# What is the relation between the USD Swaps Rates and US treasuries?

I asked this question HERE and redirected to https://quant.stackexchange.com

I understand a swap rate is the fixed leg on a IRS (source), and a swap spread is the difference between a swap rate and the interest rate of a US treasury of the same/similar maturity. (source)

I also came across these charts of USD Swap Rates like for example here: link

If I understand correctly, if I am paying a floating rate like the 10y UST rate, I could get into IRS contract with a bank so they would pay the floating rate and then I would pay the swap rate associated to the 10y UST according to the chart in the provided link, is this correct?

This means that I would start at a loss if the USD swap rate is higher than the corresponding UST yield and at a gain if it is lower. Is this correct?

First I was under the impression that in an IRS both legs started with the same value and the floating leg would move up or down but if that was the case there would not be a need for USD swap rates because they would be the same as the UST yield, am I wrong?

How are the USD swap rates determined? Is it determined by supply and demand of the fixed and floating legs? (so that if there is more demand on the fixed leg the swap rates would be positive and in the opposite case they would be negative)

Mainly I want to check if my understanding is correct or not.

interest-rate

• Hi, could you please add the sources / links to your question? edit: OK, i see you have the links in the original question... :( Nov 6 '20 at 11:36
• I don't understand "I am paying a floating rate like the 10y UST rate", do you mean paying the 10 year swap rate? "floating rate" usually means 3 month LIBOR rate. Nov 6 '20 at 11:40
• @noob2 It is my understanding that in a IRS the floating rate can be any non-fixed interest rate (LIBOR, EURIBOR, SOFR etc..) Including UST interest rate. Nov 6 '20 at 11:55
• According to this "A swap spread is the difference between the fixed component of a given swap and the yield on a sovereign debt" meaning a treasury yield can be used as the floating leg. I am assuming a UST swap rate would be the fixed component. Nov 6 '20 at 12:01
• Swap spread = swap rate - yield on govenment bond Nov 6 '20 at 12:16

You are mixing things up. A standard interest rate swap has 3month Libor as the floating leg. The swap rate is the rate on the fixed leg of this swap. A swap spread is the difference between this fixed rate and the yield on a Treasury bond of comparable maturity.

A swap where the floating leg is a long dated Treasury yield reset every 3months is called a CMT swap- it does exist, but considered an exotic instrument beyond the scope of this question.

• If I understand correctly, you are saying that I am confusing "swap rates" for "TREASURY SWAP RATES". swap rates refer to the fixed leg of a standard IRS where the floating leg is a 3 month LIBOR and treasury swap rates are related to CMT swaps Nov 6 '20 at 12:43
• so in this link article, swap rate = fixed leg where floating leg is 3 month - LIBOR, and swap spread = difference between swap rate and 3 month - UST yield Nov 6 '20 at 12:51
• ok, so the rates in this link are not related to swap rates, do they relate to CMTs? Nov 6 '20 at 13:06
• There are swap rates corresponding to each UST maturity Nov 6 '20 at 13:09
• Those are the swap rates for a few different maturities. I don’t see any reference to Treasuries
– dm63
Nov 6 '20 at 13:17

Your question (What is the relation between the USD Swaps Rates and US treasuries?) is valid and interesting. You would think that (under simple assumptions) the 10 year swap rate should be almost equal to the 10 year Treasury rate, and perhaps the swap rate should be slightly higher because of higher credit risk. In fact there can be significant differences in both directions (i.e. swap rate can be below Treasury rate)

You will find some discussion of the factors which could explain this in the following article from the New York Fed

Essentially it involves obstacles to arbitrage between the 2 markets. They are not perfect substitutes.

Great question(s)!

If I understand correctly, if I am paying a floating rate like the 10y UST rate

When the market for interest rate swaps arose and developed in the 1970s, it developed some "market conventions". People follow them even through it's easy to think of other conventions that might be better in some way. (Think of it as th question, why do we drive cars on the right in the U.S., and on the left in the U.K.? neither way is better; it's just the way it happened historically.)

For interest rate swaps denominated in U.S. dollars, the market convention is that the floating leg pays 4 times a year, using "Actual days / 360" daycount convention, the rate is determined at the beginning of the period from a rate called 3 Months USD LIBOR. The fixed leg pays twice a year using a "30 / 360" daycount. I just googled and found some page that explains it nicely. For other currencies (e.g. EUR), the market conventions are not necssarily "better", but are "different".

We are, actualy,in the middle of switching from LIBOR (see 'LIBOR cessation') to a new index called SOFR. In the future the most standard USD IR swap is likely to have both legs paying once a year; and the floating leg will use SOFR reset in arrears (at the end of the period).

You can trade interest rate swaps with other terms and conditions (more on this below), but you will pay more bid-ask spread for the privilege. If you want a really unusual swap, then you will pay a ot of bid-ask.

I would pay the swap rate associated to the 10y UST according to the chart in the provided link

Not quite. The Chatham Financial page that you quoted lists a lot of rates.

U.S. Treasuries these are not swaps. Rather these are the yields on U.S. treasury debt. It's bad style not to provide a footnote explaining what these numbers are. Are they trying to confuse readers on purpose?

Swaps – Semi-bond I really don't like salespeople who mis-use what they think is "Wall Street jargon" in communications with clients, hoping to confuse and/or impress the latter. Semi-bond is shorthand for what I wrote above - 3 month libor versus semi-annual fixed. This is by far the most common kind of USD IR swap.

Swaps – Monthly Money this is jargon for 1-month LIBOR - see the page I cited above (again, going away to be replaced by SOFR within a few years).

Swaps are traded "over the counter" (OTC). This implies that there is no list of permitted swaps and "thou shalt trade no other". If someone wants to trade a swap that would, for example, pay 6M (rather than 3M) USD LIBOR and receive fixed, or for example, pay 3M USD IBOR and receive 6M USD LIBOR, etc, etc - it's easy to find someone to trade with and to see quotes for such swaps. It's just that the most commonly quoted USD swap rate is the fixed rate versus 3MO LIBOR.

If someone with tens of millions of dollars to spend, and the appropriate agreements in place, really wanted to trade a bespoke swap that you described - paying US treasury yield and receiving fixed - they'd probably be able to find some bank wiling to do it. But the bank would charge a lot for this work (by paying less fixed or receiving more fixed). I can't think offhand why someone would want to trade that.

A way to see a treasury is a as a swap fixed-float, where the floating rate is the overnight repo rate. With LIBOR being replaced by SOFR, the swap spread will end being ... ? pretty much nothing