# break-even analysis

Hi All,

I am having trouble with break-even analysis with global bonds. I do not undersatnd how the formula is derived and have trouble with calc. I am doing cfai eoc 22 on page 150 in CFAI book 4.

Can anybody explain this to me?

it seems straight forward enough…

Take the difference between the two 10 yr govt bond yields (the spread).

Divide this spread, by the larger of the durations of the 2 countries, in this case, from the table given, 9.12 duration of japan 10yr is larger than us 10 yr duration of 7.79…so go with japan.

You get your answer…but don’t forget to divide by 4 or multiply by 90/360 (if you must) to get the break even spread change over the quarter which is what the question specifically asks for.

As for understanding, the spreads on bonds can be different due to various, credit/supply reasons, you need to consider the duration with respect to that to work out how cheap or volatile that bond may be…Hence your “break even”.

the great thing with the multi choice is that when you run the calcs on the 3 answers, only one fits when you divide by 4 or allow for quarterly.

I am happy enough with questions like this, as you have an answer and it isn’t subjective or spurious, where you are not left with a “I suppose so”, “must remember how they think on exam day!”

I’ll give it a shot. I haven’t the CFA Institute books (yet), so I’ll create an example.

Suppose that a GBP investor owns a JPY-denominated bond. Compared to a comparable GBP-denominated bond, the JPY bond pays an extra 100 bp of yield, with a spread duration of 5.3 years. Over the next three months, how much can the spread widen before the JPY bond loses its advantage over the GBP bond?

If you recall the formula for (approximate) percentage price change from Level I, you’ll have this thing nailed:

%ΔP = -MDur × Δyield

The JPY bond offers an additional 25 bp of yield over 3 months, so, to lose its advantage, its price will have to drop by 25 bp compared to the GBP bond. Because we’re looking at relative prices (JPY bond vs. GBP bond) instead of absolute prices, we alter the Level I formula slightly:

Relative %ΔP = -SpreadDur × Δyield

Thus, we need to solve:

-25 bp = -5.3 × Δyield

Δyield = -25 bp ÷ (-5.3)

= 4.7 bp

Thus, if the spread on the JPY bond increases by 5 bp, it will lose its yield advantage over the GBP bond.

Notice that this formula is taking a total-return approach: the yield advantage (which may come from additional coupon or price appreciation or both) is being annihilated exclusively by a (relative) price change.

predition,

Thanks for your explanation. I got the calculations but did not get the reasoning behind picking Japan. What are we looking for? I understand that rates increase, and price goes down, but I cannot get the relationship here.

If you can elaborate alittle for me, I will appreciate very much.

Thanks a bunch buddy.

The reason you pick japan, is that it is the only one of the 3 calculations that correctly matches an answer given.

e.g, for sing , answer “a” they give 6.03

calc = 4.62 - 2.74 / 8.19

= 0.2295

1/4rly = .2295/4

= .0574

or 5.74 bp…so it’s not answer a with the 6.03 basis points they quote as answer “A”.

Read the question, they are not asking which break even is best, they are asking which one of these 3 matches the calculation of break even we have given as an answer.

Do the other 2 calcs above and it should make sense in what they actually asking.

magician,

Thanks for coming to the rescue. I am still not clear about one thing though. Spread is 100 bp already. So by widening you mean it still goes up? Doesn’t it give you more yield advantgae? I understand that price of that bond will decrease comparatively. May be I am confused between the yield and the chnage in spread?

Thanks again.

My bad. I did not see the answer. Thanks a lot for clearing that up.

Yes, by widening I mean that the spread increases: the market requires a (relatively) higher return on the JPY bond. To get that, the price of the JPY bond has to drop (relative to that of the GBP bond).

Over time – 5.3 years in my example – the value of the JPY bond will recover to the same level at which it would have been had the spread not widened; thereafter, it will once again produce a higher yield. (In all this, we’re assuming one spread change, then a constant spread thereafter. In the real world, of course, spreads change often.)

Why does the country beta not come into play? Shouldn’t you be concerned about how much the the foreign bond’s price changes from the domestic perspective?

deleted. Wrong assumption

Also have the same question as green 7157. This also came up in the 2014 Morning Exam, Question 7A. Why don’t we incorporate country beta into the breakeven yield analysis?