Management of Financial Institutions

Management of Financial Institutions
1. Select the following variables for a US treasury bond:
a. coupon rate (between 2% and 6%)
b. yield to maturity (between 3% and 7% and not equal to the coupon rate).
c. between 5 and 15 years

2. Determine the value of the bond you describe in question 1
a. if coupons are paid annually.
b. if coupons are paid semi-annually.

3. Determine the duration of the bond you describe in question 1
a. if coupons are paid annually.
b. if coupons are paid semi-annually.

4. Determine the duration of the following bonds (make the changes for each subpart separately).
a. with the yield to maturity and maturity that are the same as 1b and 1c, and an annual coupon that is double the coupon rate selected in 1a.
b. with an annual coupon and maturity that are the same as 1a and 1c, and a yield to maturity that is 2% higher than the yield to maturity in 1b.
c. with an annual coupon and maturity the same as in 1a and 1b and a maturity 5 years longer than 1c.

5a. Select a maturity between 10 and 20 years for a zero coupon bond and a yield between 3% and 7%. Determine the price and duration of this bond.
b. Select a coupon rate between 2% and 5% and a yield between 2% and 5% (but not equal to the coupon rate) for a British consol – a bond that pays an annual coupon in perpetuity and never repays the principal. Determine the price and duration of this bond.
c. Select an interest rate between 4% and 7%, a yield between 4% and 7%, and a maturity between 10 and 20 years for an amortized mortgage. Assume payments on the mortgage are made annually, determine the price and duration of the mortgage.

6. Determine the convexity of the bond described in question 1 if coupons are paid annually.

7a. Using only the duration from 3a, estimate the percentage change in value for the bond from question 1 if the yield to maturity decreases by 1% (e.g., it decreases from 4% to 3%). (That is, do not actually use the new yield and the payments to calculate the value of the bond.)
b. Using the only duration from 3a and the convexity from 6, estimate the percentage change in value for the bond from question 1 if the yield to maturity decreases by 1%.

8. Assume a financial institution has $250 million market value of assets with a duration of 5.65years and $214 million market value of liabilities with a duration of 3.45 years.
a. What is the leverage adjusted duration gap for the financial institution?
b. What is the duration gap if you do not adjust for leverage?
c. What is the expected percentage in equity value and the dollar change in equity value if interest rates which are currently 3%increase by 0.25%? (Assume the financial institution has no assets and liabilities that are not rate sensitive).

9. An investor holds investments in the following bonds:
(i) $1,000,000 face value of the bond from question 1with semi-annual coupon payments.
(ii) $750,000 face value of the zero coupon bonds from 5a.
(ii) $500,000 face value of the British consolsfrom question 5b.
(v) $1,000,000 face value of the mortgage from question 5c.
Determine the duration of this portfolio?

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