You work at a fixed income hedge fund. You observe that the yield to maturity on a AAA-rated 5-year bond is 4.50% and that the yield to maturity on a BBB-rated 5-year bond is 5.07%. Historically, the mean difference between AAA-rated 5-year bonds and BBB-rated 5-year bonds is 35 basis points (or 0.35%).

(a) (i) (1 mark) Is the BBB-rated bond over-valued or under-valued relative to the AAA-rated bond, relative to historical data?

(a) (ii) (1 mark) Your manager says that you should take a long position in the BBB-rated bond if you believe it is under-valued relative to the AAA-rated bond, or a short position in the BBB-rated bond if you believe it is under-valued relative to the AAA-rated bond. Explain why this is a risky strategy.

(a) (iii) (2 marks) You suggest that a combination of appropriate long and short positions is a better way to profit from the data above (i.e. is a better way to profit from the observed bond yields for the AAA-rated and BBB-rated bonds). Carefully explain the long and short positions you would take, in order to profit from the yield differential between AAA-rated and BBB-rated bonds.

(a) (iv) (2 marks) Carefully explain how it is possible to generate a loss even if you use the long and short positions in (a)(iii) above.

(b) (4 marks) You are working at a fixed income hedge fund and your manager says to you that they believe interest rates will increase. They suggest that an appropriate strategy is to increase the convexity of your portfolio. Carefully explain whether you agree or disagree with this statement.