Fixed-income Portfolio [20 marks]

Afin-Super is the largest superannuation and pension fund in Macquarieland. To promote pension and annuity service, Afin-Super is serving a short-term experience plan(STEP). Plan joiners will be paid $10,000 once a year for a 2-year period (2 payments in total). The first payment will come in 5 years from now.

The yield curve is flat at 5% for all maturity. Interests are compounded annually.

(a) What is the Macaulay duration of STEP? [2 marks]

(b) Afin-Super plans to use 5-year and 8-year zero-coupon bonds to immunise STEP. How much money should Afin-Super allocate to these bonds for each STEP obligation? [4 marks]

(c) If the whole yield curve suddenly shifts to 2% right after the first payment be made 5 years from now:

(i) How much will Afin-Super be short of in the last payment, if Afin-Super do not immunise the obligation? [4 marks]

(ii) How much will Afin-Super be short of in the last payment, if Afin-Super keep their immunising portfolio? [6 marks]

(d) Explain the differences in the result of (c i) and (c ii). [2 marks]

(e) Give one pros and cons of immunising obligation using bond funds. [2 marks]