The money invested by the administrators bolstered Chile’s capital markets, which stimulated economic growth and yielded reasonable returns. Today six A.F.P.s — half of them owned by foreign companies — manage $171 billion in pension funds, equivalent to about 71 percent of Chile’s gross domestic product, according to the office of the supervisor of the pension funds.

But the pioneering privatized system has failed to provide livable pensions for most retirees. If the stock market dips or investments go awry, workers’ savings and retirees’ pension checks decline.

“The pension system is unfair,” said Romina Celis, a 28-year-old teacher who marched in one of the protests. “I don’t know what formula we can use, but there has to be more state participation. We must continue protesting. The thought of reaching old age so precariously is scary.”

Women fare worse than men do because they earn less, are more likely to work intermittently, retire earlier (the retirement age is 65 for men and 60 for women) and have a longer life expectancy.

A commission on pension reform, appointed in 2014 by President Michelle Bachelet, found that the median A.F.P. pension was equivalent to 34 percent of a retiree’s last average salary (24 percent in the case of women and 48 percent for men). The overall figure rose to 45 percent with supplements from a federally funded safety net established during Ms. Bachelet’s first term in office.

After warning that the pension system was “in crisis,” her government in 2008 introduced a minimum pension of about $140, funded by the state, for those who were unable to save for retirement during their working lives, and additional payments for retirees whose pensions did not reach that amount. More than 1.3 million Chileans, two-thirds of them women, receive such benefits.

But when examining projections for the next 10 to 20 years, the commission found that “it only gets worse,” said David Bravo, the director of the Catholic University of Chile’s Longitudinal Survey and Study Center, who presided over the commission.