# breakeven analysis from sch. practice vol1.

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In schweser practice vol1. exam 3am, 9.D, the question asks for the size of the spread-widening that will make total returns equal over the 6 month period….

bond Y has yield 7.05% w duaration 6, bond X has yield 4.55% w duration 7.

schweser choose bond X to calculate the spd as follows
(7.05% - 4.55%)/2 / 7

I understand that it usually picks the bond with largest duration. but the question asks for spread-widnening scneario, it seems we should use the bond with highest yield? Am I wrong?

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you should use the bond that the quesiton frames it as. could be the bond with the higher yeild.

could be the bond with the lower yeild.

could be the bond with thel onger duration. could be the one with the shorter duration

the question will specify bond a or b. Jus tmake sure you compute apples to apples.

that is, if the question asks for an analysis of bond a….use the spread differential (positive or negative) over bond b and ALSO use bond A’s duration to calculate the break even yeild movement.

Its asking about Spreads Widening. Now this is referring to Single issuer spread b/c you are holding the other spread constant. Now since the Bond B (4.55% 7D) has the lower Yield, it is the Bond who’s spread will need to Widen inorder to make up for the Yield advantage. So [(7.05-4.55)/2]/7 = 17.857bps means that over the next 6 months the spread on Bond B must widen by 17.857bps to match teh Yield on Bond A.

Now if I asked how much will spread Narrow. YOu will use Bond A. [(4.55-7.05)/2]/6 = -20.83bps, which means Bond A’s spread must narrow by 20.83bps to lose its Yield Advantage and/or for Bond B’s Yield to equal Bond A’s yield.

Remember, we are considering only 1 of the Bond’s spreads not both. If they both Increased or decreased then it would be (7.05-4.55)/2/(7-6) = 1.25% would mean that Spreads overall would need to Increase/Decrease by 125bps to equate the two Yields.

no. Schweser is saying that the higher duration be used ALL THE TIME. Please check the question. No bond is specified, and you pick duration =7 from X, simply because it’s the higher duration.

- sticky

strikershank Wrote:
——————————————————-
> you should use the bond that the quesiton frames
> it as. could be the bond with the higher yeild.
>
> could be the bond with the lower yeild.
>
> could be the bond with thel onger duration. could
> be the one with the shorter duration
>
> the question will specify bond a or b. Jus tmake
> sure you compute apples to apples.
>
> that is, if the question asks for an analysis of
> bond a….use the spread differential (positive or
> negative) over bond b and ALSO use bond A’s
> duration to calculate the break even yeild
> movement.

- sticky

Well then I want to say that Schweser is Incorrect. There is no reason to “Always” use the bond with the higher duration…

bigwilly Wrote:
——————————————————-
> Well then I want to say that Schweser is
> Incorrect. There is no reason to “Always” use the
> bond with the higher duration…

and that would be correct

yuppers - Bigwilly and CSK know…

check out schweser page 103 question 18…you do a breakeven analysis, like i said, WITH BOTH BONDS….using both the smaller and larer duration.

agree with bigwilly, csk, and strikershank

you use duration based on how the question is framed, not just blindly follow “use higher duration” rule

strikershank Wrote:
——————————————————-
> yuppers - Bigwilly and CSK know…
>
> check out schweser page 103 question 18…you do a
> breakeven analysis, like i said, WITH BOTH
> BONDS….using both the smaller and larer
> duration.

if the question has been specific, of course you use the duration of the mentioned bond. What I am saying is that the question does not have to be specific with which bond every time (and I think this is more likely) and for this case, you pick the higher duration to work out a worse scenario.

- sticky

- sticky

the quesiton always will mention a bond. how much the yeild on one has to rise (aka price drop) or how much the other must fall (price increase) the nullify the yeild difference making total return equal (assuming a tax free scenario).

Straight from CFAI material:
Volume 4 page 38 (first paragraph after the example)
“Note that the breakeven spread widening analysis must be associated with an investment horizon and must be based on the higher of the two countries durations. The analysis ignores the impact of currency movements.”

Is everyone as confused on this as I still am?

Big Babbu, the reason for this probably is that break even analysis tries to find the minimal interest rate change that will wipe out yield advantange. This can be done at looking at higher duration bond

I was about to write the same although the logic that BW states here is very reasonable one..

Then I don’t understand what we are trying to discuss ….

comp_sci_kid Wrote:
——————————————————-
> Big Babbu, the reason for this probably is that
> break even analysis tries to find the minimal
> interest rate change that will wipe out yield
> advantange. This can be done at looking at higher
> duration bond

comp_sci_kid Wrote:
——————————————————-
> bigwilly Wrote:
> ————————————————–
> > Well then I want to say that Schweser is
> > Incorrect. There is no reason to “Always” use
> the bond with the higher duration…
>
> and that would be correct

- sticky

sticky, you are right. we need to define what we mean by “break even analysis”. Is it a minimal parallel shift in interest rate curve which will wipe off yield advantage? If it is then i presume yes, you have to take bond with higher duration

Guys, i am trying to understand it myself :) sorry if i confused anyone

And thus my confusion.
The logic presented in this thread is totally correct IMO.
BUT, the stupid CFAI text says you MUST use the bond with the higher duration. I’ve read it about 20 times trying to find if there’s any way to use the logic BW presented. But I can’t and if anyone can explain that the text is in any way referring to use the duration of the relevant bond please please please explain it to me.
So if it comes down to a MC question, what poison are you going to pick.

I am using the higher duration up in this piece!!!!

Do both, and if they both show up and it doesnt state which bond specifically then go with Highest Duration bond…. If its Essay, then use Highest Duration if it doesnt specify any other way

That’s how I will roll b/c if the CFAI text says so then that’s what i do :)

Ok I have another question on breakeven yield analysis, do you have to take into consideration the currency returns into the yield advantage calc? I am almost positive I have seen this both ways, I don’t understand why you would not take into consideration currency movements.

if you want the minimal rate shift you use the bond with teh higher duration (we’ve been over this with another thread)

but step away from the books for a second.

breakeven can happen in TWO directions, spreads widen or spreads narrow. And for a widen spread you use the bond with the bigger yeild. With spreads narrowing you’ll use the bond with teh smaller yield.

and one of these bonds will have a longer duration with the other. BUT if you want to find breakeve for a narrowing spread and the bond with the smaller yeild also has the smaller duration then you’ll get the question wrong if you use the bond with the bigger duration.

no, you don’t have to take into account currency returns. both Schweser and CFAI state this explicity.

strikershank Wrote:
——————————————————-
> if you want the minimal rate shift you use the
> bond with teh higher duration (we’ve been over
>
> but step away from the books for a second.
>
> breakeven can happen in TWO directions, spreads

I don’t think “breakeven spread analysis” is defined to cater for TWO directions. It’s only spread widening, which means either higher yield bond increasing yield, or lower yield bond decreasing yield.

Do you have any CFAI or Schweser page reference for this?

> And for a widen spread
> you use the bond with the bigger yeild. With
> spreads narrowing you’ll use the bond with teh
> smaller yield.

disagree. See above.

- sticky

- sticky

Q15.6 vol 1 exam III PM takes appreciation/depreciation return into consideration for breakeven analysis. i.e. the yield advantage is 1 percentage for a qtr period but that bond’s currency is expected to depreciate by 1.5 so they use +.5 for the other bond.

Striker! Yes! Thank you for bringing up that point!!! IF THEY WANT MINIMAL SPREAD WIDENING, then YES use LARGEST DURATION. That is probably why CFAI says to always use Largest Duration. If they just said how much does Bond A need to widen, then use Bond A’s duration, or if it says Bond B need to Widen then us Bond B’s.

Striker I completely forgot about that little tidbit when they ask those questions, got too caught up :)

THANKS! Now I owe you a pint.

I agree with the majority here.

The way I look at this.

Bond X yields 4.55%, duration 7
Bond Y yields 7.05%, duration 6

The spread between the two yields in 2.5% with Y plotting over X.

After the spread(this is spread between X and Y, and not between either of them over the Treasury yield) widens, one of the following is true:

1) X’s yield stays the same, Y moves up. You need to use duration for X.

2) Y’s yield stays the same, X moves down. You need to use duration for Y.

3) Both X and Y move by different amounts, the net of which is a higher spread between X and Y. Here you need to use both durations. But, you only have one equation and two variables. There can be a range of solutions for how much X and Y move.

fsa-sucker, CFA

I already submitted this problem to Schweser last week. Of course they haven’t responded at all to my inquiry… I want my points back…

fsa-sucker Wrote:
——————————————————-
> I agree with the majority here.
> The way I look at this.
>
> Bond X yields 4.55%, duration 7
> Bond Y yields 7.05%, duration 6
>
> The spread between the two yields in 2.5% with Y
> plotting over X.
>
> and not between either of them over the Treasury
> yield) widens, one of the following is true:
>
> 1) X’s yield stays the same, Y moves up. You need
> to use duration for X.

I think you should use duration of Y.

> 2) Y’s yield stays the same, X moves down. You
> need to use duration for Y.

Duration of X should be used.

> 3) Both X and Y move by different amounts, the net
> of which is a higher spread between X and Y. Here
> you need to use both durations. But, you only have
> one equation and two variables. There can be a
> range of solutions for how much X and Y move.

I think both CFAI and Schweser try to avoid discussing this scenario, and sticking to the assumption that one interest rate is fixed. Breakeven spread analysis is for comparing 2 international bonds (in 2 different interest rate environments) — check LOS (29.j). So it’s not a bad assumption to say one bond has i change but the other doesn’t.

- sticky

- sticky

- sticky

oops. got that switched. you are right.

fsa-sucker, CFA

I was about to write something similar to what fsa-sucker said above, but let me throw a numeric example to prove his point (with which I agree after the correction on switching X and Y).

Lets say we have Country A and Country B, with respective Bond A and Bond B. Bond A has duration of 10 and yields 5.0%, Bond B has duration of 20 and yields 6.0%.

So from this the difference in yields is 100 bps. So we go ahead and purchase higher yielding bond, Bond B

What should happend to eliminate this yield advantage of Bond B?

1) if yield on Bond A decrease by 10 bps, Bond A will increase in price by 1% (or will yield additional 100 bps; 10 bps * 10 duration = 100 bps); since we didn’t buy Bond A, we don’t get any benefit from this price increase but it tell us that tells us that decline in yields by 10 bps is a breakeven point.

2) if yield on on Bond B will increase by 5 bps, Bond B will decrease in price by 1% (or will yield negative 100 bps; 5 bps * 20 duration = 100 bps); this derectly affetcs us, since we are holding Bond B and increase in its yield by 5 pbs eliminates our yield afavntage, so its also breakeven point.

In the first case the spread widened by 10 bps, creating a breakeven point and in the second case spread widened by 5 bps also creating a breakeven point.

Spread could also widen as a result of changes in yields of both bonds, then as fsa-sucker said, you would use both durations, and by having one equation with 2 uknowns there will a range of possible solutions.

Now lets use this “faulty” logic of using just the bond with higher duration.

From this logic we would take Bond B duration of 20, do 100 bps / 20 = 5 bps; and “wrongly” claim that the spread has to widen by 5 bps to eliminate the yield advantage.

What happens if the yield on Bond A declines by 5 bps. That would satisfy “widen by 5 bps claim”, however in such an event, the price of Bond A would only increase by 50 bps, price of Bond B won’t change.

And how can you claim that this gives you a breakeven situation? The bond A is now yielding 5.5% (5% old yield + 50 bps price improvement), Bond B is still yielding 6%. So, you still would prefer Bond B, hence the “widening of spread by 5 bps” blanket claim doesn’t produce a breakeven solution.

To conclude, the only statements that can be made in this example are:

1) Breakeven spred is 105 bps (5 bps spread widening) as a result of increase in yield on bond B by 5 bps.

2) Breakeven spread is 110 bps (10 bps spread widening) as a result of decrease in yield on Bond A by 10 bps.

3) There maybe multiple combinations of this statement, but for example: Breakeven spread is 106 (6 bps spread widening) as a result of increase in yield on Bond B by 4 bps and decrease on Bond A by 2 bps.

The math for statement #3 is: 4*20 + 2*10 = 100 (i.e., price decline on Bond B is 80 bps, price improvement on Bond A is 20 bps, and boh of this events combined have the same effect of eliminating yield advantage of 100 bps).

I posted this example on breakeven spread last night to clarify the confusion people had.

hope it helps

Got an answer from the Schweser Team:

>
Dear xxxx,

The question states to use Bond X versus Bond Y. For the exam you must be prepared to use either bond to calculate your answer.

Regards,
Schweser staff
>

Edit: Someone needs to post the excerpt from the question… I don’t recall the exact wording they used.

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