Reading 23 - Question 20

[Galli]

Apologize in advance for the multiple questions from this reading, i’m struggling mightly!
This question asks:
“Based on exhibit 1 and assuming interest rates remain unchanges, which bond will have the highest hedged return.”
The hedge part was confusing. I initially thought the question was looking for some sort of violation of the forward premium/discount supplied in Exhibit 1. I attempted to capture the expected return on the 1-year interest rate +/- difference in expected Fx rate changes via CIRP.
Turns out I was supposed to look at the local spread between the RF and the 10-year and see which country would have the highest return. Wait what? How would I know (from the info provided) the return was the spread between the 1-year interest rate and the 10-year? The framing of the question and the information provided seemed pretty weak
How did you guys/gals address this question? How do you know they’re just looking at the market with the higest local return - return being the spread between the RF and the 10-year? Why do we not address the implied appreciation/derpeciation differences vs. the forward rate?

 

[myriam2222]

You don’t have to bother about fx rate changes as such because you are looking at hedged returns here. Regarding fx, you just have to bother about the forward rate of the hedged you entered in.
Now remember that hedged returns = foreign bond return in local currency terms + forward discount or premium (1)
And forward discount or premium = domestic rf rate -local risk free rate (2)
Replace equation (2) in equation (1) and you will see that to compare the hedge returns of the 3 countries you just need to compute for each if them “foreign bond return in local currency terms - local rf rate”. You don’t need the input of the us rf rate to answer the question because it is the same for each country’s hedged return computation and you just want to compare the results.
The 1 year interest rate here is used as a proxy for rf rate (they give you that info). This is key.
Sorry not very readable. I am writing from a smartphone…
Hope it made sense.
I will call it a day! Looking forward to reading some new posts tomorrow. Cheers

 

[myriam2222]

Ps: so the return IS NOT the spread between 1y and 10y, it’s just that you don’t need to compute the return to answer the question (ignore us rf rate)

 

[Galli]

myriam2222 wrotes: so the return IS NOT the spread between 1y and 10y, it’s just that you don’t need to compute the return to answer the question (ignore us rf rate)

Thanks for the detailed reply.
Can you expand on why the return is not the spread between the 1-year RF rate and the 10-year yield? The answer uses this spread to justify the highest return across the countries.
Thanks in advance

 

[myriam2222]

The hedged return is
foreign bond return in local currency terms + domestic rf rate - local risk free rate
You get this from combining equation (1) and (2) from my previous post (but you have all of this in the CFAI course on hedged returns.)
So here, hedged return is
foreign 10-year yield + us rf rate - foreign 1 year yield
(because 1 year yield is used as the proxy for rf rate).
So in order to determine which country offers the highest hedged return, you just need to determine for which country “10 year yield - 1 year yield” is the highest. Of course you can make the full hedged return computation by adding the us rf rate to your computation.
But if A + C> B + C then A > B and vice versa
You don’t need the US risk free rate (C) to actually answer the question.

When I first read your post I had no clue. To solve it I simply opened the course on hedged returns and applied the formula. I tried to find in the question the items that corresponded to each item of the formula. And I figured it out. I would recommend you go through these steps as well. You will find it fairly easy and I am sure it will all make sense

 

[Galli]

Thanks, all of what you are saying makes sense.
I adjusted the formula:
foreign 10-year yield + (us rf rate - foreign 1 year yield)
OR
Foreign 10-year yeild + (forward premium/(discount) = Total hedged return.
Since the investor has the us rf rate in all of his hedged investments, you remove it as this variable essentially cancels out across the comparisions. That’s fair enough to me but i’ll likely just use the full formula.
I think this is exactly what I was trying to solve for but got a different answer when using the forward/discount premiums supplied in the 3rd row of the exibit.
————————————————————————————————————
Supplied expected 1-year UK Forward Premium/Discount .10
UK forward Premium/Discount via 1-year rates = 5.30 - 6.24 = -.94
Therefore the actual UK hedged return (using calculated premium/discount from supplies 1-year rates) = 5.04 - (5.3-6.24) = 6.24 hedged return
versus
5.04 - .10 (forward premium supplied)) = 5.04% return
Can someone justify the logic above? Am i missing someting here between the two forward premiums? Shouldn’t the UK .10 supplied premium be the same as the one calculated using CIRP? If they’re different, doesn’t that mean the investor can take advantage of the mispricing which would enhance the overall hedged return in question?

 

[myriam2222]

the 1 year forward premium / discount is of no help here. They are just providing this info in the question to trick you into using it. This is the 10 year forward premium /discount you are interested in because you invest in a 10 year bond

 

[Kirtika]

example 17 pg 252 has a similar situation. higher the risk premium in a country higher the fully hedged return in that country.

 

[Galli]

myriam2222 wrote:
the 1 year forward premium / discount is of no help here. They are just providing this info in the question to trick you into using it. This is the 10 year forward premium /discount you are interested in because you invest in a 10 year bond

They’re not using a 10-year forward premium / discount though. Row 3 of the exibit is the 1-year premium/discount which should be the same as doing a premium/discount calculation via CIRP.

 

[Galli]

Kirtika wrote:
example 17 pg 252 has a similar situation. higher the risk premium in a country higher the fully hedged return in that country.

Thanks. I saw that example as well but thought the question was different since they specifically reference a local risk-premium return versus a bond return in hedged local currency. Bond return in this case being nominal total where risk-premium return would be adjusted. I digress… sigh

 

[myriam2222]

Galli wrote:
They’re not using a 10-year forward premium / discount though. Row 3 of the exibit is the 1-year premium/discount which should be the same as doing a premium/discount calculation via CIRP.

Yes I see your point. I guess you are right.
The only thing is, they are saying “consider the 1 year yield is a proxy for rf rate” and they don’t say rf rate on which period. It seems quite absurd that the 1 year yield would be a good proxy for the 10 year rf rate, you would rather think 1 year here of course, but in the absence of any other info that would give us a rf rate, and since we need it, if I was at the exam and the question was that misleading, I would use this one.
Now I agree that the way this question is asked does not seem rigorous at all.

 

[Galli]

myriam2222 wrote:

Galli wrote:
They’re not using a 10-year forward premium / discount though. Row 3 of the exibit is the 1-year premium/discount which should be the same as doing a premium/discount calculation via CIRP.

Yes I see your point. I guess you are right.
The only thing is, they are saying “consider the 1 year yield is a proxy for rf rate” and they don’t say rf rate on which period. It seems quite absurd that the 1 year yield would be a good proxy for the 10 year rf rate, you would rather think 1 year here of course, but in the absence of any other info that would give us a rf rate, and since we need it, if I was at the exam and the question was that misleading, I would use this one.
Now I agree that the way this question is asked does not seem rigorous at all.

Yeah I think im just worried it didn’t immediately occur to me they were looking for the local return premium… Going to have to be extra cautious on this one i guess.
Thanks for the help myriam!

 

[myriam2222]

Galli wrote:
Yeah I think im just worried it didn’t immediately occur to me they were looking for the local return premium… Going to have to be extra cautious on this one i guess.

No no, don’t think about it this way. When you have such a question, don’t think in terms of local return premium because that’s not the way to go. It is more a coincidence here (because the local rf rate they say you need happens to be the local 1 year local premium).
When you have a question on hedged or unhedged returns, go to the basic formula given in the course. Then see where you can find the right figure for each component of the formula separately (local rf rate, domestic rf rate, and foreign return in local currency) or by grouping some elements (local rf rate and domestic rf rate grouped into forward premium / discount). You had the right approach when you tried answering the question. I agree that the practice problem is misleading. Normally the difference in rf rates you are looking at (to define the forward premium or discount) should be over the period of the bond (here 10 years).
I think you got it. No worries for the exam on this topic for you.
Cheers

 

[Galli]

thanks again Myriam!