Interest Rate Swaps
The interest rate swap come into being because of certain kinds of market imperfections that one borrower has access to low cost funding in their local area (for instance, because their government likes them) and no one else has access to that. And so they use that access as a source of profit for themselves, to use that access to then swap it to somebody else and make money on that. Swap are actually breaking down these inequalities across markets.
Interest Rate Swaps are a kind private sector yield curve, a kind of corporate bond term structure yield curve. And usually we think of the Interest Rate Swap curve as being a spread over the Treasury curve. The difference between the Interest Rate Swap curve and the Treasury curve is called Swap Spread. Since the financial crisis, the swap spread has gone a little crazy:
- In short term, the spread is positive, the Interest rate swap curve is above the Treasury curve.
- In long term, the spread is negative, the Interest rate swap curve is below the Treasury curve.
There’s an arbitrage where you would short corporate bonds and long treasuries. There’s something seriously skewed in the structure of the capital market.
What is a swap? Suppose there are 2 firms, AA who is able to borrow relatively cheaply at a long-term fixed rate (say, a 10-year bond), and on the other hand, BBB is able to borrow at a short-term flexible rate (say a 3-month LIBOR).
[ Fixed rate @5.50
|Long-term fixed rate (bond) @5.375|
|Short-term flexible rate (LIBOR) @+1/4|
Fixed rate @5.50 ]
BBB would like to have long term funding, and AA is also happy to have some short-term lending. So they can do a swap, where they swap exposures. They need a parallel loan structure:
[ Fixed rate | LIBOR ](meaning paying LIBOR and receiving a fixed rate) for AA, who is the seller of the swap (shorting swap position).
[ LIBOR | Fixed rate ](meaning paying Fixed rate and receiving a LIBOR) for BBB, who is the buyer of the swap (longing swap position)
The parallel loan structure for the short swap position
[ Fixed rate | LIBOR ] is like owning a bond and financing it in the REPO market – short term financing of a long term bond. A REPO in which you have a long term corporate bond and you’re using it as collateral for a loan that’s maybe a few months.
In a way, this parallel loan structure is also like forward contracts, it is like a six month loan on the Asset side and a three month deposit on the Liabilities side. A swap really is a portfolio of forward contracts. If you’re a dealer in swaps, you can hedge your position in the forward market, and of course it means you can hedge it in the futures market.
Why People Do Swaps?
Suppose AA and BBB can get these quote from the market:
|Short term (Term Loan flexible rate)||Long-term (5-year Fixed rate Eurobond)|
|BBB||LIBOR + 1/4||5.850|
|AA||LIBOR + 1/8||5.375|
|Diff||1/4 – 1/8 = 12.5 bp||5.850 – 5.375 = 47.5 bp|
For both long-term and short-term, AA always get a lower (better) quote than BBB. There is a “cake” which is worth
47.5 bp - 12.5 bp = 35 bp between AA and BBB. There will be a negotiation to split that cake.
Let AA and BBB do a swap at rate 5.50, in the example above:
- Firm BBB is actually paying
5.50 + 1/4 = 5.50 + 0.25 = 5.75, which is 10 bp less than
5.850(if BBB does it on their own).
- Firm AA is acquiring funding at
LIBOR + 5.375 - 5.50 = LIBOR - 0.125, which is 25 bp less than
LIBOR + 1/8(if AA does it on their own).
So in total, AA gets 25 bp and BBB gets 10 bp from the cake (35 bp). It allows AA to get live funding at less than LIBOR (the standard going rate). However this is because there’s some kind of exposure of AA to the potential problems the BBB has. In other words BBB could run into trouble rolling its (short term flexible rate) loan, and if BBB runs into trouble rolling its loan, it could run into trouble paying the swap that it’s promised to AA.
But it’s not really the same as credit risk because it’s a swap. If BBB stops paying AA, then AA just stop paying others. And that’s the end of the story. You are not losing some huge principle that they owed you, you are just losing a payment. So the credit risk that’s involved in a swap is a lot less than an actual parallel loan.
There’s an incentive for a dealer to go inside and set this whole thing up and ask a share of the “cake”. The spread between the bid-ask prices (usually 3 bp) is what the dealer is harvesting. Dealers are using their own balance sheets to stand in between the short side (AA) and the long side (BBB).
|Swap||Swap (AA)||Swap (BB)||Swap|
Now by putting a dealer (say an investment bank) in between AA and BBB, the situation of exposure is improved, because AA’s exposure is now to the dealer, not to BBB. BBB’s exposure is being held by the dealer.
Most of the money market swap market is inter-bank market. Suppose a bank that receives from some client a one-year deposit. However the bank does not want to hold the one-year deposit, they want to hold floating rate deposit, so the bank do swap with a dealer (say. JPMorgan).
The dealer exposed too much interest rate risk, it finds another firm LBO who wants to swap the opposite direction. LBO was able to raise 3-month floating for a leveraged buyout.
3-month LIBOR ]
[ 3-month LIBOR
|3-month floating |
4.47 - 4.44 = 3 bp is the profit of the dealer for setting this thing up.
There’s no actual loans happening here. These are swaps of IOU’s. You make money, because you’re selling one IOU for a higher price than you’re buying the other IOU, and that’s basically the business. This is banking, but without the actual loans. The core of the modern system works like this. This interest rate swap apparatus was developed to create liquid markets in corporate securities, which is the most natural thing in the world.
Credit Default Swaps
A corporate bond has a lot of credit risk. A credit default swap is a way of peeling that risk off and selling it separately, just as an interest rate swap, which is a way of peeling off interest rate exposure and selling it separately.
Fisher Black wrote a memo to himself in 1970, he said:
Thus, a long-term corporate bond could actually be sold to three separate persons: one would supply the money for the bond, one would bear the interest rate risk, and one would bear the risk of default. The last two would not have to put up any capital for the bonds, although they might have to post some sort of collateral.Fisher Black
That’s the world that came to be.
A risk-free security = A risky security + Interest rate swap + Credit default swap
Suppose there are:
- a buyer of insurance (long swap, equivalently short credit risk), who owns risky corporate bond before doing any swap
- a seller of insurance (short swap, equivalently long credit risk)
[ Corporate bond
[ Treasury bond
Treasury bond ]
Treasury bill ]
[ Treasury bond
[ Treasury bill
Corporate bond ]
Treasury bond ]
The buyer can go short corporate bond and buy treasury bond, i.e
[ Treasury bond | Corporate bond ], then the buyer’s net exposure is the treasury bond. If the buyer further go short the treasury bond, and long a treasury bill, i.e.
[ Treasury bill | Treasury bond ], then their net exposure will be the treasury bill. This example actually demonstrates 2 kinds of swaps together
|Credit default swap|
Treasury bond is the same maturity as the corporate bond
Carving off (shorting) the original credit risk from the Corporate bond
The net is the credit exposure
|Interest rate swap|
Being long flexible rate thing and short fixed rate thing.
Think of the credit default swap as an insurance premium
U paid by the buyer to the seller, that:
- The buyer of the insurance
- Pays default, every time when the bond doesn’t default.
- When the bond defaults, the buyer is able to trade the (Corporate) bond for a Treasury bond. The buyer gets the difference between the Treasury bond price and the value of the (Corporate) bond, i.e.
F - P(s).
- The seller / dealer just
LIBOR + Utimes the face value of the bond from the buyer, meanwhile pays
LIBORtimes the face value of the bond to the buyer, so the net cash flow is
Utimes the face value of the bond.
[ Treasury bond
LIBOR + U ]
Corporate bond ]
The value of CDS is going to fluctuate, okay, with the value of the bond. The point that you might buy CDS, is not so much as insurance against default (for buyers who pay premium), but as a way of getting credit risk exposure to the underlying bond (for seller who receives premium).
Sellers ‘ dealers write CDS on bonds. A portfolio of CDS is like a portfolio of corporate bonds. The dealer could hedge that they could find somebody on the other side who wanted to take a position in bonds. If the dealer can not find somebody like that, CDX can be used. CDX is an index that is a diversified portfolio of bonds.
There might by an asset manager who’s looking to get exposure to a portfolio bonds. Instead of individual people wanting to trade individual CDS on individual bonds, more characteristic of what the world really looks like is sort of where:
- There are people (the buyer) who want to hedge exposure on something, they buy from an investment bank.
- The investment bank (the dealer) creates a portfolio of that and hedges that with somebody else (the asset manager).
- The asset manager is not concerned about individual bonds, about the bond market or something like that.
Liquidity matters because once you have a dealer in the middle, the order flow is going to push CDS prices around, but it doesn’t necessarily move the bond prices. Somebody will do an arbitrage in order to push the bond prices around.
So a lot of arbitrage opportunities seem to appear in the world when you have dealers making markets and quoting CDS prices. Whenever the CDS prices are out of line with the bond prices, it looks like an arbitrage opportunity.
For more on Interest Rate Swaps and Credit Default Swaps, please refer to the wonderful course here https://www.coursera.org/learn/money-banking
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