The CEO of American Airlines netted a profit of $13.4 million from selling shares and options that he accumulated while running US Airways.Doug Parker sold more than one-third of his stake in the company formed by the merger of American and US Airways, but he still owns nearly 1.4 million shares, according to a regulatory filing. That stake was worth nearly $47 million at Friday’s closing price. Fort Worth-based American disclosed the stock transactions by Parker and other top executives in filings with the Securities and Exchange Commission.American and US Airways merged in December, and shares and options in each airline were converted to the new company, American Airlines Group. Parker acquired 505,375 shares on Thursday by exercising options he received for the 2005 merger of US Airways and America West, and which were due to begin expiring later this month. That boosted his stake to more than 2 million shares, and he sold 702,375 shares on the same day. A company spokesman said that about half of Parker’s profit came from selling shares that he bought in 2008 as a show of confidence at a time when the airline industry was struggling with skyrocketing fuel costs. Parker told employees this week that he and his wife would donate $1 million to a fund that helps employees with financial problems. American’s shares (ticker: AAL) fell 61 cents, or 1.8 percent, to close at $34.41 on Friday.