Happy days are here again. That could be what some investors are singing, with the S&P 500 rising more than 20% below the low set on Oct. 12, 2022. 

Many are cheering that the S&P is at long last in a bull market. Not me. Here are three simple reasons why I'm not celebrating a new bull market.

A hand turning a wooden block from spelling bear to spelling bull.

Image source: Getty Images.

1. It's arguably not a new bull market yet.

The most important reason why I'm not jumping up and down is that it's arguably not a new bull market yet. Sure, some investors mark the beginning of a new bull market as a 20% increase above the previous low in a bear market. However, that's not enough for all investors.

For many investors, two things are required for a new S&P 500 bull market to be declared. First, the index must rise 20% above its previous bear market low. Second, the index must reach a new all-time high.

The S&P 500 has clearly met the first criterion, but it hasn't achieved the second yet. The index has another 11% or so to go to check off the second requirement.

^SPX Chart

^SPX data by YCharts

2. Too few stocks are participating.

I also have another concern about the S&P 500's latest rally. While it's great that the index has risen strongly, too few stocks are participating in the move.

Analysts often look at market breadth -- how many stocks are participating in a move for an index. In one way, the market breadth for the current S&P 500 uptrend is the weakest it's ever been. The percentage of stocks in the S&P 500 that have outperformed the overall index is unusually low.

Sure, many of the biggest stocks in the S&P have soared this year. The three largest of all -- Apple (AAPL -0.12%), Microsoft (MSFT -0.68%), and Alphabet (GOOG -1.33%) (GOOGL -1.33%) -- are each up close to 40%. Amazon's shares have vaulted nearly 50% higher. Nvidia, Tesla, and Meta Platforms have each more than doubled year to date.

AAPL Chart

AAPL data by YCharts

But it's a much different story for most other members of the S&P 500. Nearly half of the stocks in the index are in negative territory so far in 2023. More than 100 of the stocks that have delivered positive year-to-date gains are underperforming the index.

3. The rally could only be temporary.

Finally, I'm not celebrating a new S&P 500 bull market because I realize the current rally could only be temporary. Why am I so cautious? Mainly because of the Federal Reserve.

The Fed's own economists have warned that the U.S. economy will likely enter into a mild recession this year. It's possible that the stock market could hold up well during a recession, but I wouldn't bet on it.

Also, I think that some of the bullishness we're seeing right now is because many investors expect that the Fed's interest rate hikes are over. However, inflation has remained stubbornly high. I wouldn't rule out the possibility that the Fed could still raise rates again. If that happens, it just might derail the S&P's rebound.

Why I'm still bullish on stocks

Although I'm not celebrating a new bull market yet just, I'm absolutely still bullish on stocks -- over the long term. While it would be great if the S&P 500 began a new bull market that was universally accepted this year, it won't hurt my feelings if it doesn't.

Whatever happens, I'll continue to own stocks of companies that I think have excellent long-term prospects. They include several of the big winners of 2023 so far, such as Apple, Microsoft, and Alphabet. I'll also selectively initiate new positions even if the S&P 500 pulls back.

Maybe stocks will go up more this year; maybe they won't. Regardless, I know that they tend to rise more over time than they fall. It's easy to be a bull with this understanding -- even when there isn't a bull market in progress.