# CFAI - R23 - Practice Problems Q 22

Hey everyone I really struggled with this question, whereas all the previous Breakeven questions were fine.

Could someone please have a look and provide their opinion.

Exhibit 1 gives the expected difference in return between four pairs of 10yrs Govt. bonds.

Based on those differences, question 22 asks to identify the spread widening that would wipe out the yield advantage for the investor who purchased 10yrs Note. It then provides three options, two of which should be proved false.

We can deem answer ‘C’ false without calculations as the investor who purchased 10yrs Notes does not have a yield advantage vs the 10yrs Gilt (i.e. 10yrs Gilts yield more than 10yrs Notes).

As to the remaining two options:

Option A. :

the yield differential between US and Singapore for the 10yrs is

4.62(US) - 2.74(S.pore) = 1.88 per annum,

1.88/4 = 0.47 per quarter.

This quarterly positive yield spread of +0.47% would be wiped off if we had a negative price return of 0.47%. How much should the S.pore 10yrs bond yield increase vs the 10yrs US bond (i.e. how much spread widening) to produce a price decline of .47% for the S.porean bond? From the equation

-duration * %change in yield = %change in price,

we derive that

%change in price/-Duration = %change in yield

-0.47% / - 8.19 (higher of the two durations) = 0.057% (i.e. 5.7bps)

Answer A is therefore false as it suggests that the spread widening of the S.pore bond vs US 10yrs note that wipes out the yield advantage is 6.03bps ≠ 5.7bps

We are left with B which can be proved correct by going through the calculation as we did above.

Good luck, Carlo

@Carlo, thank you for clearing that up man! Very easy now that you have cleared it up.

Can I also ask is the reason why we always pick the higher duration between the 2 bonds we are comparing is because it makes sense to use the measure that is more sensitive to the interest rate change.

Hi Syd, I would rephrase that slightly by saying that we always pick pick the higher of the two durations unless the question directs us otherwise.

If the question is silent as to what bond is causing the spread between the two bonds to widen (it could be the Japanese bond’s required yield declining or the US T-Note going up) then choosing the higher of the two durations will give us the smaller measure of break-even yield change, i.e. the most conservative measure for our analysis and, yes, as you put it, it all ties back to the concept of higher duration higher sensitivity to interest rates change.

All the best, Carlo