Many foundations and educational institutions are caught up in questionable relationships involving donors and trustees, and the banks and business tied to them, according to a Twentieth Century Fund report.

The report, made public today, was written by Chris Welles, a financial journalist, who states that "boards of trustees that rigorously maintain arm's-length relationships and pursue the best interests of the endowment fund above all still tend to be more the exeception than the rule."

A university may not sell off a certain company's stock in its portfolio because the shares were donated by the chairman of the company, who also happens to be a trustee of the university. Or a local bank's mishandling of a university's investment portfolio may be tolerated because the bank's chairman is a big donor and a trustee.

Welles cites numerous examples of apparent trustee influence on university portfolios.

Emory University's endowment and trust funds had a market value of $169.7 million as of Aug. 31, 1976, and 46.5 per cent of that amount was in a single company, Coca-Cola Co. Coke is well represented on the Emory board of trustees.

As of Dec. 31, 1975, nearly 40 per cent of the University of Rockester's endowment assets were in the stock of two companies, Eastman Kodak Co. (825,000 shares) and Xerox Corp. (735,000). Three executives from Kodak, including the chairman and president, and two from Xerox including the chairman, sit on the university's 34-member board of trustees.

The endowment fund also has holdings in three other financial institutions - all based in Rochester - each of which is represented on the board. The chancellor of the university is on the board of two of these corporations.

As of June 30, 1976, Washington University in St. Louis held stock in numerous companies, each of which had representation on the university's board.

The report points out that "failure to diversify portfolio assets is regarded by nearly all investment experts and some courts as inherently imprudent."

While the University of Rochester "unquestionably benefited from its Kodak and Xerox holdings, most such acquisitions are less successful," the report says.

Welles notes that "in addition to accepting gifts, endowment funds often purchase trustee-linked stocks on the open market."

One problem for a university in having a major holding in a single corporation is that the university may hesitate to dump the company's stock for fear of antagonizing the donor. And if enough shares in one company are dumped, it could force the market price down and cause the donor of the stock to have second thoughts about giving to the university next time.

Welles notes that colleges and universities often use commissions "to reward trustees and donord for their services."

He quotes one investment manager as saying: "Alumni at brokerage houses are always crying to the treasurer, talking about how generous they are during annual giving. Trustees feel it important to support alumni at brokerage houses who are or could be potential givers."