Hello everyone and welcome back to my YouTube channel. In today's video we're
going to learn about comparative advantage and swaps. OK, YouTube today
we're going to work through a problem that a lot of students have difficulty
with. It's an idea that we cover in my class on financial derivatives and it's
also covered in the CFA Exams and FRM exams. A lot of students seem to struggle
with this problem I've seen online people posting on CFA internet forums
about this and so I figured I would try and explain it as clearly as possible in
today's video. In economics, the law of absolute advantage states, that countries
should specialize in producing the goods that they are best or most efficient at
producing, and then they should exchange these goods with other countries making
both countries better off. David Ricardo's vital contribution to economic
thought was the law of comparative advantage, an economic theory stating
that even if one country is more efficient in the production of all goods
thus meaning that they have an absolute advantage in all goods compared to other
countries, all countries will still gain or still benefit, by trading with each
other as long as they have different relative efficiencies. and I'll put a
link to to the law of comparative advantage in economics below if
you are interested in it. But this law helps to explain why countries engage in
international trade even when one country's workers are more efficient at
producing every single good when compared to workers in other countries.
For the comparative advantage problem in Swaps, we take that idea from
macroeconomics and apply it to the world of corporate finance and derivatives.
It's easy to understand how if one company is able to get a better deal in
fixed-rate borrowing but prefers to borrow at a floating rate while another
company is in the equal and opposite situation it might make sense for these
to come to enter into a swamp this is like the
absolute advantage argument in economics in a situation where one firm has better
access to the capital markets than all others it might still make sense for
them to enter the swaps market and this is where the comparative advantage
argument comes in and so this is the problem that that you're often given to
solve in exams so let's work through an example of this we'll start with two
companies company X is able to borrow at three and a half percent fixed or live
or minus 0.2 percent slow ting so that's below LIBOR LIBOR being a floating rate
and now sometimes people get confused when they see LIBOR - the reason a
company could borrow below LIBOR is because LIBOR is a rate at which banks
lend to each other at and of course if your company is a better credit than a
bank you'll be able to borrow at a lower rate so in this case LIBOR - 0.2%
floating now company Y is able to borrow it either four and a half percent fixed
or LIBOR plus 0.4 percent floating so as you can see in this example company X is
able to borrow at a better rate in both the fixed and the floating rate markets
so a lot of people would then look at this and say there's no situation in
which company X would benefit from an interest rate swap well let's look at it
and see if we can work out a way so the first step in solving this problem is to
analyze how much better or a company X can borrow out in either market than
company Y company X can borrow fixed at a 1% better rate than company Y but only
a 0.6% better rate on a floating basis company X has a comparative advantage in
the fixed rate borrowing markets so what I mean by that is that they have a
greater they have an absolute advantage they're better in both markets but they
are the best in the fixed rate market right so all we've done there is
to look at the magnitude of the rate differences in each market and note them
down and so we'll call that step one so the difference between three and a half
percent fixed and four and a half percent fixed is one percent often
people will describe this as a hundred basis points or hundred bips, but it all
means the same thing one percent. Then let's look at the difference between
LIBOR minus 0.2 percent and LIBOR plus 0.4 percent that is 0.6 percent now if
you're not calculating that correctly it's because you're not paying attention
to the minus right because it's LIBOR minus 0.2 percent compared to LIBOR plus
0.4 percent so the difference between that is 0.6 of a percent or 60 basis
points if company X prefers to borrow floating and company Y prefers to borrow
fixed they can enter into a swap agreement with each other and improve
both of their borrowing costs now this only works if company X prefers to
borrow floating and company Y prefers to borrow fixed if it's the other way
around there'll be no benefit from swapping the fixed advantage of 1% - the
floating advantage of 0.6 percent is 0.4 percent so we're just taking 1% minus
0.6 percent and the difference is 0.4 percent and then the question it says
that this can be split evenly between the two counterparties now most of the
questions that I've seen on this topic from the CFA exam have you split the
benefit evenly like this but of course in the real world it can be split
however the two companies might agree to it but for this example we're gonna say
it's being split evenly so what we've done there a step number two is just to
subtract 0.6 percent from 1% that gives us 0.4 percent and because in our
question the two companies are splitting this evenly between themselves that
means that we just take 0.4 percent divided by 2
and that gives us 0.2% so at this point we're actually most of the way through
our problem all we have to do now is to draw the
Swap diagram if you don't know how to draw a swap diagram do watch my last
video which was just on swaps I'll link to it above so what we have to do now is
we're gonna draw the swap diagram and we're gonna show each company borrowing
at the rate at which they have a comparative advantage right because what
they're going to do is they're going to borrow at the rate in which they have a
comparative advantage and then they're going to swap to convert their fixed
borrowing into floating or they're floating borrowing into fixed we're
gonna put LIBOR at the bottom of this diagram and then solve for a fixed rate
at which each of our borrowers is 0.2 percent better off you only actually
need to solve this problem on one side and it's automatically solved for the
other side for the purposes of this video I'm gonna do the calculation on
each side just to show you how it can be done by starting on either company
exercise our company wise side but I shall see at the end we'll get to the
same answer no matter which way we do it so let's just start by solving it from
the company x side of the diagram to begin with so company eggs will be
borrowing a three and a half percent fixed and that is the rate that they
have a comparative advantage in that's the fixed rate that they can get from
the market and it's where they have the greatest advantage so they're then going
to swap into floating we know their eventual borrowing rate will be LIBOR
minus 0.4 percent so where did I get that from well the rate that they're
able to borrow out in the market right now is LIBOR minus 0.2 percent but we
know that they're going to be better off than that so their initial floating rate
was LIBOR minus 0.2 and we calculated in step two that they would be zero point
two percent better off because we're splitting that zero point four percent
difference evenly between the two companies sum to zero point four percent
was just a difference between one percent advantage and the zero point six
and advantage so if they're going to be borrowing at LIBOR minus 0.4 and we put
LIBOR at the bottom of the swap diagram that they have to be bringing in 0.4
percent more in the fixed leg of the swap that they're receiving from company
why they have to be bringing in 0.4 percent more than the three and a half
percent that they're paying out in the fixed-rate market right because we have
to get to LIBOR minus 0.4 and we're paying out LIBOR so we need to be
bringing in an additional point four in order to be that much better off so we
just add zero point four percent to three and a half percent which they're
paying out and that gives us three point nine percent now three point nine
percent is coming in from company-wide through the swap and three and a half
percent is going out that means zero point four percent is left over as an
excess and that just means when we've got LIBOR going out at the bottom that
they're effectively borrowing at LIBOR minus 0.4 percent which is of course
zero point two percent better off than if they had borrowed in the floating
rate market where they would have gotten LIBOR - 0.2 percent company why is also
zero point two percent better off with this rate for company why you can see
LIBOR coming in on the swap and LIBOR plus point for going out that means that
there's an extra point for going out than is coming in but then also they're
paying three point nine percent out to X as the fixed rate in the swap and so
there's three point nine plus zero point four gives us four point three percent
initially they were able to borrow at four point five percent so by borrowing
floating and swapping into fixed they've managed to borrow at four point three
percent fixed which is zero point two percent better off than they would have
been otherwise so that's actually the problem solved
at this point you're you're done if you're in an exam situation the problem
is solved now for the purposes of this video we'll resolve the problem but this
I'm just starting on the company y side of the equation in order just to show
you that we can solve it from either side of the equation so to resolve the
equation we're going to follow steps one and two just like we did before and if
you want to see those calculations again just rewind the video and watch from
that point and we find that there's zero point four percent difference just like
before and we have decided to split it evenly between them just like before and
so each company will be better off by 0.2 percent which is just half of that
0.4 percent so so far everything is the same as we did it before we then draw
our diagram and have each company borrow at the rate which they have a
comparative advantage in so that is once again just like before and so they're
going to borrow in the style that they have this comparative advantage and then
they'll swap into the style of borrowing that they actually wanted to borrow so
company Y is borrowing floating at LIBOR plus 0.4 percent because that's where
they had the comparative advantage and then they're swapping into fixed and we
know that they have to end up with a rate that is 0.2 percent better than the
rate that they would have naturally gotten and that means that they have to
end up with a rate of 4.5% minus 0.2 percent which is 4.3 percent so they
have to end up with a fixed borrowing cost of 4.3% now they have LIBOR coming
in at the bottom and LIBOR going out but actually a bit more than LIBOR is going
at LIBOR plus 0.4% is going out and so point four more is going out than it's
coming in and to end up with an effective fixed borrowing rate of 4.3%
we need to subtract 0.4 percent from four point three percent and thus the
fixed leg of the swap will have to pay three point nine percent that that means
that three point nine percent is going out on the swap and zero point four
percent is going out in the floating rate market so they're effective fixed
rate is 4.3% which is 0.2 percent better off
than they would have done without the swap so that's all we have to do to
solve this problem hopefully you found this video useful and can now solve this
type of problem as you can see there's no fancy mathematics going on it's just
addition and subtraction if you're still confused please just re-watch the video
and do the calculation alongside with a pen and paper one additional
complication that is sometimes added to this problem is to have a middleman in
there who charges a fee that's simply enough dealt with if the difference
between the two rates was 0.4% like in step one of this calculation and a
broker was taking out a fee of will say 0.1% on the swap we would just take the
fee out at that point so 0.4% minus 0.1 percent gives us 0.3
percent that can then be split evenly between the two making them 15 bits that
are often before rather than 20 bits as we did in our worked through example so
that's all you need to do if there's a brokerage cost coming out let me know in
the comments below if you need me to explain this any further I can answer
questions that you ask in there if you found the video useful please hit the
like button and subscribe if you'd like to see more content like this have a
great day and see you soon best of luck in your exams bye
you