If you close your eyes, you can almost hear the sounds of stock market bells ringing and bulls stampeding. Stock market euphoria is back, it seems.

Between May 4 and June 15, the Nasdaq has jumped 15%, while the S&P 500 is up 9%, and even the stodgy Dow Jones Industrial Average has tacked on 4%. Those indexes are responding to generally solid first-quarter earnings results, excitement over artificial intelligence, and signs that the underlying economy (including consumer demand and the labor market) has remained solid even as the Fed has jacked up interest rates and inflation has moderated.

Many financial-media outlets have declared that a new bull market has begun in all three indexes. Generally, they are defining a bull market as sustained gains of at least 20% from a recent low, and that declaration also appears to be boosting stocks as investors don't want to miss out on the next big rally.

A silhouette of a bull

Image source: Getty Images.

What's a bull market, really?

There's no strict definition for a bull market, and no organization makes it official -- unlike, say, a recession, which is officially declared by the National Bureau of Economic Research, based on a wide range of data points.

While the gains in the stock market do fit one definition of a bull market, others believe that a new bull market hasn't begun until indexes set new all-time highs. In this case, the Dow is still down 7% from its peak, the S&P 500 is off 8%, and the Nasdaq is 15% below its previous record.

It's also unusual for a new bull market to begin while there's so much economic uncertainty. Most economists still expect a recession to hit in the second half of the year. The Federal Reserve is still giving mixed signals about whether it will raise rates more. And though headline inflation has declined to 4% year over year, core inflation -- which excludes the volatile food and energy categories -- remains sticky at 5.3%. 

Meanwhile, a number of retailers like Target (TGT -0.91%) are still warning of weak consumer spending, though that might be partly because consumer dollars have shifted away from discretionary goods like clothes to services like travel, entertainment, and restaurants.

It's all about sentiment

There's no easy way to precisely gauge market sentiment, but investors seem to have turned bullish, fueled in part by excitement over artificial intelligence, an emerging industry that could be worth trillions of dollars in the coming years. 

Wall Street has also responded to the recent stock market surge with some analysts upping their end-of-year price targets. Goldman Sachs now sees the S&P 500 closing the year out at 4,500, up from an earlier target of 4,000, as the investment bank expects market laggards to catch up to the big tech stocks that have driven this year's rally. Bank of America and Evercore ISI also made similar hikes in their price targets.

Not everyone is so bullish, however. Morgan Stanley maintained its year-end target of 3,900, a decline of about 11% from current levels.

In other words, Wall Street can't seem to decide if we're in a new bull market or if this is just a bear market rally.

What it means for investors

Before you start riding the bull, it's worth remembering that the 20% threshold is just arbitrary, and there's no science behind deeming it a new bull market. It's just a convention. It should also be noted that in the past two bear markets, in 2000 and 2008, stocks rallied more than 20%, only to give up those gains and sink deeper into the bear market.

The good news is that the economy is in a stronger position than it was a year ago or six months ago. Inflation has fallen, unemployment has remained low, and corporate earnings have generally been solid. Even in the tech sector, which experienced a wave of layoffs, the worst now seems to have passed.

Whether this is a new bull market or not, investors are best off focusing on the long term, which means buying quality stocks at fair prices. With the market expected to remain volatile, you might want to keep some dry powder on hand in case it does experience another pullback.