I studied the history of futures trading. The CBOT pit traders would talk about this stuff. Spread trading in futures is hugely important to understand, not only because the exchanges give performance bond offsets (SPAN margin credit), but because the spread market is more important than the outright market in many cases.
In order to understand the yield curve, you have to learn how speculative traders look at it. All the economists and market forecasters will do classic analysis on the curve, and compare all the economic indicators and historical relationships, but the most important thing to understand is the liquidity flows and market making going on here. I studied guys like Gary Phillips, Danny Riley, Borsellino, .. old school traders. I made sure to learn the lingo/jargon they would use.
Go here to find the spread ratios for futures.
https://www.cmegroup.com/trading/interest-rates/intercommodity-spread.html
This is an (old) chart of a butterfly and outright bond futures. The ratio is the differential of the futures contract notional values. This is long the 10s, 30s, ultra butterfly (grey) and the white line is the outright ultrabond contract. Even an idiot can see the relation.
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Now, trading this fly would be called "trading the yield curve", but it's actually not so much different from an outright bond trade. Think about it like this. If you are short the ten year and the ultra bond contracts on a DV01 weighted basis, your blended duration exposure is approximately somewhere in between these terms. In other words, you are trading a synthetic (implied AND tradable) ZB contract AGAINST an outright position in ZB.
That's the key to understanding yield curve trading. The entire curve moves with the outright market and you can be long/short in-front of and in-back of a maturity by doing this. You can essentially create a synthetic bond, bill, or note, and trade it against an actual bond, bill, or note rate instrument. And the exchanges will give you the leverage to do it. Insane leverage...
I use IBKR for execution, and the API with Excel, and I also program models in thinkScript using TD Ameritrade. These are cheap ways to do it. There are many other more expensive software solutions ranging from professional to simple retail. I can program only so much so I use these two.