A portfolio manager currently has a portfolio consisting solely of investment-grade corporate bonds with an analytically computed duration of 6.6
The portfolio manager wants to sell 20% of the portfolio holdings and invest the proceeds received in high-yield corporate bonds. The client has granted the portfolio manager permission to do so. The portfolio of the investment-grade corporate bonds after selling sufficient bonds to purchase the bonds from the high-yield corporate bond sector is 6.2 (i.e., the portfolio ignoring the high-yield corporate bond sector has a duration of 6.2). In addition, the portfolio manager wants to reduce the portfolio duration from 6.6 to 6.0 (i.e., the target duration is 6.0). The analytically computed duration for the high-yield corporate bonds to be purchased is 5.4 .
What is the portfolio's analytical duration after the increase of 20% to the high-yield corporate bond sector?
This question highlights the need to properly estimate the duration of high-yield bonds in a portfolio and to also considers a common problem faced by portfolio managers who want to add high-yield bonds to a portfolio that contains investment-grade bonds. For our problem, we assume the following:
• The current duration of a portfolio has an analytical duration of 6.6 and the portfolio manager wants to reduce the duration to 6.0 (i.e., the target duration is 6.0).
• The current portfolio has no exposure to the high-yield corporate bond sector.
• In rebalancing the portfolio to achieve the target duration, the portfolio manager decides to increase exposure to the high-yield corporate bond sector to 20% of the portfolio and the analytical duration of the bonds from that sector that it acquires has an analytical duration of 5.4 .
• The portfolio of the bonds after selling sufficient bonds to purchase the bonds from the high-yield corporate bond sector is6.2 ignoring the high-yield corporate bond sector.
The portfolio's analytical duration after the increase of 20% to the high-yield corporate bond sector is given by
analytical duration after 20% increaseto the high-yield bond sector = (1 –a)(b) + a)(c)
where
a = percent increase in exposure to the high-yield corporate bond sector
b = portfolio of the bonds after selling sufficient bonds to purchase the bonds from the high-yield corporate bond sector
c = the analytical duration of the bonds from that sector that it acquires
Inserting in our given values, we have:(1 – a)b + a(c) = (1 – 0.20)6.2 + 0.20(5.4) = 6.04 . Thus,portfolio's analytical duration after the increase of 20% to the high-yield corporate bond sector is 6.04 .
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