Andrew Caspersen, a former Wall Street executive and scion of a wealthy family, pleaded guilty on Wednesday to federal charges that he defrauded friends, relatives and a hedge fund billionaire’s foundation of nearly $40 million.

Accompanied by his lawyer, Mr. Caspersen, 39, arrived at a federal courthouse in Manhattan to a small crowd of family and friends. Dressed in a dark suit with a bright orange tie, Mr. Caspersen pleaded guilty to one charge of security fraud and one charge of wire fraud, charges that each carry a maximum penalty of 20 years in prison.

It represents a steep fall for Mr. Caspersen, an Ivy League-educated financier whose lawyer has argued that a “compulsive gambling addiction and mental illness” prompted him to mastermind a Ponzi-like scheme earlier this year.

“The people I harmed were people I cared for the most,” Mr. Caspersen said, reading from a statement. His voice wavered as he stumbled over the last words, “I could not be more sorry or ashamed for my crimes.”

Mr. Caspersen’s decision to plead guilty does not come as a surprise, because his lawyer said last month he would not contest the charges. It is unclear, however, whether Judge Jed S. Rakoff of Federal District Court will use leniency in sentencing Mr. Caspersen by viewing his mental health affliction as a mitigating circumstance.