NEW YORK – Would you buy stock in a company that has hemorrhaged tens of billions of dollars for years and run through four bosses in quick succession just because it has turned a profit for a few months?

That is essentially what General Motors will ask investors to do when it takes itself public again with one of the largest initial stock offerings ever. With the stock market already on edge, it’s a lot to expect.

The good news: Longtime investors say buying during bad times is the best way to make money with auto stocks, provided you have a stomach of steel. And for the brave, GM may offer a perfect opportunity.

“The stocks look expensive when profits are low, but that’s traditionally when you should get in,” says Standard & Poor’s analyst Efraim Levy.

GM filed papers Wednesday with regulators detailing its plans to return to the stock market. Though it didn’t specify a date, experts say the offering could come as early as October.

The company earned $1.3 billion from April through June, its second profitable quarter in a row and a remarkable turnaround since its 2009 bankruptcy. Investors in initial public offerings, or IPOs, like to see several quarters of earnings, especially from manufacturers.

GM also said CEO Ed Whitacre would be leaving Sept. 1. He will be replaced by board member Daniel Akerson, who will be the fourth CEO in 18 months. And GM has the misfortune of planning an IPO when demand for new public shares remains low.

Still, U.S. carmakers have proved to be good investments if you get the timing right.

That is the conclusion of McGinn Investment Management, run by self-described “contrarian” investor Bernie McGinn, after studying five-year returns for investors who put money into GM and Ford a year before the start of recessions. The firm looked back over three decades.

Over the five years that began in July 1980, GM and Ford stock rose 83 percent and 185 percent before dividends, respectively, versus a 58 percent gain for the S&P 500.

They also beat the broader market in the years surrounding the early ’90s recession, too. GM stock rose 38 percent and Ford 51 percent. The S&P: 29 percent.

McGinn started his calculations a year before recessions because stocks tend to slump in anticipation of economic slowdowns. Many economists think the Great Recession ended a year ago, so it’s not clear the trend here could apply to GM shares. Then again, stocks are still down sharply from before the recession, and fears of another downturn are rife.

The exception to the winning pattern was the period surrounding the dot-com stock bust and subsequent recession. The S&P fell 19 percent in the five years between March 2000 and March 2005. But the two carmakers lost more than twice as much as investors pummeled them for spending too much on salaries and benefits and not coming up with enough hot cars.

“The question now is, has the American auto industry turned the corner?” asks McGinn, who has been managing money for 30 years. “Do they have their costs in line? Do they have focus?”

McGinn, who owns Ford shares, thinks U.S. car makers have improved. But he says he will wait until GM announces the price of its stock before deciding whether to buy.

The “bull” case for “Government Motors,” as GM is derisively called, is that it is making solid profits even though U.S. sales are still near historic lows, running at an annual rate of about 11.5 million cars and trucks this year.

Most industry analysts predict sales will rise above 12 million next year and reach about 14 million in 2013. So if GM can hang on to or increase its market share, its profits will rise as well.

GM can make money at lower U.S. sales rates because it shed billions of dollars in debt during last year’s bankruptcy. Also, it shifted billions in retiree health care costs to a United Auto Workers union trust fund, and the UAW agreed to contract concessions allowing it to pay new hires about half the wage rate of older workers. It closed 12 factories, and is using those remaining at more than 90 percent capacity versus 38 percent a year ago.

So, do you buy GM or not? It’s too early to tell, of course, until a price is set.

Kirk Ludtke, an analyst at CRT Capital Group, argues that GM could be worth more than ever in the stock market. But former U.S. budget director David Stockman, who made and lost millions in the auto industry while working on Wall Street, urges caution. He says the U.S. faces a glut of cars for years to come, and even a leaner and meaner GM is likely to get hurt.