An institutional investor invests in a commercial bond for a term of six years. As per the bond agreement, the investor will receive annual periodic payments at a rate of 10% p.a. The face value of the bond is $50,000 which is also its current market price.

Required:

a. Calculate the Duration of this bond.

b. Suppose interest rates were forecast to fall by 100 basis points. Using Duration calculated in (a) above, calculate the percentage change in price of this bond.

c. What is the new price of this bond due to the change calculated in (b) above?

d. Now consider using the bond pricing formula to calculate the bond price. If interest rates were forecast to fall by 100 basis points, what would be the new price of this bond?

e. Calculate the difference (if any) between the two prices calculated in (c) and (d) respectively. Briefly explain the difference between the two prices?

f. Calculate the convexity of this bond.

g. Suppose interest rates were forecast to fall by 100 basis points. Using this information and after adjusting for convexity, calculate the new price of this bond. Comment on the difference between this new price and the price calculated in (d) above.