐴− 𝐷𝐿𝑘]∗ 𝐴 ∗
∆𝑅
1 +𝑅 2
= −[8. 23225]∗ 1, 000,000 ∗(0. 003)= − 24,
e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates?
Immunizing the equity from changes in interest rates requires that the DGAP be 0. Thus, (DA-DLk) = 0 ⇒ DA = DLk, or DA = 1.8975x0 = 1 years.
Solution 4 - FI lecture 5 2021-2022
Matière: Financial Institutions
Université: Université de Lausanne
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