Please assist with part a) and B) part i and ii 5. Interest rate risk management
ID: 2786135 • Letter: P
Question
Please assist with part a) and B) part i and ii
5. Interest rate risk management (12 marks) (a) Assume that the term structure is flat with spot rates of 5% for all maturities. Consider a market with the following two bonds: Bond A is a 2-year 3% coupon bond with a face value of $100. It trades for $96.28. · Bond B is a 3-year 4% coupon bond with a face value of $100. It trades for $97.28. Work out the Macaulay Duration of the two bonds.(4 marks) Bons a Maca eo os) (b) Suppose you have a liability consisting of 2 repayments, the first due in 2 years time of $500 and the other due in 3 years' time of $1000. Set up a portfolio using the bonds which immunises this liability. i. Calculate the duration of this liability. (4 marks) For mnisaton, the clsaton mut equa) to ^emi Calculate how many ‘units' of each bond you should buy, assume $100 face value = 1 unit. (4 marks) ii.Explanation / Answer
Macaulay Duration=TIme weighted present value of cash flows/Price
Price=96.28
TIme weighted present value of cash flows=1*3/1.05+2*(100+3)/1.05^2=189.7052
Macaulay Duration=189.7052/96.28=1.9703
Price=97.28
TIme weighted present value of cash flows=1*4/1.05+2*4/1.05^2+3*(100+4)/1.05^3=280.5831
Macaulay Duration=280.5831/97.28=2.8843
For immunisation, duration of assets would equal to duration of liabilities
Duration=2+3=5
Bond A: 5/1.9703=2.537685
Bond B: 5/2.8843=1.733523