By Joseph Ax

Nov 19 (Reuters) - A former trader was sentenced to 2 1/2 years in prison on Tuesday for an unauthorized purchase of about $1 billion in Apple Inc stock that eventually led to the demise of financial services firm Rochdale Securities.

David Miller, 41, was sentenced by U.S. District Judge Robert Chatigny in Hartford, Connecticut, seven months after pleading guilty to wire fraud and conspiracy.

Prosecutors said Miller, of Rockville Centre, New York, conspired with another individual to buy 1.625 million Apple shares on Oct. 25, 2012, the same day that the company planned to report third-quarter results, in the hopes that the share price would rise.

The alleged co-conspirator was not named in court papers.

Miller falsely told Rochdale the trade was for a customer who had, in fact, only asked to buy 1,625 shares, prosecutors said.

When the gamble failed, Rochdale faced $5.3 million in losses on the additional unauthorized shares, leaving the firm undercapitalized, according to a related civil lawsuit filed against Miller by the U.S. Securities and Exchange Commission.

As a result, the firm eventually collapsed, the SEC said. Rochdale, which was based in Stamford, Connecticut, was not a defendant in either case and did not face allegations of wrongdoing.

Prosecutors also said Miller defrauded another brokerage by convincing it to sell 500,000 shares of Apple to hedge against the purchase he had made at Rochdale.

The second brokerage, which prosecutors said was able to trade out of the position at a profit, was not identified in court papers.

Miller deeply regrets the harm his actions caused, said his defense attorney Kenneth Murphy.

"As we said on the day of his plea, this was a good and decent man who had led an otherwise exemplary life who acted out of desperation rather than greed," he said. "Judge Chatigny saw this to be the case and gave David a fair and reasonable sentence considering all these factors."

The cases are U.S. v. Miller, U.S. District Court, District of Connecticut, No. 12-mj-00288; and SEC v. Miller in the same court, No. 13-00522.