Pictures show the answer is shockingly little.
Oil vs Yields Key Points
There is little if any correlation between the price of oil and long-term Treasury yields.
There is little if any correlation between the price of oil and the Fed Funds Rate
The secular bull market in long-term bonds is over
Price of Oil vs Treasury Yields and Fed Funds Rate Detail
Detail Key Points
The Fed ignored bond market pressures, the CPI, and PCE, holding the Fed Funds Rate at zero, too low, too long.
The Fed adhered to its preposterous forward guidance and kept up QE when it was obvious to the world an inflationary inferno was building.
In Late 2022, long-term bond yields kept rising despite dramatically declining oil prices.
Over the long haul, there has been little if any correlation between the price of oil and Treasury yields. At times they are correlated and at times not.
Current State of Affairs Interpretation
The bond market does not believe in oil-price disinflation.
Why should anyone else?
These charts put a further spotlight on numerous Fed errors, ridiculous reliance on forward guidance, QE to infinity, and paying interest on reserves to force the Fed’s view on the market.
It also suggests the Fed should pay more attention to signals from the bond market about being behind the curve instead of setting targets based on what the Fed wants to believe.
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