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#### afterworkguinness

##### Active Member
Hi,
Can you quickly clarify for me how to determine a comparative advantage ? I simply don't get it.

As per Hull 7.4:
Company | Fixed | Floating
AAACorp | 4.0% | LIBOR -0.1%
BBBCorp | 5.2% | LIBOR + 0.6%

I only see the absolute advantage.

#### afterworkguinness

##### Active Member
Please ignore. I (think) I get it now, funny how that happens after I've posted it.

The comparative advantage is because AAACorp can borrow 1.2% less than BBB in the fixed market vs only .07% lower than BBB in the floating. Thus AAA is "stronger" in fix than floating compared to BBB. At the same time BBB is "less" worse off compared to AAA in the floating market since it borrows 1.2% more in the fixed market bu only 0.7% more in the floating.

Cheers

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi afterworkguinness Exactly! And that thinking leads to the efficient math test: are the differentials equal? if yes --> comparative advantage; if no --> no comparative advantage. In this example above, the fixed differential is 5.2-4% = 1.2% and the floating differential = 0.6% - (-.1%) = 0.7%, just as you said. If there is no fee to the intermediary, then the total gain from the swap will equal the "difference between theses differentials" (they will share this total advantage). As 1.2% - 0.7% = 50 basis points, this is quantification of the total benefit achieved by the comparative advantage; e.g., if they spit the benefits, then each can gain 25 bps, thanks,

#### sharman.jamie

##### Member
I'm having some issues on this, I understand from your example that comparative advantage can be when a > b. But can there also be when b > a
(where a = difference in fixed rates, b = difference in floating rates)
ie can a swap be created that benefits both of the below?
Company | Fixed | Floating
AAACorp | 4.0% | LIBOR -0.1%
BBBCorp | 4.2% | LIBOR + 0.6%
Diff 0.2% 0.7%
b - a = 0.5%
Or is it strictly only when difference in fixed > difference in floating?

#### sharman.jamie

##### Member
I think the answer must be No, because I can create a swap that nets, but both parties are worse off.

A borrows at Libor - 0.1, lends to B at 3.85 fixed
B borrows at 4.2, lends to A at Libor

A -- 3.85 --> B
L - 0.1 <-- A B --> 4.2
A < -- L -- B

Net:
A = - (Libor - 0.1) + Libor - 3.85 = -3.75%
B = 3.85 - Libor - 4.2 = 0.35 - Libor

Could it be for there to be comparative advantage in the case floating diff > fixed diff, they need to be able to also lend at these rates? Which cannot happen because no one in the market will want to borrow from BBB at 4.2.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @sharman.jamie I think we just need (a-b) <> 0; ie, i think the answer is "yes." I input your example assumptions into my comparative sheet, see https://www.dropbox.com/s/uscl4h47rl4dna4/0902-comparative.xlsx?dl=0

For reference, here is how it looks for Hull's (9th edt) example 7.4:

and then with your assumptions where b>a. Note that we do require, in the case, for AAA Corp (who has the floating advantage) to want to net out to fixed borrowing; and BBB Corp (who has fixed advantage) to want to net out to floating. But notice my XLS shows how both split the 50 basis points advantage:

#### sharman.jamie

##### Member
Hi David, thanks a lot for following up on this so quick! Lucky to have you!

I think I was getting tripped up with sign convention, of course both sides end up with negative inflows, they are borrowing!

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Sure thing, it took me a while to create all these XLS but they save time in the long run because putting number in cells really forces clarity