Your uneasiness is warranted.  The easy part of the question is the unrelated business income issue.  The Courts have regularly held that net income received on investments maintained in a margin account is income from “debt financed property” and therefore subject to unrelated business income tax (“UBIT”). (See Nonprofit Issues®, Tax Matters, 11/1/10.)

Whether the account itself is improper is a matter of state law that depends on a number of different issues.  My guess is that it isn’t illegal per se, but may be riskier than you want.  First, it sounds as though you have delegated investment discretion to a brokerage firm to invest and reinvest for you without consultation.  Under the general “prudent investor” rules, this is permissible if you have given a qualified professional sufficient investment policies within which to act for you.

Second, is the amount pledged as security for the account “true” endowment composed of funds given to the organization by donors who want the principal to be held forever and only income used for current expenditures, or is it simply accumulated reserves that you can spend at any time you want?  Courts and Attorneys General are much more protective of endowment than they are of reserves.

But even with true endowment, the Uniform Prudent Management of Institutional Funds Act, now adopted in some form in every state except Pennsylvania (See Ready Reference Page: “New UPMIFA Sets Rules For Management of Charitable Funds”) does not prohibit loans directly to businesses or pledges as security for other assets.  A trustee is required to “invest the fund in good faith and with the care an ordinarily prudent person in a like position would exercise in a similar situation.”  Management decisions are not reviewed on an individual basis, but in the context of the total portfolio.  There is obviously a lot of leeway in a board’s thoughtful decision-making.

Since a margin account increases the leverage available for investment and exaggerates both the good and the bad, it should have been pretty good for the last few years, but could have been disastrous during the market crash in 2008 and 2009.  Because no one can know the future of the market (though many will predict it), it costs money to pay the interest on the loan borrowed to play with a margin account, and you have to share any of your winnings with the federal government, you may decide that the likely benefits are not worth the risk. You will never have a hard time justifying that decision.  You may have a hard time if you lose big time in the next crash.