You are an investment consultant working for a superannuation firm. One of the fixed-income portfolio managers wants to understand more about managing interest rate risk in the portfolio, and she is particularly interested in understanding the concept of duration. The portfolio currently contains option free bonds but the manager is considering adding bonds with embedded options into the portfolio. The manager is also considering purchasing a three-year 8% annual coupon paying bond.

1. Using the par rates for annual coupon sovereign debt in the table below and bootstrapping method to obtain the zero coupon curve.

[5 marks]

1-year	2.3%
2-year	3.4%
3-year	4.3%

2. What is the value of the option free bond that is being considered for purchase? [3 marks]

3. Establish the maximum Macaulay duration of an option-free fixed-rate bond with 3 years remaining until maturity? Carefully explain your answer. [3 marks]

4. Suppose the manager has now added a new bond with embedded option. You find that the value of the new bond with embedded option is $92. Using your price technique, you find that the value of a normal bond (i.e. option free) with similar characteristics is worth $90 and the value of the option is $2. The embedded option is most likely:

• Call option
• Put option

Please circle your answer.

Based on your answer, please indicate below by circling whom does the embedded option benefit and explain your answers.

• Issuer
• Investors

[4 marks]