Year 5 10 30
parallel 1 1 1
steepness 1 0.5 -1
curvature 0.5 0 1
key rate duration 1.8 3.6 8.7
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.”
Can anyone please explain to me why steepness will result in a loss, and curvature will not have any effect on the bond?
I have spent 90 minutes on this and pulled half of my hair out. But I figured out.
Yield curve flattens. It means the change in the interest rates is the least for the shortest maturity, a bit higher for the middle, and the highest for the longest.
LEt’s suppose: 10 bps, 50 bps and 100 bps.
Now calculate the change in portfolio value based on the equation (both curriculum and schweser has it):
the sensitivities are positive for the first two maturities and negative for the third.
the change in rates is negative for all of them.
I cannot copy the equation but check equation 20 from curriculum.
Based on the above figures your portfolio change will be:
But the key is that because sensitivity is negative for the longest maturity you have minus x minus x minus which makes up minus as a result.
Was I clear (I hope, I have tor rush now.)
Curvature has effect only if the rates increase for some and decrease for other maturities.
Or don’t move for some and increase/decrease for others.
Level means equal shift (up or down) for all maturities.
Moosey when the curve flatten shouldn’t the shorter-term rates increase and the longer-term rates decrease, while the middle rates stay the same, not least by the shorter-term and highest by the longer-term? My way to understand this question is that when yield curve flattens, the 5-year rate increase and the 30-year rate decreases by the same amount (100bps for example), take the portfolio’s key rate duration with each maturity into account then the change in portfolio value should be: (1 x 1.8 x 100bps) + (-1 x 8.7 x 100bps) = LOSS in value
You need to understand what this table tells you.
A 100bp steepness change means that the:
Apparently your portfolio has a 10-year maturity (because you say that curvature has no effect, and the maturity at which the curvature sensitivity is zero is 10 years). Because the 10-year rate increases by 50bp for a 100bp steepness change, your portfolio will experience a loss.
Don’t complicate this stuff. It’s straightforward.
Also the answer mentions that for “A flattening 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 × –0.01 ×–8.7 × 0.333).”
I understand the -100 represents the decline in 100bp but can someone please explain:
(a) What is the 0.01 and why is there a negative sign in front of it?
(b) Why is there a negative sign in front of the effective duration of 8.7?
Thank you.
It’s 1 percent; that converts basis points to percent.
Because the 10-year steepness factor sensitivity is −1. As I wrote above, you multiply the change in steepness by the sensitivity at each maturity to get the YTM change at that maturity. It’s that simple.
Because when effective duration is positive bond prices go up when YTM goes down and vice versa.
You’re welcome.
so is the loss from steepness at the long end because the 30 year has a higher key rate duration, so the lower rate that results from flattening of the curve actually causes a loss because it has a negative sensitivity (rates drop, value should go up, but goes down because its -1, not 1, and it has highest duration so it overpowers the rest)?