The stock market will suffer only temporary weakness if the Federal Reserve, as it now seems likely to do, hikes interest rates at its mid-September meeting.

That's assuming the stock market performs as it did on average following past occasions when the Federal Reserve began raising rates following a rate-cut cycle - so-called first hikes. The stock market's weakness before and after past first hikes began only about a month before the hike and lasted for only about a month after.

This may help to explain the stock market's recent weakness, since the market is betting that a rate hike will emerge from the U.S. central bank's Sep. 15-16 meeting. (The CME's FedWatch tool reports that there's a 64.2% probability of a hike.) The S&P 500 currently is about 1.7% below its all-time high of Aug. 13, which is quite close to the index's average decline over the month prior to past first hikes.

Over longer horizons, however, the S&P 500 on average barely suffers a hiccup because of first hikes. As you can see from the accompanying chart, the S&P 500 on average sat on a decent gain three months after them. At the 12-month post-rate-hike mark, the S&P 500's average gain was even greater than the stock market's long-term average.

While these results may surprise some investors, they make sense. The Fed doesn't begin to increase the federal-funds rate unless it believes the economy is strong enough to withstand the hike. In fact, not infrequently first hikes occur when the economy is so strong that it is in danger of overheating. When that is the case, a rate hike does not necessarily pose a risk to corporate earnings' continued growth.

By this logic, stock-market investors should be more worried about first cuts than first hikes, since first cuts often indicate that the Fed is worried that the economy is too weak to withstand rates remaining stable. And, sure enough, the S&P 500's average return following past first cuts was lower than following first hikes.

I hasten to add, however, that the difference in stock-market returns following first hikes and first cuts is not statistically significant at the 95% confidence level that statisticians often use when assessing whether a pattern is genuine. This doesn't mean that interest rates don't matter, of course. It just means that the relationship between Fed rate decisions and the stock market is far more complex than can be exploited by a mechanical market-timing model.