Wall Street’s unrelenting campaign to put private assets in Americans’ retirement plans has given rise to impassioned claims both for and against. A recent study suggests neither hysteria nor hyperbole is warranted: The outcomes for most people, frankly, might be lackluster.

By adding even a small allocation of private equity or private credit to retirement portfolios, retirees could expect a bit more annual income, according to a new paper from Morningstar Investment Management. The most benefits accrued to those with bigger portfolios and higher savings rates. For those with the largest balances and ample contributions, the median marginal increase ranged from about $210 a year to just over $1,770, depending on the allocation to private assets.