Wall Street rallied Tuesday following the testimony of Federal Reserve Chairman Jerome Powell at his Senate confirmation hearing.

The Dow Jones Industrial Average was up 0.51%, the S&P 500 gained 0.92% and the tech-heavy Nasdaq Composite jumped 1.41%. Crude oil rallied 3.69%.

Investors heard Powell provide some positive comments. First, he reaffirmed the position that the Fed is determined to fight inflation, which chips away from the paychecks of working Americans. At the same time, it pushes long-term interest rates higher, hurting equity valuations.

“If we have to raise interest rates over time, we will,” said Powell.

Bond traders liked to hear that. Thus, the rise in bond prices and the fall in bond yields during the testimony.

Second, he pushed the unwinding of the Fed's balance sheet to the second part of 2022, though he didn't provide a specific date. Instead, he reiterated the old position, which is the timing of dealing with the Fed's ballooning balance sheet depends on economic conditions.

Both bond traders and equity traders love to hear that, as it eases concerns of the Fed taking liquidity out of the economy, turning risk-off for speculative assets. It created a big rally in technology shares and cryptocurrency markets.

Third, Powell talked about three rather than four interest-rate hikes. They will come in the second part of the year rather than by March, as Wall Street has inferred from the FOMC minutes released last week. And again, the exact number will depend on market conditions.

Both bond and equity traders loved to hear that, too. A slower and gradual pace of short-term interest-rate hikes helps equity and bond valuations.

The trouble is that some of these statements made by the Federal Reserve chair sound contradictory. High levels of liquidity have fueled inflation, though the Fed chair doesn't explicitly recognize that.

Instead, he insists that inflation is caused by supply-side shocks like supply chain bottlenecks and labor market friction, which will magically disappear once the economy returns to normalcy.

But the Fed chair’s somewhat contradictory statements on inflation and monetary policy seem to be the talk for another day for Wall Street. For the time being, the Fed chair's words brought a sign of relief to traders and investors on the long side of the markets. These market participants have seen significant losses since the release of the FOMC minutes that prompted the Wall Street sell-off.

While some traders and investors saw the Fed chair’s statement as a relief, others saw it as an opportunity to get back into technology shares that experienced the most significant correction during the sell-off, adding fuel to the relief rally.

Conservative investors should be very cautious in buying aggressively into the relief rally ahead of two major inflation reports scheduled for release in the next few days. They include the release Wednesday of the consumer price index, a measure of retail inflation, and the release of the producer price index on Thursday, a measure of inflation at the wholesale level.

Any upside surprise in either of the two numbers will force Wall Street to re-evaluate the Fed chair's statements and reach the conclusion that the nation’s central bank is "behind the curve" in fighting inflation.