Bonds may just be fighting the Fed.

U.S. Treasury yields have been falling since the Federal Reserve put through its first interest rate cut in over a decade on Wednesday, with the 10-year yield dipping to its Nov. 2016 low on Friday.

That's unusual given Fed Chairman Jay Powell's commentary on the cut, which cast it as a "midcycle" move done to hedge against emerging "downside risks" rather than the beginning of a cutting cycle.

Still, "the bond market remains vigilant" in its view that the Fed will put through several more cuts by the end of 2020, and that's creating a "bifurcation in financial markets," Paul Ciana, chief FICC technical strategist at Bank of America Merrill Lynch, said Thursday on CNBC's "Futures Now."

"The bond market here is trying to base in yields and trying to put up the possibility of a sell-off to see 2-year yields rise and respond to the less dovish Fed, but bond market participants are remaining somewhat resilient," he said, referencing a chart of the 2-year U.S. Treasury yield.﻿

Factor in the 10-year Treasury yield's retracement of its Nov. 2016 levels, and it's clear to Ciana that "the bond market remains vigilant. They don't necessarily believe in the convergence story right now," he said.

Interestingly, the market that has accepted the Fed's less dovish positioning — made clear by Powell's unwillingness to guarantee further rate cuts and his stated reliance on economic data — is that of the U.S. dollar, the strategist said.

"The market that's believing more in the convergence [of the U.S. market and the Fed's messaging] is the dollar, because if the Fed either delays future hikes or becomes increasingly less dovish, the value of the dollar should appreciate as markets seek out that carry trade," Ciana told CNBC in a phone call on Friday.

A carry trade is a strategy in which an investor borrows money when interest rates are low and invests in an asset with a higher return on investment.

"The technical landscape here is the market's been buying dollars," Ciana said. "The market and the world want U.S. assets. They want the U.S. stock market, they want the U.S. dollar and they want U.S. bonds."

And, "if the Fed becomes increasingly less dovish, then that will continue," he said. The dollar tanked Thursday and Friday following the Trump administration's announcement that it was preparing more tariffs on Chinese goods after hitting a two-year high on Wednesday.

In this environment, Ciana's recommended trade was to short the euro-dollar index at its Friday level of 1.11, which he called "the perfect sell point for the remainder of the downtrend in euro-dollar, [which could] potentially [fall] as low as the French election gap at about 1.08."

As for Treasury yields, however, Ciana didn't see much safety in those trades.

"As this [trade] story evolves, we keep revising our medium-term targets lower and lower," he said in the Friday phone call with CNBC, adding that a 1.85% yield on the 10-year Treasury "certainly makes sense." The 10-year yield ended trading on Friday around 1.85%

"If Treasury yields don't reverse soon, the conversation has to start circulating around, do the all-time lows break and do we go to 1%?" Ciana warned.

The S&P 500 and Nasdaq Composite indices ended their worst week of 2019 on Friday.

Disclaimer