When all cash flows are assumed to be discounted by a single yield, why is there no difference between the duration (sensitivity to yield), interest-rate duration (sensitivity to rates), and spread duration (sensitivity to spreads)?

Question

What will be an ideal response?

Answer 1

From our answer in the previous problem, we saw that formulas for duration and spread durationgenerated the same value.Continuing with the bond problem described in our previous, let us suppose the yield investors want for the bond changes by 50 basis points. Regardless of whether the change is from the level of the Treasury yield or from a change in the credit spread, the approximate change in the bond's price will be the same. Suppose that the change of 50 basis points is due to a 40 basis point change in the Treasury yield and a 10 basis point change in the credit spread in the same direction. Then we know that 0.4 / 0.5 = 0.8 or 80% of the total change of 100% comes from the change in the Treasury yield and 0.1 / 0.5 = 0.2 or 20% comes from the change in the credit spread.

Two points are worth noting. First, to demonstrate the calculation of spread duration, all cash flows are assumed to be discounted by a single yield. This is why there is no difference at all between the duration (sensitivity to yield changes), interest-rate duration (sensitivity to rate changes), and spread duration (sensitivity to spread changes). Although all three appear to be the same, in practice, this sameness becomes blurred and so we need to distinguish between them. In particular, the distinction becomes worth noting when considering discounting cash flows using a constant spread over a Treasury curve. Furthermore, consider the spread duration for a floating-rate bond. The difference between spread duration and Treasury duration becomes truly important when considering floating-rate corporate bonds, which can have near-zero interest-rate exposure but large spread durations.

The second point provides the motivation for other measures. The textbook provided an example of where both the change in the Treasury yield and the change in the credit spread moved in the same direction. However, there is empirical evidence that there is at times an inverse correlation between the change in the level of Treasury yields and the change in credit spreads. This second-order effect should be taken into account when measuring a portfolio's exposure to changes in interest rates.