breakeven spread

CFA Level III
#1

hello guys,

if I buy a 4.6% YTM bond in the US with a duration of 6 instead of a japanese bond yielding 2% with duration of 8, and i want to know the breakeven spread, or in other words how much would rates increase so that i lose my excess yield of 4.6% over 2%

What looks logical to me is to divid the excess spread by the duration of the US bond of 6, (2.6% / 6 = 43 basis points) because an increase of 43 basis points in the US would strip me of the gains i would have made while holding the 6 duration bond.

in the CFAI text however, they use the “highest” of the 2 durations as the denominator (in this case 8), can anyone please care to explain why ?

thanks a lot!!

#2

Just assume a more conservative calculation . if you quote the break-even spread as 43 bps and the japanese bond increases by 43 bps , your loss is now greater than the 2.6% advantage you begn with . ( -0.0043*8=-3.44% , easily more than the 2.6 % yield advantage you began with ). So you are now in negative territory , not breaking even.

If you use the higher of the two durations , then theoretically the break-even spread is the worst possible before losses begin

#3

if you had the japanese bond to start with, you have not started with an advantage whatsoever, you have started with a disadvantage of -2.6% and it just got worse for you !! this is how i see it…

#4

In this case I believe you would need an increase in rates to break even on the two bonds. Because the Japanese bond has a higher duration it will increase in value faster as interest rates go up, thereby negating the excess yield of the US bond.

So the correct equation would look like this: (-.026)/-8 = .00325. (remember duration is negative in this formula!) This means you would need an increase in rates of about 32.5 bps to negate the excess yield you are earning on the US bond.

At least thats how I understand it!

#5

So you are holding on to the US bond, wihch has 2.6% of yield advantage over the Japanese Bond. To breakeven this yield advantage, you are looking at the increase in capital appreciation of the Japanese Bond has over the US Bond, as the higher duration of 8 vs 6, will add more appreciation when interest rates FALL.

Hence the use of the Japanese Bond duration of 8. 2.6%/8 = 32.5bps.

Therefore, a fall in interest rates of 32.5bps, will negate the excess yield from the US Bond over the Japnese Bond.

Thats my understanding