# Interest Rate Risk Management]

1

PBF-Assessment 3 [Due date: 3 Dec 2023] [Topic 6- Interest Rate Risk Management]

Question 1 – Macaulay Duration of Bond Portfolio + Modified Duration [8 marks] (a) An investor decides to construct a bond portfolio made up of

\$10,000 in the 4-year 5% coupon bond and \$30,000 in a 3-year zero coupon bond. Assume the par value of bond is \$1000 and the market interest rate = 4%. What is the Macaulay duration of this bond portfolio? (4 marks)

(b) Estimate, using modified duration, the change in the price of the 4-year 5% coupon bond if the market interest rate decreases from 4% to 3%. (4 marks) Question 2- Income Gap + Overall Duration Gap [17 marks] (a) Consider the following balance sheet of Banco Credit:

Assumptions – Fixed rate mortgages repaid in the coming year = 25% – Savings deposits that become rate sensitive in the coming year = 20% – All commercial loans are rate sensitive – All money market deposits are rate sensitive

Using income gap analysis, calculate the change in net interest income over the coming year if interest rates increase by 1% from 4% to 5% (4 marks) (b) What is the duration gap for Banco Credit? (4 marks) (c) What is the estimated change in the value of equity (in \$s) for Banco Credit if interest rates increase by 1% from 4% to 5%? (4 marks) (d) Explain why a bank with a positive duration gap is estimated to see a fall in the value of its equity when interest rates increase. (5 marks) Remark:  Submit to: Canvas Assignment [doc or pdf file]  Filename: Class — Name — Index Number [eg. L41 Robert Lee #100]

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