What is the duration gap for this financial institution

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Reference no: EM132179146

Management of Financial Assignment -

Please show enough of your work that I can determine how you obtain your answers, (e.g, by turning in the spreadsheet you use to do the calculations). For questions 1-8, assume the face value of the bond or loan is $1 million. Except where the question specifically indicates otherwise, assume payments are made annually.

1. Select variables for a US treasury bond as follows:

a. coupon rate (between 2% and 6%)

b. yield to maturity (between 3% and 7% and not equal to the coupon rate).

c. maturity between 5 and 15 years

2. If coupons on the bond from question 1 are paid annually, what is the bond's value?

3. If coupons on a bond with coupon, yield and maturity from question 1 are paid semi-annually, what is the bond's value?

4. Determine the duration of the bond in question 2.

5. Determine the duration of the bond in question 3.

6. Based on the answers to questions 4 and 5, how does the frequency of payment affect the duration of a bond?

7. Calculate the duration of a bond with the maturity and yield from question 2 if the coupon rate on the bond is 2% higher than the coupon rate in question 2.

8. Calculate the duration of a bond with the maturity and coupon from question 2 if the yield on the bond is 2% higher than the yield in question 2.

9. Calculate the duration of a bond with the coupon rate and yield from question 2 if the bond's maturity is 5 years longer than the maturity in question 2.

10. Comment on how the coupon rate, the yield and the maturity affect a bond's duration.

11. Select a maturity between 10 and 20 years and a yield to maturity between 3% and 7%. Determine the price and duration of a zero coupon bond with the selected maturity and yield to maturity.

12. Select a coupon rate between 2% and 5% and a yield to maturity between 2% and 5% that is different from the coupon rate. If a bond that pays an annual coupon at the rate specified each year with no maturity (that is, the principal is never repaid), what is the price and duration of the bond.

13. Select an interest rate between 4% and 7%, a yield to maturity between 4% and 7%, and a maturity between 5 and 15 years. Determine the price and duration of the mortgage with that interest rate and the yield to maturity if the mortgage is fully amortized with level quarterly payments (i.e., each payment includes interest and principal and the principal is fully repaid by payment of the required quarterly payments.)

14a. Using the duration of the bond from question 2, estimate the percentage change in value of the bond if the yield to maturity decreases by 0.5%.

b. Calculate the actual change in value of the bond from question 2 if the yield to maturity decreases by 0.5%.

c. Comment briefly on the difference between the estimates from a and the calculate from b.

15. An investor holds a portfolio consisting of the following:

$1,000,000 face value of the bond from question 2,

$5,000,000 face value of the zero coupon bonds from 11, and

$2,000,000 face value of the bonds from question 13.

Determine the duration of this portfolio?

16. Assume a financial institution has $1.250 billion market value of assets with a duration of 6.85 years and $1.025 billion market value of liabilities with a duration of 3.25 years.

a. What is the duration gap for this financial institution?

b. What is the leverage adjusted duration gap for this financial institution?

17a. What is the expected change in equity value (in $ and %) for the bank in question 16 if interest rates which are currently 3.775% increase by 35 basis points?

b. Explain what a bank manager could/should do in this situation.

18a. What is the expected change in equity value (in $ and %) if interest rates which are currently 3.775% decrease by 25 basis points?

b. Explain what a bank manager could/should do in this situation.

Reference no: EM132179146

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