Suppose that the present value of the liabilities of some financial institution is $600 million and the surplus $800 million (Surplus = market value of assets market value of liabilities). The modified duration of the liabilities is equal to 5. Suppose further that the portfolio of this financial institution includes only bonds and the modified duration for the portfolio is 6.

a) (3 marks) What is the market value of the portfolio of bonds?

b) (1 mark) What does a duration of 6 mean for the portfolio of assets?

c) (1 mark) What does a duration of 5 mean for the liabilities?

d) (5 marks) Suppose that interest rates increase by 50 basis points; what will be the approximate new value for the surplus?

e) (4 marks) Suppose that interest rates decrease by 50 basis points; what will be the approximate new value for the surplus?

f) (1 mark) What would be your conclusion from the above example about the liability / asset management in controlling interest rate risk?