Fixed Income - Effects of Steepness, Curve and Level

Assuming rates change as described by Akron and based on Exhibit 3, the impact on the portfolio as outlined in Module 6 would be most†likely†be a loss in value from changes in:

level and a loss from changes in steepness.

level and a gain from changes in steepness.

steepness and a gain from changes in curvature.

A parallel shift of the yield curve would result in a loss across each key rate duration given a sensitivity of 1.For example, a 100 basis point (bp) parallel shift would generate an approximately 4.7% loss in value. Aflattening of the yield curve in the long end would result in a loss given a sensitivity of 1.For example, a 100 bp decline in the 30 year key rate duration would result in a loss of approximately 2.9% (100*1*8.7*.333).There is no impact from curvature, since the curve did not “twist”.

Does ayone understand the response to this? How does a 100 BP decline in the yield curve is multiplied by both the Steepness factor (1), Key Rate duration (8.7) and some factor of (.333)?

took me a while to get my head around this but i think it goes something like:

with a effective duration of 4.7 (best used for parrelel shifts) and a parrelel shift in the yield curve of 100 basis point, your change in bond price would be calculated -4.7 * .01 (the negative sign is based on what happens because of bond prices, when rates increase bond prices drop) which would indicate a 4.7 % loss in value so there is the first part to the question.

Second part of the question, if i remember correctly the question or vignette words says if the curve “flattens but doe not twist”. How would/can the curve flatten? There would be a decrease in long term rates (if you think of a linear curve). With a decrease in long term rates you get your 100 bps decrease in rates, in the exhibit it shows the level (based on steepness is -1 for the long term 30 yr rate) the calculation with a key rate duration of 8.7 is -8.7 * -1 * -.01 = loss in value because negative times negative = positive * negative = negative again… the .333 is just the weighting in the portfolio

Thanks for the reply - this clarifies a lot.

But just a general question then… do you always multiply the Key-rate duration by the sensitivity of steepess/level/curvature and then by change in rates?

I would’ve thought that you just multiply the sensitivity of steepness/level/curvature by the change and rates (which in this case would just be -1*-.01 = increase in value).

apparently so lol.

This explanation does not make any sense and the formula is also different.

can anyone help, please?