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 6% annual coupon paying bond. The one-year spot rate is 4%, the two-year spot rate is 3%, and the three-year spot rate is 4%. A. What is the value of the option free bond that is being considered for purchase? State all formula and working used. [3 Marks] B. Discuss yield to maturity and how it would apply to the following statement "Relative to sovereign bonds, non-sovereign or corporate bonds with similar characteristics most likely have a yield to maturity that is higher and trade at lower prices". [4 Marks] C. Duration provides a good approximation of changes in the price of an option-free bond, when the change in yield is relatively small. However, for large changes in yield a convexity adjustment needs to be incorporated. With the aid of your own fully annotated diagram, discuss the statement above and address why a convexity adjustment is necessary. [6 Marks] D. Calculate the convexity adjustment for a bond if the initial price is $104.45, price if yields increase by one percent is $100 and price if yields decrease by one percent is $109.16. Show all formulas used. [4 Marks] E. The relationship between bond prices and yields is very important to fixed-income investors. Explain the characteristics of a bond that affect its price volatility. [7 Marks]