Most of the largest mutual fund companies, including BlackRock and T. Rowe Price, have pricing committees that work independently from the portfolio managers who bought the shares. This is done, Mr. Larsen said, to prevent money managers who might have a stake in keeping a valuation high from influencing the valuation.

In the case of Fidelity, it valued its stake in Snapchat at $22.91 a share as of Sept. 30, down from $30.72 in the previous quarter, according to data compiled by the research service Morningstar.

The move by Fidelity was reported earlier by The Financial Times. The markdown of Dropbox by BlackRock was reported earlier by The Information.

One late-stage investor in Dropbox said that the drop in that company’s value by mutual funds was a result, in large part, of the fact that the company is often compared with Box, a storage company that went public in January and currently has a market value of about $1.6 billion.

Dropbox, by comparison, was valued in its last fund-raising at around $10 billion. The large discrepancy between Box’s market capitalization and Dropbox’s private valuation has become a factor as mutual funds worked to create an accurate estimate of how much their Dropbox shares were worth.

It is unclear why Fidelity marked down its investment, and whether the move was because of faltering performance in Snapchat or because of rough comparisons to publicly traded social media companies. Twitter, for example, suffered a nearly 26 percent drop during the third quarter, though Facebook rose almost 5 percent during that same time.

But those companies are very different from Snapchat, making comparisons difficult if not impossible. The service is a combination of photo and video messages — including the famous disappearing photos that first made its name — and a publisher of mobile content from companies like Vice and CNN through its Discover section.