A federal judge in Manhattan on Thursday rejected a request that a gold trader from Turkey be granted an unusual form of release pending trial that would have allowed him to sign a $50 million bond, secured by $10 million in cash, and to live in a kind of self-financed gilded cage.

Judge Richard M. Berman, in denying bail to the trader, Reza Zarrab, said his proposal to live in a recently leased apartment under 24-hour armed guard and GPS monitoring, all at his own expense, “is unreasonable because it helps to foster inequity and unequal treatment in favor of a very small cohort of criminal defendants who are extremely wealthy, such as Mr. Zarrab.”

Judge Berman said prosecutors had shown that Mr. Zarrab, 32, posed a risk of flight and that no conditions, “including privately funded armed guards, will reasonably assure his appearance at trial.”

Mr. Zarrab, who was born in Iran and moved to Turkey as an infant, was arrested in March during a trip to Florida with his wife and daughter, and sent to Manhattan to face charges that included conspiring to violate the United States sanctions on Iran. Mr. Zarrab has pleaded not guilty.