If a stock-market selloff is coming, September might appear to be a likely time for it to start.

Over the past century, September has been by far the worst month on the calendar for the Dow Jones Industrial Average, with an average loss of 0.8%. That contrasts with an average gain of 0.8% in the other 11 months.

This track record prompts some short-term traders to sell stocks as September approaches, or to postpone investing cash they have accumulated. This year, concern is particularly heightened because it has been three years since a correction, defined as at least a 10% decline. The historical average is one correction every 12 months or so.

But a closer look shows that a drop is no more probable this September than it was earlier this year — or will be in coming months.

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One reason not to make changes to your portfolio just because Labor Day is approaching is that September’s reputation derives mainly from years in which the market already was declining — which it isn’t this year. Over the past century, when the Dow was sporting a year-to-date loss through the end of August, it proceeded to lose 2.7% on average in September and fell in the month more than two-thirds of the time.

By contrast, when the Dow had a year-to-date gain through August, it gained an average of 0.3% in September, and rose as often as it fell. This year, the Dow is up 3% through Thursday. Last year, the Dow had a year-to-date gain through August, and it proceeded to rise 2.2% in September.

Another indication that the arrival of September isn’t a harbinger of doom comes from a list of historical bear markets compiled by Ned Davis Research, a quantitative-research firm based in Venice, Fla. Though a few bear markets in the early part of the last century did begin in September, most notably the one that preceded the 1929 stock-market crash, in recent decades September has seen a below-average number of bear-market beginnings. Over the past 60 years, for example, twice as many bear markets started in April than in September.

Additional evidence shows up in the performance of investment advisers tracked by the Hulbert Financial Digest. Advisers who tend to perform the best in September are the same ones who do well during the other months of the year.

The adviser with the best record over the past five years, among the 200 monitored, is Teal Linde, editor of the Linde Equity Report, which has logged an average gain of 29% annually over that period, versus 17% for the S&P 500, assuming reinvested dividends. Sure enough, Linde also is the second-best performer during the past five Septembers.

The implication for most investors is that they should stick with whatever stock allocation they have concluded is appropriate for January or May or any other month. If you had 60% of your investments in stocks heading into August, chances are that is a reasonable allocation for September, too.

Most investors are best-served by investing in broad, low-cost index funds, such as the Schwab U.S. Broad Market SCHB, -1.06% exchange traded fund and the Vanguard Total Stock Market VTI, -0.97% ETF. They charge annual expenses of 0.04% and 0.05%, respectively, or $4 and $5 per $10,000 invested.

If you want to try your hand at doing better than the overall market, you can turn to stocks and funds that are especially popular among the 40 Hulbert Financial Digest-monitored investment advisers who have beaten the overall stock market over the last 15 years. That is a long enough period to largely eliminate the role luck plays in an adviser’s return.

Two stocks are recommended by eight of these market-beating advisers: consumer-technology giant Apple AAPL, -3.17% and drug company Pfizer PFE, -0.51% . Nearly as popular, each recommended by seven market-beating advisers, are another drug company, Johnson & Johnson JNJ, +1.36% ; a utility, Southern Co. SO, -1.32% ; and railroad company Union Pacific UNP, -0.91%

Two actively managed bond funds are each recommended by five of these market-beating advisers: the Fidelity Floating Rate High Income Fund, which invests in variable-rate bank loans that typically offer higher yields, and the Vanguard Short-Term Investment-Grade Fund, which invests in lower-yielding debt that is of the highest quality. The funds charge annual fees of 0.70% and 0.20%, respectively.

Mark Hulbert is editor of the Hulbert Financial Digest, which is owned by MarketWatch/Dow Jones. Email: mark.hulbert@dowjones.com