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Corporation $A$ has an excellent credit rating and can borrow at a fixed rate of $5\%$ or a floating rate of LIBOR + $1\%$. Corporation $B$ has a somewhat less excellent credit rating and can borrow at a fixed rate of $7\%$ or a floating rate of LIBOR + $2.5\%$. Both firms wish to borrow $10,000,000$ for $3$ years and $A$ would rather borrow at a floating rate and $B$ would prefer to borrow at a fixed rate.

What are the comparative-advantages and total gains that $A$ and $B$ could attain if they engaged in a swap contract

The solution to this from what I have been provided is $$\Delta \ \text{fixed}(B-A) - \Delta \ \text{float} (B-A) = (7-5) - ((L+2.5) - (L+1)) = .5$$

I do not understand this at all, if anyone could give me some insight and provide a detailed solution I would greatly appreciate it.

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    $\begingroup$ The "comparative advantage" theory of swaps never made much sense and is largely obsolete today. (unfortunately it apparently still appears in some exams). $\endgroup$ – Alex C Apr 23 '17 at 3:06
  • $\begingroup$ I agree with @AlexC 's view. This is explained in detail in many introductory textbooks - e.g. Hull's "Options, Futures and Other Derivatives". $\endgroup$ – LocalVolatility Apr 23 '17 at 8:44
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It is actually rather simple.

Lets start with the fixed rate market. A can borrow at 5% while B can borrow at 7%. Simply said, A has a comparative advantage of 2% in the fixed rate market.

In the floating rate market, A borrows at LIBOR + 1% while B borrows at LIBOR + 2.5%. From here, I'm guessing you already know that A has the comparative advantage as well of 1.5%.

Now by this 2 factors, we can automatically assume that A will borrow in the Fixed rate market due to higher comparative advantage while B will borrow from the floating rate market to not lose out so much.

The question you are asked is simply asking what is the total gains both A and B would get if they were to be engaged in a swap. The answer is simply the difference in the credit spread between the two markets, 2% - 1.5% = 0.5%

Note that 0.5% is the TOTAL gains from the swap. If they were to spread the gains equally, it would mean A would enjoy 0.25% cost savings in the floating rate market while B would also enjoy 0.25% cost savings in the fixed rate market using the swap.

The swap can easily be conducted using the following steps:

1) A borrows 10,000,000 from fixed market at 5%

2) B will pay A monthly fixed interest payments of 6.75%

Note that the net effect here is that B essentially pays fixed payment of 0.25% less than he would have without the swap. A gains a total of 1.75% from this cash flow.

3) B borrows 10,000,000 from the floating market at LIBOR + 2.5%

4) A pays B monthly floating interest payments of LIBOR + 2.5%

From this cash flow, B has a net effect of 0 in the floating rate payments. A will then use the 1.75% gains in the previous cash flow to offset the cash flow here, enabling A to pay only LIBOR + 0.75% monthly. A essentially pays 0.25% less than he would have without the swap as well.

The swap thus allows both parties to gain from the credit spread of 0.5% equally.

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