CFA Mock Exam Portflio key rate duration Q42 AM

Doubt for the question below- 1.How is the key rate duration calculated?(1.8, 3.6, 8.7) for instance shunt key rate duration for year 30 be 30*1/(300*.01)=10 2.Why is C the correct answer? Wont there be a gain from change in steepness as 5*1+.5*10+(-1*30)=-20 so shouldn’t that be a gain of 20 on a portfolio of 300.

“Consider a portfolio of zero-coupon bonds that mature at different times in the future. Changes in interest rates are not always parallel across maturities, so let’s analyze what happens as rates change across the yield curve. Let’s assume that the portfolio has sensitivities to factors as provided in Exhibit 3. The portfolio has equal weightings in each key rate duration and an effective duration of 4.7. I would like you to assess the impact on the return of the portfolio if rates rise evenly across the curve and also when the curve flattens but does not twist.”

Exhibit 3 Factor Movements per One Standard Deviation Shift and Portfolio Key Rate Durations

Year 5 10 30

Parallel 1 1 1

Steepness 1 0.5 –1

Curvature 0.5 0 1

Rate Durations 1.8 3.6 8.7

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:

  1. A level and a gain from changes in steepness.
  2. B steepness and a gain from changes in curvature.
  3. C level and a loss from changes in steepness.

Bump because I came to post the exact same thing. So if a parallel IR shift upwards causes bond price to decrease, then how does a steepness decrease also cause bond price to decrease. The steepness of the IR has declined and if IR decline bond prices increase which would result in a gain. I don’t understand the logic behind their answer.

https://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91358367

Thanks for the link.