Why for the high-yield corporate bonds in which the portfolio manager has invested will the true duration be less than the analytical duration of 5.4?
What will be an ideal response?
The high-yield corporate bonds in which the portfolio manager has invested will have a true duration that is less than the analytical duration of 5.4 . The reason we know this is based on empirical evidence. Factors can be given to explain differences in empirical and theoretical duration. The difference between analytical and empirical duration will depend on the following three factors that must be estimated empirically: (1) the correlation between the parallel shift in Treasury yields and the change in credit spreads, (2) the standard deviation of the relative change in credit spreads, and (3) the standard deviation of the change in parallel shifts in Treasury yields.
Below we illustrate how the portfolio manager can attempt to reduce the duration to the target without considering any adjustment based on empirical evidence.
Because the target duration is 6.0, this means that based on the analytical duration, the portfoliomanager must modify the portfolio to reduce the duration from 6.04 to 6.0 . This would be doneby rebalancing the non-high-yield bond portfolio duration so that the portfolio duration is 6.0 . That is,(1 – 0.20)X + 0.20(5.4) = 6.0 . Solving algebraically, we get X = 6.15 . Thus, the duration of the non-high-yield bonds in the portfolio must be decreased from6.2 to 6.15.
However, we know empirically that the high-yield corporate bonds in which the portfolio manager has invested will have a true duration that is less than the analytical duration of 5.
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