Consider a 5-year bond with annual coupon payments. The bond has a face value (principal) of $100 and sells for $95. Its coupon rate is 3%.

Question 1. Duration and Banking (4 marks). Consider a 5-year bond with annual coupon payments. The bond has a face value (principal) of $100 and sells for $95. Its coupon rate is 3%. (The coupon rate is the ratio
between the coupon value and the face value). The face value is paid at the maturity
year in addition to the last coupon payment.
1. Calculate the bond’s yield to maturity (YTM) and duration using its YTM. (1
mark)
2. Suppose the bond’s YTM changes in the same way as a 5-year T-bill interest rate.
Use the bond’s modified duration to evaluate the relative change in the 5-year bond’s
value if the interest rate on 5-year T-bills falls by one basis point, that is, by 0.0001.
(1 mark)
This part was extracted from the balance sheet of the First Bank of Australia:
Assets (Billion AUD) Liabilities (Billion AUD)
Bond 80 Fixed-rate liabilities 60
where “Bond” here refers to the bond we specified above and the fixed-rate liabilities
(banks future payment obligations) have an average duration of 4 years and YTM of 3%.
Their YTM changes in the same way as a 5-year T-bill interest rate.
3. Bank’s equity is the difference between its assets and its liabilities. How does bank’s
equity change, if the T-bill interest rate increases by 10 basis point? (2 marks)

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