Comparative advantage and the gain from a swap
1. The idea
Two companies are offered different rates, fixed and floating. Often one of them gets better rates in both markets, yet a swap can still help both. What matters is not where a company’s rate is lowest but where its advantage is greatest: its comparative advantage.
An example. Company A can borrow at a fixed 3.6% or at the floating rate + 15 basis points (a basis point is 0.01%). Company B can borrow at a fixed 4.85% or at the floating rate + 70 basis points. A wants a floating rate and B a fixed one. A’s advantage is 125 basis points in fixed rates but only 55 in floating ones, so A’s comparative advantage is in fixed rates and B’s in floating ones. If each borrows where its comparative advantage lies, A fixed and B floating, and they swap interest payments, together they pay
\[ \text{gain} = \left|\,\text{gap in fixed rates} - \text{gap in floating rates}\,\right| = |125 - 55| = 70 \]
basis points less than if each borrowed directly what it wants. Shared equally, each saves 35: A pays the floating rate + 15 − 35, that is, the floating rate − 20 basis points, and B pays \(4.85\% - 0.35\% = 4.5\%\).
When a bank stands between them, it keeps part of the gain, and the companies share the rest. The same reasoning works for investing: each invests where its comparative advantage lies and swaps into what it wants, and the gain raises both returns.
Part of such a gain is often not real. Floating-rate borrowing is usually a series of short loans, and at each renewal the lender can raise the spread if the borrower’s credit worsens, while a fixed rate is set for years. So the gap between two companies’ rates partly reflects the risk that the weaker one defaults.
In two currencies. It also works when the companies borrow in different currencies. Say A can borrow dollars at 4.4% and euros at 6.2%, and B dollars at 5.9% and euros at 6.6%, and A wants euros and B dollars. A’s advantage is 150 basis points in dollars but only 40 in euros, so A borrows dollars, B borrows euros, and they swap the principals and the interest payments through a bank: a currency swap. The gain is again \(|150 - 40| = 110\) basis points. If the bank keeps 10, each company gets 50: A pays \(6.2\% - 0.5\% = 5.7\%\) on its euros, and B pays \(5.9\% - 0.5\% = 5.4\%\) on its dollars. The bank then receives 1.0% a year more in dollars than it pays, and pays 0.9% more in euros than it receives. Its 10 basis points count a basis point the same in both currencies, so the bank carries the exchange-rate risk; the questions here leave that risk out when they share the gain.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
4. One worked example, then your turn
In the worked example, the two companies swap through a bank.
Now two investors, with hints, one step at a time.
Then two companies that borrow in two currencies, through a bank, with hints.
And one on your own.
5. Practice
Each question has new numbers. You master the skill when you get three right in a row, with at least one right answer for two borrowers, two investors, a swap through a bank and two currencies. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: