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Question 22.
Based on Exhibit 1, for investors that purchased 10year U.S. notes, the spread widening in basis points that will wipe out the additional yield gained for a quarter is closest to:
A. 6.03 in Singapore
B. 8.09 in Japan
C. 13.48 in the UKAnswer:
B is correct. The spread widening equals the additional yield income per quarter (4.62 – 1.67) / 4 = 0.7375% for Japan, divided by the higher of the two countries’ durations, that is, 73.75 / 9.12 = 8.09My questions:
1. When the question asked “spread widening in bps that will wipe out the additional yield gained for a quarter”, what are they referring to? I thought any amount of increase in I/R would mean they are making a loss regardless of the level of rate? e.g. if they purchased a bank note at 4.62% yield and if the yield went up by 0.1% they would already be making a loss since rate up price down?2. if the investors purchased a 10year US notes, wouldn’t the “additional yield gained” refer to 4.62% why did they take the difference of Japan’s notes (1.67%) ?
3. Why did the answer divide 73.75 by the higher of the two durations?

@vincentt – I got this question wrong, my answer is A.
Let me attempt to rationalise my thought process (and partially answer your question), other Level 3 candidates @Jwa , @RaviVooda , @AjFinance , @Alta12 feel free to chime in!
1. When the question asked “spread widening in bps that will wipe out the additional yield gained for a quarter”, what are they referring to? I thought any amount of increase in I/R would mean they are making a loss regardless of the level of rate? e.g. if they purchased a bank note at 4.62% yield and if the yield went up by 0.1% they would already be making a loss since rate up price down?
This question is asking for comparison vs. a 10 year US note investment. So what it’s saying that assuming the investor bought a US 10 year note, what is the interest rate increase for US interest rate that will wipe out the quarterly yield gains for US notes vs. other countries’ 10 year note yields. It’s a way to assess the sensitivity of notes yield to interest rate (duration) when choosing which country’s note to invest. Hope this answers your question 2.
In fact, if you look at the answer choices, UK notes have a higher yield than US and I’d eliminate that option right away without any calculations, simply because they use the word ‘spread widening’ in the question, rather than spread “change”. Compared to UK notes, there’s no additional yield gain for US.
My answer was A actually, so I don’t fully understand why I got it wrong (yet)?
Here’s the thought process:
For Singapore, the additional quarterly US yield would be 0.47% (= (4.622.72)/4 ). For US and Singapore’s yield to be equivalent, I took 47 bps divided by 7.79 (US’ bond duration)= 6.03. This means that if US interest rates increases by 6.03 bps, the quarterly yield advantage of US 10 year note over Singapore becomes 0. Which is the reverse calculation of what i did above.
This relates to your 3rd question, I don’t fully get why it should be the higher of 2 duration either. If they are asking what % spread widening will eliminate the US yield advantage, it should be calculated based on US bond duration. Perhaps I’m missing something here?

@Sophie I didn’t get your explanation for #2 until i read the line “the quarterly yield advantage of US 10 year note over Singapore becomes 0.”
That’s exactly what I didn’t get at first. So they are just comparing the additional yield of US notes over other countries, that also means the answer UK should be wrong outright since there’s no advantage to begin with?
Thanks so much again! But yeah the higher of the two duration just doesn’t make sense i thought you would have to compare it with the ‘base’ which is US’s duration.







@vincentt , the concept here is that if we are trying to take advantage of carry trade, what kind of change in yield while evaporate those profits. so, when we see with respect to a country, we divide the yield difference with the respective country duration and not with the higher of the two.

@RaviVooda “we divide the yield difference with the respective country duration and not with the higher of the two.”
respective country being the country we are comparing with or the ‘base’ country?


Yes that’s what I thought @RaviVooda – so you agree with my analysis?


@RaviVooda @vincentt @sophie In the CFAI notes, it clearly states that you must divide by the higher duration of the two countries in your breakeven spread widening analysis (CFAI p. 135). I think by using the higher duration of the two countries, it will give you a more conservative answer.

@Alta12 ,@vincentt,@sophie
Consider this problem. I think this will give good clarityFor Canada: Local Bond Return:4.8%, Duration:3.4
For US: Local Bond Return:5.5%, Duration:6.2For a 6month time horizon, and ignoring the currency differential, what would be the breakeven change in yield between the Canadian and U.S. bonds?
A)Canadian bond yield decreases by 5.65 basis points.
B)Canadian bond yield increases by 10.29 basis points.
C)U.S. bond yield increases by 5.65 basis pointsSolution:
The yield differential for a sixmonth horizon is (5.5% − 4.8%) / 2 = 0.35%. Thus, either the Canadian bond yield must decrease (increase in price of the Canadian bond) or the U.S. bond yield must increase (decrease in price of the U.S. bond).
The breakeven yield change in basis points = 100 × (% change in price / −duration).
The change in the U.S. bond yield is 100 × (−0.35 / −6.2) = 5.65 basis points.
The change in the Canadian bond yield is 100 × (0.35 / −3.4) = −10.29 basis points.The calculation should be based on the bond with the higher duration which is the U.S. bond
My understanding is that what would be case from the perspective of a higher duration bond

Another question I have with me
Mary Brickland, CFA, is analyzing two different domestic bonds. Bond A has the longer modified duration at 9.50 with a yield of 9.12%. Bond B has a modified duration of 7.30 and a yield of 7.80%. Brickland has an investmentholding period of one year and expects a favorable credit quality change for Bond B to increase its market value during this time frame. If Brickland buys Bond B, what is the required basis point change in the spread (in terms of the required yield on Bond B) to offset Bond A’s yield advantage?
A)13.89474 bp due to a decline in the yield.
B)14.72190 bp due to an increase in the yield.
C)18.08219 bp due to a decline in the yieldAnswer: C
Bond A has a yield advantage of 132 basis points relative to Bond B. An increase in Bond B’s credit rating will increase its price and lower its yield. Since we are looking at this in terms of Bond B: (1.32/7.30) x 100 = 18.08219bp, the breakeven change in yield is –18.08219bp, or a decline in the yield on Bond B resulting in the widening of the spread between A and B by this amount. The increase in price for Bond B will result in capital gains for Bond B, which will offset A’s original yield advantage. Note that the CFA curriculum specifies using the bond with the greater duration which in this case would be bond A although as we have demonstrated in this question the bond with the shorter duration can also be used. Thus, if you are not told which bond to use to perform the calculation you should use the one with the greater duration.

Thanks for posting this question @RaviVooda – I got the same answer C and agree with the calcs as well. I don’t get this part though?!
Note that the CFA curriculum specifies using the bond with the greater duration which in this case would be bond A although as we have demonstrated in this question the bond with the shorter duration can also be used. Thus, if you are not told which bond to use to perform the calculation you should use the one with the greater duration.
Where in CFAI did they mention using the bond with greater duration? Just wanted to have a better context as it’s seems odd to have such a blanket statement that clearly requires thoughtful analysis and application.



The analysis ignores the impact of currency movements.
Yes this is right. And frankly I’m surprised at such statements from CFAI. Counterintuitive in fact for an exam that requires analysis. This statement pretty much invalidates any thinking you need for financial analysis of such questions. *OK rant over!*
:wThanks for adding this question to the discussion, now I get why they had such a random answer!

@RaviVooda I’m a little lost here, is the last sample question from CFAI? Is the conclusion to use the higher of the 2?
Which part in the question mention to use Bond B? Was it the part where it mention “if Brickland buys Bond B” ? Wouldn’t that be the same as my first question which means it should use US bond’s duration?


@RaviVooda both the materials seem very contradicting, but thanks for the info!

Hey guys, I know I’m a bit late to the party, but I believe there is a reason for using the higher duration (I’m talking about the original question here). In this case, we are talking about spread widening, which is relative. Of course, we don’t know whether the yield for Japan decreases or the yield for the US increases or a combination of the two. So there isn’t a single answer, as a spread widening of 10 basis points can have be by any combination of US yields and Japan yields changing. In the WORST CASE though, the yield change will be in the bond with the higher duration, and in that case it will wipe away your ‘yield advantage’ the quickest.
The point here is that they are asking for a single number, although the problem is in a sense ‘twodimensional’ as it depends on two inputs. Mathematically, the answer would be 0.7375% (the quarterly spread) = 9.12 * (increase in Japan yield) – 7.79 * (increase in US yield), so that given a change in one yield you can calculate the required change in the other to wipe away your advantage, and this will give you the spread. This is too complicated, so the answer simplifies this by (implicitly) asking “what spread change could in the WORST CASE wipe away the advantage?”
Hope this helps!


Hi @vincentt, I suppose you mean the question from April 18?
“Mary Brickland, CFA, is analyzing two different domestic bonds. Bond A has the longer modified duration at 9.50 with a yield of 9.12%. Bond B has a modified duration of 7.30 and a yield of 7.80%. Brickland has an investmentholding period of one year and expects a favorable credit quality change for Bond B to increase its market value during this time frame. If Brickland buys Bond B, what is the required basis point change in the spread (in terms of the required yield on Bond B) to offset Bond A’s yield advantage?”
It does seem inconsistent. I think in this particular case, the question states that there will be an event that affects the yield of Bond B. Then the question has this phrase as well “(in terms of the required yield on Bond B)”. This leads me to believe that they expect the yield on Bond B to change and not on Bond A – so it makes sense to use Bond B’s duration.
This does almostbutnotquite contradict the situation described earlier, as in that case we don’t know which of the two bonds will move to make the spread decline.

@mm12 ah.. i missed that “in terms of the required yield on Bond B”, initially I thought the key was to focusing on which bond the investors bought and use that as the ‘base’ e.g. “if Brickland buys Bond B”, and the first question “for investors that purchased 10year U.S. notes”.
Thanks again!



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