Bond sensitivity - Curious case

CFA Level I Fixed Income
#1

Hello All,

I was working through these two bonds. I am not sure why A has higher sensitivity to increase in YTM by 0.01%.

A: Initial Price = 101.886; Coupon rate = 5%; Annual; Time to maturity = 2 years; YTM = 4%; FV = 100

B: Initial Price = 100.0; Coupon rate = 6%; Annual; Time to maturity = 2 years; YTM = 6%; FV = 100

Now after 0.01% increase in yield,

A1: Initial Price = 101.8096; Coupon rate = 5%; Annual; Time to maturity = 2 years; YTM = 4.04%; FV = 100

B1: Initial Price = 99.8900; Coupon rate = 6%; Annual; Time to maturity = 2 years; YTM = 6.06%; FV = 100

Therefore, percentage change in price of A= 0.075% and that of B = 0.11%. This result is surprising because B’s sensitivity should be lower because it has higher coupon rate and YTM than A. I am definitely missing something. My results are wrong.

Can someone please help me?

Thanks in advance.

#2

The 0.01% increase is higher for bond B. The results are only comparable if you change the yield by the same absolute margin i.e. 100 basis points. Naturally, because bond B has a higher yield initially the margin that the yield increases from a 0.01% increase is higher than that for bond B so the comparison isn’t right.

#3

I didn’t quite get it. Why? 1bps = 0.01%. Hence, even if we consider an increase by 100bps, doesn’t it mean that I will increase the yield by 1%. Hence, new yields become (1.1)*4 = 4.4 OR (1.1)*6 = 6.6. Isn’t it?

Thanks

#4

Aah…Actually, I think I am making a mistake. bps is not a percentage change. It’s an additive change or an absolute change (or in mathematical terms-- modulus). Right?

#5

Yep

#6

from where did you get this exercise from?

I calculated the duration which is consistent with your answer:

Duration A: 1.9529

Duration B: 1.9433

what means that Bond B is less sensitive to changes in Yiel than Bond A.

I’m confused as well…