Company executives have little confidence that the stock market will return to all-time highs any time soon.

That is worrisome because insiders, as they’re known, presumably know more about their companies’ prospects than the rest of us do.

It’s therefore not particularly surprising that the stock market Thursday gave back — and more — its huge rally from the day before. The Dow Jones Industrial Average DJIA, -3.12% surged 932 points Wednesday and fell more than 1,000 points Thursday.

In April, insiders aggressively picked up the pace of selling. Nejat Seyhun, a finance professor at the University of Michigan and one of academia’s leading experts on interpreting the behavior of insiders, says this is perhaps the most bearish thing insiders can do. That’s because they normally are contrarians, selling more as the market rises and increasing the pace of buying as the market declines.

When insiders sell into a market decline, Seyhun reasons, it means they don’t believe their companies’ shares will be significantly higher any time soon.

And sell into a decline is what insiders, on balance, did in April, when the DJIA fell 4.9% and the S&P 500 SPX, -3.56% dropped 8.8%. Consider the insider sentiment indicator that Seyhun calculates for each month; it represents the percentage of publicly traded companies that saw net buying in that month among their officers and directors.

According to data provided by Seyhun, this indicator fell by 11 percentage points in April. That’s the sixth-biggest decline in the past 120 months.

Crucially, however, according to Seyhun, the five other months that saw bigger declines were ones in which the S&P 500 rose strongly. If we focus only on those months over the past decade in which the stock market declined, April was one of the only ones in which Seyhun’s indicator fell.

In an email, he classified this drop as a “steep deterioration of insider sentiment … [It] likely portend[s] additional price declines in insiders’ view.”

I’ve reported on Seyhun’s research before, most recently in late February. At that time, his insider sentiment indicator was “modestly positive.” Though the S&P 500 rose 8% over the month subsequent to that late-February column, insiders’ behavior in April represents a significant change of heart.

Following that and even earlier columns about Seyhun’s research, I received many emails wondering how to access his insider sentiment indicator. Jon Seyhun, Nejat Seyhun’s son and entrepreneur, is in the process of creating a website that will provide regularly updates of that indicator. Though the website is not yet live, you can put your name on a waiting list to be notified when it does. For the record, I receive no compensation from Seyhun or the website.)

I should emphasize that the insiders’ change of heart doesn’t mean the world is coming to an end. Seyhun’s indicator for April stood at 20%, which is just one standard deviation below the 10-year average of 26%. At a minimum, however