If possible give brief explanation of how your ans will ensure breakeven (offset yield advantage of one bond over another) 1) 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. 2) Jack Hopper, CFA, manages a domestic bond portfolio and is evaluating two bonds. Bond A has a yield of 5.60% and a modified duration of 8.15. Bond B has a yield of 6.45% and a modified duration of 4.50. Hopper can realize a yield gain of 85 basis points with Bond B if there are no offsetting changes in the relative prices of the two bonds. Hopper has an expected holding period of six months. The breakeven change in the basis point (bp) spread due to a change in the yield on bond A is: A) 10.42945 bp due to a decline in the yield. B) 5.21472 bp, due to a decline in the yield. C) 5.21472 bp due to an increase in the yield. Similar to 1 but made some changes. 3) 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. What is the required basis point change in the spread needed to breakeven. A) 13.89474 bp increase in A B) 13.89474 bp decrease in B C) 18.08219 bp decrease in B
For #1: Take the yield difference, .0912 - .078=0.0132, then divide by the duration of the bond that the question asks about, which is B. So 0.0132/7.3=0.00180822. #1 = C Didn’t read 2 and 3 but I assume they use the same method.
The idea of breakeven spread analysis is based on Total Return which is price appreciation + income. Q#3 Bond A Yield = 9.12% Bond A Duration = 9.5 Bond B Yield = 7.8% Bond B Duration = 7.3 If you were to buy Bond A straight out and with no changes in spreads/yield curve over the course of 1 year you will have 9.12% - 7.8% = 1.32% more in total return based solely on income please note if it was 6months divided each on of those in half because you will only have half that income during the course of the year. So for your total return of B to equal that of Bond A the price appreciation will have to be 1.32% to make up for the difference in yield. Duration measures the change in price for parallel shift in the yield curve. We know right off that be that the yield curve has to decrease for the price to go up. For bond B a 1% change in yield will equal a 7.2% change in price but that is too much we only need a 1.32% change in price so… .0132/7.2 = .00181 or .181% or 18.1bps
a) c b) b c) answer A and C are similar?
@ BiPolarBoyBoston : Very nice explanation of breakeven spread analysis. Use of 7.3 duration for Bond B makes sense but why does schweser (also CFAI text) suggests to use HIGHER duration out of two bonds? When to use higher of the two duration rule?
^ I have no clue why you would want to use the higher duration bond. I used Bond B because it ask how much spread needs to change to make the two total returns equal. If Rakesh can post the answer and if its C we can confirm that this is the right way to do the problem.
Rakesh, Can you please post the published model answers to confirm if the following is correct? Q1) Answer = C Spread Widening = Yield Advantage / Duration of b = (9.12%-7.80%)/7.3 = 18.08219 bps Q2) Answer = A Spread Widening = Yield Advantage / Duration of a = (6.45%-5.60%)/8.15 = 10.42945 bps Q3) Answer = C Spread Widening = Yield Advantage / Duration of a = (9.12%-7.80%)/7.30 = 18.08219 bps Thanks!
Thanks everyone 1) C Price of Bond B increaes as yield decreases. Price rise of B will offset A’s yield advantage resulting in the same total return for both the bonds (Breakeven). Here Q is specifically asking to determine the change in yield of Bond B. 2) B Same explanation. Here Q is specifically asking to determine the change in yield of Bond A. 3) Not from QB. Same as Q1 with one change. This Q is not specifically asking to determine the change in yield of any one bond. I think ans is A as unless specifically asked, use higher duration & calculate the change in yield of higher duration bond as it will result in more conservative estimate & seems more appropriate. Summary. If Q asks you to determine the change in yield of any specific bond…use duration of that bond. If Q asks you to determine the change in spread without asking for the change in yield of any specific bond…use higer duration. Schweser ans 1) C was correct 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. 2) B was correct! By purchasing Bond B Hopper can realize a yield gain of (6.45 – 5.60) = 85 basis points if the yield spread does not increase. The yield advantage for the 6-month time horizon is (85/2) = 42.5 basis points to bond B. This is the yield advantage that must be offset in order to break even, hence we use 42.5 basis points in the formula to indicate the price of bond A will increase. Since we are looking at this from the standpoint of a change in yield on Bond A: (0.425/-8.15) x 100 = -5.21472, implying that the change in yield for bond A is -5.21472bp and the spread must increase by 5.21472 basis points. This change will result in capital gains for Bond A, which will offset B’s yield advantage.