The two portfolios have the same dollar duration; explain whether their performance will be the same if interest rates change

What will be an ideal response?

Even if the yield curve shifts in a parallel fashion due to changes in interest rates, two portfolios with the same dollar duration will not give the same performance if they have differences in dollar convexity. Although with all other things equal it is better to have more convexity than less, the market charges for convexity in the form of a higher price or a lower yield. But the benefit of the greater convexity depends on how much yields change. As can be seen from the illustration in
the second column of Exhibit 24-5, if market yields change by less than 100 basis points (up or down), the bullet portfolio, which has less convexity, will provide a better total return that the barbell portfolio.

The last two columns Exhibit 24-5 illustrate the relative performance of a bullet portfolio and
a barbell portfolio for a nonparallel shift of the yield curve. Specifically, the first nonparallel shift column assumes that if the yield on the bullet portfolio (consisting of the intermediate-term bond) changes by the amount shown in the first column, the short-term bond in the barbell portfolio will change by the same amount plus 25 basis points, whereas the long-term bond in the barbell portfolio will change by the same amount shown in the first column less 25 basis points. Measuring the steepness of the yield curve as the spread between the long-term yield and the short-term yield, the spread has decreased by 50 basis points. Such a nonparallel shift means
a flattening of the yield curve. As can be seen in the exhibit, for this assumed yield curve shift, the barbell outperforms the bullet.

In the last column of Exhibit 24-5, the nonparallel shift assumes that for a change in the intermediate bond's yield, the yield on the short-term will change by the same amount less 25 basis points, whereas that on the long-term bond will change by the same amount plus 25 points: Thus, the spread between the long-term yield and the short-term yield has increased by 50 basis points, and the yield curve has steepened. In this case the bullet portfolio outperforms the barbell portfolio as long as the yield on the intermediate bond does not rise by more than 250 basis points or fall by more than 325 basis points.