For investors who place stock in seasonal trends, the arrival of the month of March can be cause for renewed optimism. "March is actually a pretty good month. February on average is the third-worst-performing month for the S&P 500 going back to 1945," as Sam Stovall, chief investment strategist at CFRA, told CNBC. Since that year, the S&P 500 Index (SPX) has been up 66% of the time in March, and 69% of the time in April, Stovall added, while also noting that April is the second-best month for stocks on average, while March is the third best. (For more, see also: Stocks May See 30% 'Meltup' in 2018: Bill Miller.)

Paul Hickey, the co-founder of Bespoke Investment Group, told CNBC that, since 1983, the S&P 500 has posted an average gain of 1.46% in March. During the current bull market, the index has performed even better in that month, with an average gain of 2.95%, he notes. As the calendar turns, the Investopedia Anxiety Index (IAI) continues to record extreme levels of concern about the securities markets among our millions of readers worldwide.

Longer Perspective

If you look at 90 years of market history, from 1928 through 2017, the S&P 500 was up 61% of the time in March, per Yardeni Research Inc. When March showed a gain, the average advance was 3.6%. When it incurred a loss, the average decline was 3.4%. Overall, March posted an average gain of 0.6% during those 90 years.

Looking ahead to April, Yardeni reports that the market has advanced 63% of the time in that month since 1928. When the market was up in April, the average gain was 4.3%. When it was down, the average decline was 3.8%. The overall average for April was a gain of 1.3%. This is close to the average 1.4% advance that Stovall computes for April during the period from 1945 onwards, per CNBC.

'Reality Check'

This year, the S&P 500 rose by 5.6% in January and fell by 3.9% in February, for a year-to-date gain of 1.5%. Hickey tells CNBC that, when we've had an up January and a down February, there was an average decline of 0.81% in March. But his sample size is small, with just five years out of the last 35 following this pattern.

Nonetheless, Hickey is optimistic that the market may rise this March. "Coming into the year, sentiment was really strong. In January, it got even stronger. The pullback in February was a sort of reality check, and that brought people's expectations back to reality. That's helpful," he told CNBC.

Inflation Fears

Stocks fell and bond yields rose on Tuesday after new Federal Reserve Chairman Jerome Powell indicated, in testimony before Congress, that the Fed may need to raise rates more than its current forecast. Powell is scheduled to testify before a different congressional panel today, March 1. Stovall, however, told CNBC that perhaps "people are looking for any reason to take some profits in the short term." (For more, see also: 8 Threats to the Market in 2018.)

The Fed is expected to raise rates at its March 21 meeting, and release updated forecasts of inflation and interest rates. This data could point to yet more rate hikes in the future than currently expected, to keep inflation under control, CNBC indicates. The yield on the 10-Year U.S. Treasury Note closed at 2.866% on February 28, down from 2.908% on the previous day, per CNBC.