Question: Barbell example.

On June 16, 2014, a fund manager is considering the purchase of $1 million face amount of US Treasury 1½s with a maturity date of May 31, 2019 at a cost of 990,468.75. The manager examines the bond further and, using his Bloomberg terminal, notices that the bond has a yield of 1.701% and a modified duration of 4.748. Before deciding to buy the bond the manager considers the information in the following table about two other bonds:

The three bonds in the table have maturities of approximately 2, 5, and 10 years. The fund manager could purchase the 1½ bond or alternatively a barbell portfolio consisting of the (0)3/8 and the 2½ bonds. In a barbell portfolio, part of the portfolio is made up of long-term bonds and the other part comprises very short-term bonds. The term "barbell" is based on the notion that the strategy resembles a barbell, heavily weighted at both ends and with nothing in between. Construct such a barbell portfolio and evaluate the alternative barbell strategy compared to the 1½ bond investment. Such barbell portfolio should be constructed to cost the same and have the same duration as the bullet investment. Your evaluation should consider the yield and the convexity of the 1½ bond relative to the barbell strategy.