Breakeven spread analysis Q

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Steve Kiteman, CFA, manages a domestic bond portfolio and is evaluating two bonds. Bond A has a yield of 6.42% and a modified duration of 11.45. Bond B has a yield of 8.25% and a modified duration of 9.50. Kiteman has an expected holding period of three months. The breakeven change in the spread due to a change in the yield on bond B is?
 
(8.25%-6.42%)*(3/12)/(9.5)=0.048%
So the breakeven change in the spread of bond B is +0.048%.
 
4.82bps?
threw me off when you said “change in the yield on bond B”.
so i went:
(8.25% - 6.42%) / 4 = .4575
.4575 = 9.50x
x = .0482
 
This is a typical question that throws more numbers than we need.
 
Both of you are correct. I divided it by 11.45. I thought I read it somewhere that the rule was to divide it by the bigger of the 2 modified duration, no?
 
divide it by the highest duration only when not indicated which to use, as in this one, where it said to use bond B…
 
and of course the movement that eliminates the advantage will be a widening in the spread of Bond B. since the capital loss will eliminate the spread advantage.
 
I fell into using the larger duration trap too. I had better review this section.
 
Reviving this thread. See question # 22 on page 154 of book 4 CFAI - I would type the question but it involves a table.
They, judging by the answer, are using the larger duration. What confuses me on this question is the explicit statement “based on exhibit 1, for investors that purchased 10-year u.s. notes, the spread WIDENING in basis points that will wipe out the additional yield gained for a quarter is closest to….”
Because they used the word widening, I interpret that to mean you take whichever bond is on the yield advantaged side, and use the duration of that paritcular instrument since we are trying to solve for the widening to make them equal. This means for U.K. which has a yield advantage, we use the U.K duration, and for JPY and Singapore, we use the US duration (U.S. has the yield advantage therefore must be subject to the widening to make spreads equal).
However the answer uses JPY duration but the numerator is still the U.S. yield advantage – wouldn’t this produce the amount of necessary NARROWING in JPY spreads to offset the U.S. yield advantage rather than the necessary WIDENING in U.S. spreads?….
To illustrate, if U.S. spreads (quarterly advantage of 0.7375% and duration on U.S. issue of 7.79) increased by the answer of 8.09 basis points, then the effect would be 8.09*7.79= 63.021 basis points decline in value, which is still 10 or so basis points shy of fully offsetting the yield advantage.
 
This question does not consider the currency effect and the duration may be not adjusted, but I don’t know why.
With regard to JPY bond, the beakeven yield change: [(1.67%-4.62%)/4]/9.12=-8.09bps.
So, the yield advantage of US notes will be wiped out if the JPY bond’s yield decrease by 8.09bps. The yield spread between the US notes and JPY bond is widening to breakeven.
The investor BOUGHT 10-y US notes, which does not have a yield advantage over UK bond. So UK bond is ruled out, I think.
 
I agree with your logic on the UK bond - however since the question specifically says what must the amount of WIDENING be, doesn’t that cause an issue for JPY? As you said, the JPY bond yield must fall, not rise, in order to catch up to USD.
I suppose maybe because it if a fixed rate and not a spread tht “widening” in this sense means the spread between the two gets larger.
In any event, when we are working these problems, isn’t the general rule of thumb that whichever bond’s duration you are using to calculate the breakeven spread change is going to give you the necessary move for THAT bond, and not the one it is being compared to?
So what im saying is that if you calculate using the JPY duration, you are solving for the narrowing or widening that must occur to offset the JPY and only the JPY spread differential, and that number is not transferable to the other bond it is being compared against (in this case USD) because to do that you would need to use USD’s duration.
 
jap yield is 1.67, US yield is 4.62 - so jap bond yield must widen shouldn’t it?
they always state use the bond with the higher duration …
 
To make the spread widening, yield of JPY bond has to fall or yield of US note has to rise. Adding a minus sign may help a lot.
 
I am not understanding what you are trying to say.
The way I look at it … is ….
right now Jap Bond has a 1.67% yield.
If it should increase to the US BOnd yield of 4.62% - the yield must WIDEN. (in terms of becoming MORE).
by how much? 4.62 - 1.67
now why are you and mark both saying the yield must FALL for it to WIDEN?
are you comparing the yield to some benchmark? Or are you thinking of it as a Spread?
 
cpk, yes, it [Q22] asks for the “spread widening in bps”.
 
please explain this statement …
To make the spread widening, yield of JPY bond has to fall or yield of US note has to rise
 
The text is poorly worded on this questoin IMO. They should have not used the word widen, and should have simply said “for the following bonds, the yields must either increase, or decrease, by x amount”
They use the word widen despite it not really being a spread to any benchmark. Semantics aside, when I think of widening spreads, I think of falling prices and increasing interest rates. That is why I have an issue with this problem. The wording makes it seem like you have to pick one of the 3 bonds and show how much yields in that country must increase (“widen” for their purposes) to offset the yield advantage earned. Since U.K is the only bond at an advantage to the U.S., we know that since we are working with “widening”, we must find out how much the U.K interest rates must INCREASE…. therefore we use the U.K.’s duration, and not the largest… at least that is what would make sense to me because if you try to apply the dollars duration using the breakeven number you get, it doesn’t work.
Now the text uses JPY’s duration because it is the largest – and thats the problem. They said how much must spreads on these particular bonds “WIDEN”, yet then they reference the JPY bond specifically…. but the JPY is at a yield disadvantage, so yields in JPY must decrease, or NARROW in order to catch up to the USD, not WIDEN.
This is hard to word properly, I am doing my best…. I do believe this is either an error or a very poorly worded question
 
Now the text uses JPY – and thats the problem. They said how much must it “widen”, and they reference the JPY bond specifically…. but the JPY is at a yield disadvantage, so yields in JPY must decrease, or NARROW in order to catch up to the USD.
Specifically - how is this statement being arrived at.
Japanese yield is at 1.67% - right
US is at 4.62
Is JPY yield is to reach the US Yield - it must widen mustn’t it?
Why are you and tulkuu saying it must fall? That I cannot understand …
 
I think the confusion is from the yield and total return.
1. The yield of JPY is only 1.67%, which is a disavantage in yield, but it’s also means that JPY bond is more “expensive” than the US notes.
2. Although the yield is not the total return, the total return of JPY bonds is lower than that of the US notes.
So, the fall of JPY yield [interest rate] will lead to the increase of the JPY bond price, and so does its total return.
 
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