Question: A portfolio manager has a portfolio consisting entirely of investment grade corporate bonds. The portfolio manager intends to sell 30% of the portfolio holding and invest in non-investment grade bonds. After the sale of the current holdings, the analytical duration of the remaining investment grade bonds is 7.6; the analytic duration of the non-investment grade bonds in 7.4. The manager's target duration is 6.0.
(a) What is the portfolio's analytic duration after the sale and purchase?
(b) Why will the true duration of the high yield bonds be less than the analytical duration of 7.4?
(c) If the true duration of the high yield bonds is 40% of the analytical duration, what is the true duration of the high yield bonds and of the portfolio?
(d) What action should the manager take to achieve the duration target? Assume that all of the change is in the duration of the investment grade bonds. What analytical duration for the investment grade bonds should the manager target? Assume the true duration and analytic duration of the investment grade bonds is the same.