Harrow is a portfolio manager and would like to decrease the convexity but maintain the same duration for one of her portfolios. She currently has no opinion on which direction she thinks interest rates will move in the future. The portfolio contains Treasury bonds with a PVBP of 0.228 and par value of $20 million. It also contains call options and put options, both with a PVBP of 0.197.
Based solely on the information above, which of the following statements is correct? Ignore the option premiums.
A) Harrow should buy the bonds and sell the puts on the basis of 1.157 par of options sold to par of bonds purchased.
B)Harrow should buy the bonds and sell the puts on the basis of 1.157 par of options sold to par of bonds purchased.
C)Harrow should sell the bonds and buy the calls on the basis of 1.157 par of options purchased to par of bonds sold.
I selected the answer as C but the answer is B and i dont understand why. From the solution I understand that when you sell option, your convexity decreases. But how does decrease in convexity impact duration?