These swaps well illustrate the dynamic nature of derivative developments today. Essentially "created" or "invented" in 1981, the "notional" principal amount subject to interest rate swaps now exceeds $20 trillion.
You pay the interest on my mortgage and I'll pay the interest on yours. Is that an interest rate swap? Dubious. Interest rate swaps typically involve large institutions and one of the institutions is often a bank or other financial institution. Interest rate swaps typically involve large sums of money. (I hope your mortgage isn't as large as what is involved in most such swaps.) Quite often one of the parties to the swap has a stronger credit standing than the other and usually one may borrow at a fixed rate of interest and the other at a variable rate.
Given the right setting, however, interest rate swaps can confer some substantial benefits to the parties to the swap. The swap may, for example, reduce the exposure of both institutions to risks relating to swings in interest rates. Furthermore, a properly designed swap may reduce the total expense for the two parties below what it would have been if they had operated alone.
Let's consider a simple example. To save space, the last three zeros from each dollar amount have been deleted so that the $50,000 note receivable on the balance sheet of MeCorp really relates to a $50,000,000 note receivable.
| MeCorp | UCorp | |
|---|---|---|
| Notes Receivable-5 years-10% | 50 000 | |
| Installment Receivables (TB+160 basis pts) | 50 000 | |
| Other Assets | 10 000 | 10 000 |
| ASSETS | 60 000 | 60 000 |
| CDs-6 mos (TB+40 basis pts) | 50 000 | |
| Notes Payable-5 years-9% | 50 000 | |
| Net Worth | 10 000 | 10 000 |
| LIABS & NET WORTH | 60 000 | 60 000 |
Suppose, for example, the treasury bill rate is eight percent for the next six months. The income statement of MeCorp, assuming the earnings from its other assets cover its other expenses, might then look as follows:
| Interest rev | $50,000 x.1 x 0.5 | $2 500 |
| Interest exp | $50,000 x.084 x 0.5 | $2,100 |
| INCOME | $2,500-2,100 | $400 |
But now consider the income statement if the Treasury Bill rate is ten percent for the next six months:
| Interest rev | $50,000 x.1 x 0.5 | $2 500 |
| Interest exp | $50,000 x .104 x 0.5 | $2,600 |
| LOSS | $2,500-2,600 | -$100 |
Likewise there's a poor match for UCorp. It finances short-term installment debt and its average receivables are for six months. While the rate on these installment notes is fixed, the rapid turnover in these receivables means that they are essentially subject to the vicissitudes of the money market. Let's say UCorp typically charges the treasury bill rate plus 160 basis points on these receivables. On the liability side of its balance sheet, UCorp has a five year note payable at an interest rate of nine percent. Again, depending on the TB market, UCorp can have a good half year or a bad half year.
Now it's your turn. Figure out the income statement for UCorp if the Treasury Bond rate is 8 percent. Then try it at 10 percent. Click the buttons to see if you have the correct answer. (After you click on one of these you'll have to close that min-window before you check the next one. By "close" it is meant that you must not just click elsewhere in the text to hide that mini-window, but you must actually get rid of that mini-window.)
Now let's make a swap. Each company will actually deal with its own creditors. Thus, MeCorp will credit the accounts of its CD holders with their interest but at the end of six months it will get together with UCorp and, depending on what interet rates have been in the last six months, it will either give a check to UCorp or receive a check from UCorp. Suppose, for example, the Treasury Bill rate in the last six months has been eight percent. In that case the settlement will involve MeCorpr sending a check to UCorp as the tabulation suggests.
| Interest expense of MeCorp | $50,000 x.084 x 0.5 | $2 100 |
| Interest expense of UCorp | $50,000 x..09 x 0.5 | $2 250 |
| Amount MeCorp Sends to UCorp | $2,100-$2,250 | $150 |
MeCorp won't be too enthusiastic about this outcome. With a Treasury Bill rate of eight percent, MeCorp would have had $400 of income as seen in the table a few paragraphs back. But, because it has to reimburse UCorp the $150 as indicated in this settlement tabulation, its income will be only $250, or $400 less the $150 settlement. Here is what its income statement will look like.
| Interest rev | $50,000 x.1 x 0.5 | $2 500 |
| Interest exp | $50,000 x.084 x 0.5 | -$2,100 |
| Settlement exp | prior tabulation | -$150 |
| INCOME | 2,500-2,100-150 | $250 |
Before we feel too sorry for MeCorp, however, let's consider what would have happened if the TB rate had been ten percent instead of eight percent. In that case, the "variable" interest expense paid by MeCorp would have been - see the prior tabulation - $2,600. Since a swap is involved, at the end of the six months, the two organizations would get together and compare the $2,600 of variable interest with the $2,250 fixed interest of UCorp and in this event the check would go FROM UCorp and it would go TO MeCorp and it would be for $350. We saw - look at the tabulation above of the income statement of MeCorp assuming TB=10% - that MeCorp's would be a loss of $100. But if it gets reimbursed $350 from UCorp that loss will turn into income of $250!
We previously saw, see the two tabulations of MeCorp's income statement, that MeCorp would either experience income of $400 or a loss of $100. Quite a difference and if we think of spread, scatter, or standard deviation as an indication of risk, this is quite a lot of risk. But notice that if a swap is made, MeCorp will have income of $250 no matter what the Treasury Bill rate might be. The swap has taken the variability or risk out of MeCorp's income statement.
It's your turn again. Assuming a swap is made, figure the income for UCorp if the TB rate is::
That's correct! No matter what the Treasury Bill rate, the income of UCorp will be $300. The swap has taken the variabiltiy or risk out of its income statement. Without a swap, UCorp's income could have been as low as $150 or as high as $650, a difference of $500. With a swap, it's income will be $300 and the range, spread, scatter, and standard deviation are all zero!
Let's go back to MeCorp and ask whether the swap is an unalloyed blessing. We have seen that the swap takes the variability completely out of its income statement and it will end up with income of $250 no matter whether the treasury bill rate is eight percent or ten percent. Let's continue to suppose that there are only the two possible TB rates for the next six months and that MeCorp believes there is a probability of 0.8 that the rate will be eight percent and only a 0.2 probability that the rate will be ten percent.
| "Partial" expectation of PROFIT | 0.8x400 | $320 |
| "Partial" expectation of LOSS | 0.2x(100) | (20) |
| EXPECTED PROFIT | 320-20 | $300 |
But suppose that MeCorp thinks the probabilities of the two outcomes are about equal, that is P(TB=0.08)=0.5 and P(TB=0.1)=0.5. If no swap is made, the expected return is - see the tabulation - $150 and the range is $500. If a swap is made, the return is $250 (that's more than $150!) and the range of expected outcomes is zero.
| "Partial" expectation of PROFIT | 0.5x400,000 | $200 |
| "Partial" expectation of LOSS | 0.5x(100,000) | (50) |
| EXPECTED PROFIT | 200,000-50,000 | $150 |
It's your turn again. Suppose UCorp likewise thinks there are only two outcomes - TB=0.08 and TB=0.1 - and that UCorp likewise assigns a probability of 0.5 to each of these probabilities. Compute the expected value of the return if no swap is made.
Yes, that's right, the expected value for UCorp if no swap was made would have been $400 if we assume each outcome is equally likely but would have been reduced to $300 by a swap. The price of eliminating the risk would be the $100 reduction in the expected profit.
Even here there are some interesting possibilities for negotiations between the parties. Suppose both agree that there are only two possible outcomes, namely TB=0.08 and TB=0.1, and both believe that the probabilties of each outcome are the same, namely 0.5. A simple swap eliminates the variability in return for both parties but it increases the expected return of MeCorp by the same $100 it reduces the return of UCorp. Perhaps a deal can be arranged where, as above, MeCorp "pays fixed and receives variable" and, in addition, MeCorp gives UCorp $100 every six months. That way both corporations end up with the same expected value as if no swap is made and both completely eliminate the risk or variability of return.
There are other potential advantages to a properly designed swap of interest rates. Is it possible, for example, that a swap would result in less total interest being paid by the two parties than if no swap was made? There are some intriguing possibilities here.
| BORROWING TYPE | STRONG CO | WEAK CO | QUALITY SPREAD |
| Fixed rate | 8 percent | 10 percent | 200 bp |
| Variable rate | LIBOR+40 bp | LIBOR+90bp | 50 bp |
| DIFFERENCE IN QUALITY SPREADS | 150 bp | ||
Let's suppose the variable rate borrowings available to them are stated in terms of the "London Interbank Offered Rate," or LIBOR. If STRONG borrows on a variable rate basis it will pay the LIBOR rate plus 40 basis points whereas WEAK will pay LIBOR plus 90 basis points. The difference between these two rates, the "quality spread," is 50 basis points. The difference between the quality spread on the fixed basis and on the variable basis, the 150 basis points, suggests a potential for an arbitrage profit.
It might be supposed that STRONG, which can get better terms on both the fixed and the variable basis, should have no truck with WEAK. Let's initially suppose that both borrow by themselves and make no swaps. Let's suppose that STRONG, believing the LIBOR rate will be around seven percent, borrows on a variable basis and will therefore pay LIBOR + 40 basis points. Suppose WEAK, either because it has a different estimate of what variable rates will be or perhaps because the risks involved in its business are such that its stockholders will simply not tolerate the additional risk that variable rates involve, borrows at the fixed rate of 10 percent.
Now let's suppose that STRONG's estimate of rates turns out to be correct and that LIBOR is, in fact, 7 percent and let's continue to suppose that each deals independently, i.e. no swap.
| STRONG CO | $100,000X.074 | $7,400 |
| WEAK CO | $100,000X0.1 | 10,000 |
| TOTAL INTEREST EXP | $7,400+$10,000 | $17,400 |
Now suppose a swap can be arranged. STRONG will borrow on the market at the fixed rate of eight percent and WEAK will borrow on the market at LIBOR + 90 basis points. They will get together right after the end of the year and STRONG will pay WEAK LIBOR + 70 basis points and WEAK will pay STRONG interest at nine percent on the $100 million.
Immediately after the borrowings are made on the market, LIBOR moves down to seven percent and stays there for the rest of the year.
| STRONG pays market | $100,000x.08 | $8,000 |
| STRONG receives from WEAK | $9,000-$7,700 | 1,300 |
| Net Expense for STRONG | $8,000-$1,300 | $6,700 |
WEAK comes out a winner on this swap also. . By making a swap, it borrows on the market and pays $7,900 but has to pay STRONG in the settlement a further $1,300 for a total borrowing cost of $9,200.
This $9,200 is $800 less than the $10,000 fixed expense it would have paid had it borrowed fixed and made no swap. And the total of the net expense to the two parties, the total of the $6,700 to STRONG and the $9,200 to WEAK, this total of $15,900 is $1,500 less than the total expense of $17,400 (see the tabulation a few paragraphs back) if they operated independently."Why," you ask, "didn't WEAK borrow at the variable rate of LIBOR + 90 basis points and end up with a total cost of $7,900 and save itself the trouble of making a settlement of $1,300 to STRONG? Wouldn't it have saved $1,300?" Indeed it would have but it required a perfect crystal ball to act in this manner.
We assumed that neither knew what the variable rate would be. We assumed that STRONG correctly estimated it would be low and was willing the accept the vagaries of the market and the risks inherent in taking a variable rate. WEAK, by contrast, wanted a fixed rate as it was reluctant to incur the additional risks implied by a variable rate. In addition, WEAK may have believed that the variable rate would have been well in excess of ten percent.
Given this orientation - that STRONG leans toward a variable rate and that WEAK wants a fixed rate - given the figures in our example it will make sense for the two to exploit the difference in the quality spread and make a swap. STRONG wants variable but it should borrow fixed and make a swap whereby it "pays variable and receives fixed." In this example, by doing so, STRONG ends up with a cost of LIBOR minus 30 basis points instead of plus 40 basis points. This difference of 70 basis points accounts for the cost reduction of $700 to STRONG. It ends up with a variable rate like it wanted but a better variable rate than it could have obtained without the swap.
Here is how STRONG can view the advantage of making a swap.
| a.STRONG pays the market fixed | 8 percent |
| b.STRONG pays WEAK variable | LIBOR+70bp |
| c.STRONG receives fixed | -9 percent |
| d.Net Cost to STRONG(d=a+b-c) | LIBOR-30bp |
Lidewise, we posited that WEAK wanted to borrow fixed and had it done so without a swap it would have paid 10 percent. By making a swap, it dealt with the market on a variable basis but the net effect of the swap was that it paid a fixed rate and that fixed rate was 9.2 percent instead of the 10 percent it would have paid if it acted independently. You can easily verify that 9.2 percent by taking the LIBOR + 90 basis points it pays the market, adding to it the nine percent it pays STRONG and subtracting the LIBOR + 70 basis points it receives from STRONG for a net of nine percent plus 20 basis points or 9.2 percent. WEAK ends up with the fixed rate it wanted but that rate is 9.2 instead of 10 percent.
These results are not dependent on the LIBOR turning out to be seven percent as in the previous calculations. Suppose the LIBOR works out to be 12 percent and the parties had made the swap as outlined above., STRONG, as you can easily verify, would have ended up with a net cost of LIBOR minus 30 basis points instead of plus 40 basis points and WEAK would have ended up with a net borrowing cost of 9.2 percent.
[If you are familiar with the arguments for free trade, you may recognize that the proposition here is the same as the "comparative advantage" argument for eliminating trade barriers. Country A may have an "absolute advantage" over country B in the production of both soy and autos; it can produce both at lower cost and without devoting comparable resources to their production. One might therefore suppose that A should be an island unto itself and not trade with B. However, country B will have a comparative advantage in the production of one or the other and the world will be better off if both A and B specialize in the production of those goods in which they have a comparative advantage and trade freely across international barriers. In like manner, in our example, STRONG has an "absolute" advantage in both the fixed and the variable interest rate markets. Nevertheless, WEAK has a "comparative" advantage in the variable rate market and should borrow at that rate and swap with STRONG which has a "comparative" advantage in the fixed market and should borrow in that market. The two can get the fixed or variable characteristics they want by making the swap.]
Where would you like to go now?