Bank question help - could someone please explain this question?

Mary Brickland, CFA, is analyzing two different domestic bonds. Bond A has the longer modified duration at 9.50 with a yield of 9.12%. Bond B has a modified duration of 7.30 and a yield of 7.80%. Brickland has an investment-holding period of one year and expects a favorable credit quality change for Bond B to increase its market value during this time frame. If Brickland buys Bond B, what is the required basis point change in the spread (in terms of the required yield on Bond B) to offset Bond A’s yield advantage? A) 13.89474 bp due to a decline in the yield. B) 14.72190 bp due to an increase in the yield. C) 18.08219 bp due to a decline in the yield. Your answer: A was incorrect. The correct answer was C) 18.08219 bp due to a decline in the yield. Bond A has a yield advantage of 132 basis points relative to Bond B. An increase in Bond B’s credit rating will increase its price and lower its yield. Since we are looking at this in terms of Bond B: (1.32/-7.30) x 100 = -18.08219bp, the breakeven change in yield is –18.08219bp, or a decline in the yield on Bond B meaning interest rates are going to go down by this much resulting in the widening of the spread between A and B by this amount. The increase in price for Bond B will result in capital gains for Bond B, which will offset A’s original yield advantage. Note that the CFA curriculum specifies using the bond with the greater duration which in this case would be bond A although as we have demonstrated in this question the bond with the shorter duration can also be used. Thus, if you are not told which bond to use to perform the calculation you should use the one with the greater duration.

I chose A as well, is this a CFA question? Although it does say: (in terms of the required yield on Bond B) That’s the trick I guess.

So how does the formula work. Can someone explain in a bit more detail please?

(9.12% - 7.80%) / 7.3 = 132bps / 7.3 = 18.08 bps (in terms of the required yield on Bond B, so the yield difference is divided by the duration of B). This is not mentioned in CFAI text. I don’t know why Schweser does this.

Thanks for the quick response, but one thing I don’t understand is that why does it divide the difference in yield by the duration?

Bond A has a yield advantage of 132bp over bond B. Therefore if we hold bond B, for the return from bond B to equal Bond A, bond B price would have to increase by 132 bp. since %change in bond price=-(duration)(change in yield) therefore change in yield required for 132bp change in b price is =%change in bond price/-(duration)=132bps/7.3