The swap curve gets weird

The biggest global markets for transferring risk (by far) are the interest rate (IR) risk markets.  A key relationship in these markets has recently broken down.  It is the relationship between the treasury yield curve and the swap rate curve.  It is another example of how broken the global financial system is, and it seems to have actually been caused, in part, by over-zealous banking regulators.

Most people have pretty good intuition about interest rate (IR) risk.  It comes from their experience with home mortgages.  They know that in a fixed rate mortgage the lender (the bank) has the IR risk and therefore the borrower (the homeowner) has to pay a higher interest rate.  Conversely, in a floating rate mortgage the borrower has the IR risk and pays a commensurately lower rate.
Clearly then, if you borrow at a low floating rate (say 0.50%) and then lend the proceeds at a higher fixed rate (say 2.00%), you will pocket the net interest rate margin, at least initially.  But, you will face the risk that the interest rate on your borrowing may rise and squeeze your 1.50% margin.  The margin could easily go negative, because interest rates are volatile.  So, the initial 1.50% net IR margin is compensation for bearing IR risk.

Figure 1:  Swap curve and treasury yield curve

Borrowing short and lending long

Imagine that you choose to absorb IR risk and receive the compensation (net IR margin) that goes with it.  There are many ways you could do that: in the treasury bond futures market, the IR swap market, the Euro-dollar futures market and others.
These markets might sound complicated but in reality absorbing IR risk always comes down to just one thing – borrowing short term at a floating IR and lending longer term at a fixed rate.
Lets consider an example of borrowing at a floating IR, that adjusts every six months, to lending at a fixed rate for 10 years.  $US dollar IRs are used.
  • Lending long term:    Buy $1 million of newly issued 10 year treasury bonds that pay an annual IR (coupon rate) of 2.00%.  The bonds will pay $10,000 in coupons every six months for 10 years and then return the $1 million of principal.
  • Borrowing short term:    Use the bonds as collateral to borrow $1 million for six months at a risk free IR of 0.50%.  Interest of $2,500 is owed in 6 months.
  • Rollover the debt every six months at whatever the risk free 6 month IR is at that time.
Profit in each 6 month period
 =  (2.00 – 6 month IR) / 2  x  $1,000,000   –   (Capital loss on the bond from rising IRs).
Note that this position is heavily exposed to changes in IRs because the 10 year fixed
rate bond has a sensitivity to IR changes of about 9 to 1 (that sensitiviy figure of 9 is called ‘duration’).
So, if in the first 6 months all IRs rise by 10 basis points (0.10%), then the price of the fixed rate bond will fall by  9 x 0.10% x $1,000,000 = $9,000.
I n that case the profit on our position is: $7,500 (net IR) – $9,000 (capital loss) =              -$1,500.  If instead of falling, IRs went up 10 basis points (bps), then our profit would be $7,500 + $9,000 = $16.500.

Receiving fixed in an IR swap

A 10 year IR swap sets up the position described in the previous example, but in a highly convenient single contract that is inexpensive to open and close.  If we agree to ‘pay floating’ and ‘receive fixed’ in a 10 year IR swap for a ‘notional’ amount of $1 million, then the following payments are made:
  • Paying floating:   Just as in the example above we will pay a floating six month IR on $1,000,000.  The IR is set at the beginning, but paid at the end, of each 6 month period.  In this case the interest is not the risk free rate, but instead it is the 6 month London Interbank Offer Rate (Libor), which is the rate at which banks lend each other money for 6 months.  6 month $US Libor is currently 0.70% (instead of 0.50%), because interbank lending is not risk free.
  • Receiving fixed:   Again, corresponding to the example above, we will receive a fixed annual rate (the ‘swap rate’) on $1 million.  The 10 year swap rate is 2.20%, so we will receive $11,000 at the end of each six month period, over 10 years.
  • The swap contract specifies the swap of floating payments for fixed payments at 20 dates in the future.  The fixed payments are $11,000.  The floating payments depend upon the level of 6 month Libor at the beginning of each of the 20 periods.
  • No money changes hands when the swap contract is created.  It is risk, not capital, that is being transferred by the opening of this risk market instrument.  Money changes hands, but only as interest rates evolve.
It is expected at the outset that the total of the 20 fixed payments will exceed the total of the 20 floating payments over the life of the swap.  The difference is the compensation the party receiving fixed gets for the absorbing IR risk.
The parties to the swap have to agree on the amount of compensation for bearing IR risk.  That is done by setting the swap rate.  The swap market is competitive.  The swap rate goes up and down continually (minute by minute) to equalise the number of market participants who want to absorb IR (pay floating) risk to the number who wish to lay it off (receive floating).

Arbitrage example    

The diagram above shows two curves.  The lower, blue curve is the treasury yield curve which shows the rate at which the US Treasury can borrow money for different lengths of time.  These are the risk free $US interest rates.  The higher, red curve shows the swap rate for IR swaps of different tenures.  This is the fixed rate that the party absorbing IR risk will receive for the life of the swap in exchange for paying floating.
These two curves are in an ‘arbitrage relationship’.  The swap curve must lie above the Treasury yield curve otherwise there is an opportunity for arbitrageurs to put in place a set of trades that guarantees a profit without:  providing any capital, taking any risk or providing any liquidity (that is the definition of arbitrage).
When the swap curve gets too close to the yield curve, for any tenure, the arbitrage opportunity invokes trades that cause the curves to separate again.  The relationship between the swap and yield curves is self correcting.
To demonstrate the arbitrage imagine that the conditions of the previous two examples hold, except that the swap rate has fallen from 2.20% to 1.80%.  The 10 year treasury yield remains at 2.00%.  How would the arbitrage trade be structured?
  • Buy 10 year Treasury bonds with 2.00% coupon and pledge the bonds as collateral to borrow at the risk free rate of 0.50% for six months, and then rolling over the short term debt.  Here we are absorbing IR risk.
  • Open a 10 year IR swap and take the position of paying the fixed rate of 1.80% and receiving an initial floating rate of 0.70% (the opposite of the example above).  Here we are laying off IR risk.
  • The fixed payments from the treasury bond (2.00%) are used to pay fixed in the swap (1.80%) and 0.20% is left over.
  • The floating payments received in the swap (0.70%) are used to make the floating rate loan payments (0.50%) and 0.20% is left over.
  • The arbitrage profit is 0.40% of the notional value of $1,000,000 which is $4,000.  Note that we have not used our own capital in the trade, or taken any risk and there is no liquidity issue.  So, this is pure arbitrage.
  • Note that since we have borrowed and lent, we have not used our own money. Moreover, since we have absorbed the IR risk and then layed it off, we have not taken any risk.  And, there is no liquidity issue.  So, this is pure arbitrage.
  • As arbitrageurs take this opportunity they drive the yield curve down by buying bonds (they must accept a lower yield to acquire the bonds), and they drive the swap rate up because they are laying off risk and must attract counterparties in the swap to absorb the risk.  The trades go on until the arbitrage opportunity is eliminated by the trades that take the arb.

The swap curve gets weird

The ‘swap curve’ has been behaving very strangely lately in $US, $A and other currencies.  The $US swap curve beyond 3yrs has moved below the US treasury yield curve – as shown in the table below.  That has never happened before for a sustained period.  It is a big issue because most commercial borrowing is referenced to the swap curve in one way or another.

Table 1:  US Swap rates and Treasury bond yields 23 Feb 2016

This breakdown in the relationship of the swap and yield curves should not happen because arbitrage trading should prevent it.  There are many factors causing this aberration, but an important one is that the heavy regulation of banks is making it harder for banks to facilitate the trading of hedge fund arbitrageurs that would force the swap curve and yield curve back into their ‘correct’ relationship.


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Dr. Sam Wylie

Director, Windlestone Education
Principal Fellow, Melbourne Business School

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