Doug Parker, chief executive of American Airlines Group Inc., on Monday exercised and sold 113,000 stock appreciation rights he received over three years when he was CEO of US Airways Group Inc.

In the 2013 merger of American and US Airways, the US Airways rights, similar to stock options, translated into new American shares on a one-for-one basis.

Mr. Parker, according to a federal filing, exercised this batch of stock-appreciation units because they expire over the next 12 months. To facilitate their sale, he set up a securities trading plan for insiders, called a 10b5 plan. This tranche of appreciation rights was exercised at $6.70 a share. Mr. Parker netted $2.37 million after the acquisition expense and taxes, American said.

The executive has other appreciation rights at award prices ranging from $3.10 a share to $38.44, but he will have to pay to exercise them before he can sell them in the open market. Their value will depend on the share price of American stock at the time they are sold.

Mr. Parker in April said he accepted a new 2015 compensation plan that consists almost entirely of 207,672 restricted stock units, the value of which will depend on American's performance. At the time, Mr. Parker said he favored a stock-based compensation plan earned by performance.

At American's current share price of $43, that award would be valued at about $8.94 million. American's shares have lost 20% of their value so far this year.

Last year, Mr. Parker's total compensation was $12.3 million, about 40% in cash, including a $700,000 base salary and an annual incentive payout of $2.8 million.

In his 2015 package, 54% of the restricted stock units will vest in April 2018 only if American's pretax income margin for the prior three years achieves a threshold performance compared with a group of rival airlines. The other 46% of the restricted stock awards will vest in two installments, two-thirds on the first anniversary of the award and the rest a year later.

According to a federal filing, Mr. Parker owns 1.66 million American shares.

Write to Susan Carey at susan.carey@wsj.com

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