Comparative Advantage

[carzymathematician]

I am having a bit of a problem working from the comparative advantage argument to setting up the swap esp Q23 in Ch 7 (Hull). If someone can explain how to reason through this question, I'd appreciate it!

[goodluck]

I am having a bit of a problem working from the comparative advantage argument to setting up the swap esp Q23 in Ch 7 (Hull). If someone can explain how to reason through this question, I'd appreciate it!

could you, please, post the problem here for those who don't have the book with them at the moment? Thanks.

[_BullDog_]

What study notes are you using?

[yanz]

I haven't done all the problems in Ch 7 yet, but my issue is that there needs to be a whole lot of specification to come up with a unique solution. So if we were given such a problem on the exam, there'd be a whole range of answers we could put down:
1. you can spread the gain differently between the companies (& potentially an intermediary) - ie, not evenly - and
2. you can also shift the spread between the fixed and floating rates - ie, make fixed & floating rates both higher or lower

It's the second point that bothers me most because having a swap that's x% fixed for LIBOR + y% means you can pick any x and y as long as their difference = some constant (based on problem). Am I missing some inherent assumption?

[TiderInsider]

It's the second point that bothers me most because having a swap that's x% fixed for LIBOR + y% means you can pick any x and y as long as their difference = some constant (based on problem). Am I missing some inherent assumption?Usually the problem specifies that both parties are equally better off. If I require a floating rate loan and I can go out and borrow LIBOR + 20bps, but I have a comparitive advantage in fixed, there's a good chance I'm not going to swap for floating unless I get a deal. In other words, I'm not going to let the other party benefit 50 bps while I only get 1 bps (that's an extreme example). The argument of comparitive advantage says that both parties have something to gain by borrowing in the market where the advantage exists.

I don't think a swap problem has shown up on C8 yet, but I'm sure if the problem didn't specify that both parties should be equally better off after the swap and you explicitly stated what you were assuming, I'd think you'd get a decent number of points.

[yanz]

I guess what I'm saying is that your clarification goes to my #1, while my #2 is a bit different.

For example, say you can borrow fixed at 10% and float at LIBOR + .5% and you nead a float but your comparative advantage is in the fixed, so you'll get the fixed loan and enter into a swap where you pay float (LIBOR + y%) and get fixed (x%). Now, just to make this simpler so I don't have to make up numbers for the other party, assume that you already know that the total gain to the two parties is 1% split evenly, so each gains .5%. So you must gain .5% by entering into the above transactions over entering into a float loan. So you set up the following equation:

-10% + x% - (LIBOR + y%) = - (LIBOR + .5%) +.5%
in other words, by paying the fixed loan and entering into the swap, you save .5% over paying the float loan.

solving that gives x% - y% = 10% so as long as that's true, it appears you can pick any x and y for the swap and you'll still gain your .5%.

So, for example, you can have a swap of 10% fixed and LIBOR + 0% float, or you can have 10.3% fixed and LIBOR + .3% float. There appear to be a whole lot of possible solutions. And (in case you're wondering) the ambiguity is not caused by the lack of info/equation for the other party, because that equation will also give you x - y = whatever, so it's not like you can solve 2 equations in 2 vars.

So, am I missing something?

[Hayden]

you can have a swap of 10% fixed and LIBOR + 0% float, or you can have 10.3% fixed and LIBOR + .3% float Aren't these outcomes identical?

[Car'a'carn]

I guess what I'm saying is that your clarification goes to my #1, while my #2 is a bit different.

For example, say you can borrow fixed at 10% and float at LIBOR + .5% and you nead a float but your comparative advantage is in the fixed, so you'll get the fixed loan and enter into a swap where you pay float (LIBOR + y%) and get fixed (x%). Now, just to make this simpler so I don't have to make up numbers for the other party, assume that you already know that the total gain to the two parties is 1% split evenly, so each gains .5%. So you must gain .5% by entering into the above transactions over entering into a float loan. So you set up the following equation:

-10% + x% - (LIBOR + y%) = - (LIBOR + .5%) +.5%
in other words, by paying the fixed loan and entering into the swap, you save .5% over paying the float loan.

solving that gives x% - y% = 10% so as long as that's true, it appears you can pick any x and y for the swap and you'll still gain your .5%.

So, for example, you can have a swap of 10% fixed and LIBOR + 0% float, or you can have 10.3% fixed and LIBOR + .3% float. There appear to be a whole lot of possible solutions. And (in case you're wondering) the ambiguity is not caused by the lack of info/equation for the other party, because that equation will also give you x - y = whatever, so it's not like you can solve 2 equations in 2 vars.

So, am I missing something?

You are right. If there is a swap problem on the exam I will make a table with the cash flows similar to the ones in JAM. Hopefully this will be enough.

[yanz]

Aren't these outcomes identical?

outcome to the companies - yes. defining a swap - no. that is precisely my point - if you're asked to create a swap, it seems as though any range of possibilities exists, so my concern was whether [if such a Q came up] the graders would accept multiple "answers"...

[Hayden]

defining a swap - no. ... [if such a Q came up] the graders would accept multiple "answers"...

Since there are (at least generally) netting provisions in swaps, I still say they are identical and there is only correct answer. However, if you do add a couple bps to both sides of the swap I could not see how the grader could count that as incorrect.

[_BullDog_]

I would think that as long as they are borrowing at the terms available to them (as defined in the problem) then you would be okay. Also it is probably best to use 10/libor instead of 10.3/libor+.3. Although I would think both are correct.

[yanz]

well, for currency swaps, you don't have the issue since you know that each party needs to receive from the swap exactly what they're paying out (or else they face exchange risk), but for a normal swap...

Anyway, thanks for the faith.

[flyingmoon]

I am having a bit of a problem working from the comparative advantage argument to setting up the swap esp Q23 in Ch 7 (Hull). If someone can explain how to reason through this question, I'd appreciate it!

Same here, I tried to understand the concept of the question. Since both X and Y cannot borrow money from their foreign country, I don't think we can use the comparative advantage concept for this case.
If I am wrong, please correct me. All we have to do is to maintain the difference of 1.5% between X and Y no matter what the net rates for X and Y are. For example, if X is 11% then Y should be 12.5% and the intermediary's profit should be 0.5%. If so, I think there should be many scenarios other than above. What do you think?

[carzymathematician]

Ok, here's da question for those who want to take a stab at it while on their lunch break! ;)

Company X is based in the UK and would life to borrow 50mil at a fixed rate for 5 yrs in US funds. Because the co. is not well know in the US, this has proved impossible. However, the co. has been quoted 12% p.a. on fixed 5 yr sterling funds.

Co. Y is based in the US and would like to borrow the equivalent 50 mil in sterling for 5 yrs at a fixed rate. It has been unable to get a quote but has been offered US dollar funds at 10.5% p.a.

Five-year gov't bonds currently yield 9.5% p.a. in the US and 10.5% in the UK. Suggest an appropriate currency swap that will net the financial intermediary 0.5% p.a.

[yanz]

I did this problem differently from JAM (I ignored the last sentence since I didn't know how to it was relevant) but ended up with the same answer:

Co X borrows UK (no choice) and must enter into a swap to pay $, get sterling. Since it's borrowing at 12%, it must receive 12% from the swap.

Co Y borrows US (no choice) and must enter into a swap to get $, pay sterling. Since it's borrowing at 10.5%, it must receive 10.5% from the swap.

So the intermediary must pay 12% UK to co X and 10.5% US to co Y so it needs to get 12% + y UK from co Y and 10.5% + x US from co X to cover the position.
x + y = .5%, so may as well set both equal to .25, so the swap for co X is 12% UK for 10.75% US and swap for co Y is 12.25% US for 10.5% UK.

[flyingmoon]

Same here, I tried to understand the concept of the question. Since both X and Y cannot borrow money from their foreign country, I don't think we can use the comparative advantage concept for this case.
If I am wrong, please correct me. All we have to do is to maintain the difference of 1.5% between X and Y no matter what the net rates for X and Y are. For example, if X is 11% then Y should be 12.5% and the intermediary's profit should be 0.5%. If so, I think there should be many scenarios other than above. What do you think?

I missed the intermediary's margin should be 0.5%, and hence there should be only one combination. If X is 11%D and Y is 12.5%P, the intermediary's margin would be 0.5%D + 0.5%P, which should be deducted by 0.25%D and 0.25%P. Therefore 11%-0.25%D and 12.5%-0.25%P would be the only combination we try to find out. Thanks yanz!