By JEFFREY SONNENFELD

April 1, 2015 7:13 p.m. ET

For all the talk about activist shareholders—usually large hedge funds—getting seats on company boards and pushing to make strategic, value-enhancing changes, these activists haven’t fared especially well. Investing in index funds would have yielded better returns over the past few years than most activist funds.

How much better? In 2013 the HFR Activist index posted a total return of 16%, less than half the S&P 500 Index’s total return of 32.4%. In 2014 the HFR Activist Index saw returns of 4.8%, far below the S&P 500’s 13.7%.

Contrary to their rhetoric, many activist investors lack the Midas touch. Their recent returns may exceed the performance of other hedge funds, but they still lag behind the broader market. Ironically, the major companies targeted today, including Apple, PepsiCo, Dell, Dow and DuPont, generally deliver returns that soar above that of activist funds.

Some funds, such as Third Point, Relational Investors, Starboard Value and TPG-Axon Capital, have driven constructive outcomes at Yahoo, Office Depot, Hewlett-Packard, Home Depot and SandRidge Energy. Yet too often activists pressure companies to cut costs, add debt, sell divisions and increase share repurchases, rather than invest in jobs, R&D and growth.

They do all this in the name of creating shareholder value. But that value is often short-lived and sometimes comes at the expense of long-term success, if not survival. Despite Carl Icahn’s successes—such as Chesapeake Energy (Netflix and Apple were great investments but they resisted his advice)—his overlooked failures include TWA, WCI Communities, Blockbuster and Dynegy, all of which are either out of business or have filed for bankruptcy.

Nelson Peltz’s Trian Fund Management and its activist assaults on the Bank of New York, PepsiCo and DuPont are an interesting case in point. Trian delivered only an 8.8% return in 2014, nearly five percentage points below the S&P 500. In 2012 Trian was up a scant 0.9% while the S&P 500 was up 15.9%. Clearly, this undermines Mr. Peltz’s argument that DuPont’s board needs Trian and Mr. Peltz to drive better returns.

Five of the 11 companies where Trian has a seat on the board underperformed the S&P 500 between the time Trian got its seat and the end of last year—Wendy’s, Legg Mason, Mondelez International, Family Dollar and Chemtura, which went bankrupt in 2009 after two years of Trian board involvement. Contrast these companies with State Street, which rejected Trian’s breakup and board-seat demands and has handsomely outperformed the S&P 500 (129.5% to 80.5%) over the past four years—without Trian’s help.

Even better returns were available to those who invested in companies that activists sought to topple. Suppose on Jan. 1, 2010, you put $100 each in DuPont, an S&P 500 mutual fund and Trian. Your investment in DuPont would be worth roughly $240 today. Your S&P 500 fund would be worth roughly $200. And your investment in Trian would we worth roughly $190. DuPont’s returns handily beat those of Trian in 2010, 2012 and 2014.

Mr. Peltz now is waging a costly, distracting proxy battle to break up DuPont to deliver short-term gains while demanding he personally have a seat on the company’s board. This despite Trian’s poor showing versus DuPont and the latter’s recent hiring of two new directors, Edward Breen and James Gallogly, two former CEOs and tough industrialists whom Mr. Peltz unsuccessfully solicited in 2014 to serve on Trian’s board of directors.

Given DuPont CEO Ellen Kullman’s success since taking the reins in 2009, it’s not surprising that Trian’s assault has been thwarted. Nevertheless, DuPont has offered to accept a current Trian board nominee—other than Mr. Peltz—out of respect for Trian’s 3% stake.

As Securities and Exchange Commission Chairman Mary Jo White said in a March 19 speech at Tulane University’s Corporate Law Institute: “Reflexively painting all activism negatively is . . . using too broad a brush and indeed is counterproductive.” Activists and their target companies, she said, should “step away from gamesmanship and inflammatory rhetoric that can harm companies and shareholders alike.”

But with activist funds now boasting $120 billion under management—up 30% in the past year—there is no harm in asking what their own investors are getting back. The most aggressive activists court governance advocates and state pension funds with costly media campaigns against target companies that, paradoxically, outperform them. Perhaps they should be more active in raising their own shareholder value.

Mr. Sonnenfeld is a professor of management and senior associate dean of leadership studies at the Yale School of Management.