Breakeven Spread Analysis Question

[jbct91]

This is found in SS 11 (Schweser) Reading 22, FI PM II:
With breakeven analysis, we’re trying to find the shift in interest rates that would generate a capital loss sufficient to eliminate the yield advantage of a foreign bond.
I understand how it works, but am getting hung up on terminology in the Schweser book.
The formula is: Chg in Yield = [Chg. in Price / - Duration]
Two questions:
1.) The book plugs in the nominal yield advantage in the “Chg. in Price” part of the formula. Why is the change in nominal yield spread the change in price?
2.) Is the nominal yield also the yield to which the end result of the calculation is applied (Chg. in Yield)?
Apologies if this is scatterbrained. Thanks for any help here.

 

[cokemicho]

jbct91 wrote:
This is found in SS 11 (Schweser) Reading 22, FI PM II:
With breakeven analysis, we’re trying to find the shift in interest rates that would generate a capital loss sufficient to eliminate the yield advantage of a foreign bond.
I understand how it works, but am getting hung up on terminology in the Schweser book.
The formula is: Chg in Yield = [Chg. in Price / - Duration]
Two questions:
1.) The book plugs in the nominal yield advantage in the “Chg. in Price” part of the formula. Why is the change in nominal yield spread the change in price?
2.) Is the nominal yield also the yield to which the end result of the calculation is applied (Chg. in Yield)?
Apologies if this is scatterbrained. Thanks for any help here.

Ok, lets do this slowly together
Suppose I have Bond1 and Bond2,
We both know that
“Chg in price of Bond1” = - Duration1 * “Chg in yield Bond1”
“Chg in price of Bond2”= - Duration2 * “Chg in yield Bond2”
(This may make you remember level 1 & level 2 aproximations )
Suppose Bond2 holds a yield advantage over Bond1, then, i need to know the “Chg in yield Bond2” that makes the price of Bond2 equal to the price of Bond 1 ( right??)
therefore i need
“Price Bond2” - “Chg in price of Bond2” = “Price Bond1”
=> “Price Bond2”- (-Duration2)*”Change in yield Bond2” = “Price Bond1”
=> Duration2* “Change in yield Bond2” = -“Price Bond2”+”Price Bond1”
=> “Change in Yield Bond2” = (“Price Bond2” - “Price Bond1”) / -Duration2
If the bonds par value is 100, then thats why in the textbook they use the yield difference
Voila! I think we did it correctly. Hope this helps you understanding the topic,
Jorge

 

[jbct91]

alright so it has to do with the par value. Thanks Jorge!

 

[hei.so]

Question from Wiley:

A fixed-income investor is comparing two bonds, details of which are listed below:

• A 5-year French government bond with 4% coupon, yield of 3.5%, and duration of 4.3

• A 7-year German government bond with 2% coupon, yield of 2%, and duration of 6.5 If the investor has a 3-month time horizon, the minimum breakeven spread widening for these two bonds is closest to:

A. 6 basis points.
B. 9 basis points.
C. 23 basis points.


Answer:
If the manager buys the French bond, she will expect to earn a yield advantage of (3 / 12) × (3.5% – 2%) = 0.375% or 37.5 bps over 3 months versus a holding in the German bond. The minimum breakeven spread widening that would erase this yield advantage would be a movement in the yield of the highest duration bond, that is, the German bond yield falling by ΔY such that 6.5 × ΔY = 37.5 bps.
This implies that ΔY = 37.5 bps / 6.5 = 5.77 bps

—

Question about which duration to use. In cokemicho’s answer, you used the duration of the bond with the yield advantage. In the question above, the duration of the highest duration bond is used, which is the one with the yield disadvantage. Why?

 

[Blackou]

It is clearly stated in the CFAI curriculum that you always have to use the highest of the two durations .
Page 136 of reading 22:
“Note that the breakeven spread widening analysis must be associated with an investment horizon and must be based on the higher of the two countrie’s durations.”

 

[Blackou]

edit : double post