Aetna Inc., which merged with US Healthcare Inc. last summer after selling its property-casualty insurance operations, reported its second-quarter earnings fell 20%. Operating earnings from continuing operations were up 24%, when one-time items were excluded. Those results were in line with Wall Street expectations, but Aetna shares plunged $14.25 to close at $102.75 on the New York Stock Exchange. Analyst Gary Frazier at Bear Stearns & Co. said the stock price slid because the Hartford, Conn.-based company offered projections in a number of areas that were below expectations. Medicare-related costs were higher than anticipated as Aetna attempted to move into new markets, and medical costs represented a higher proportion of premiums than projected. Aetna earned $230.1 million, or $1.43 a share, in the three months ended June 30, compared with $288 million, or $2.47, a year ago. Net income for the second quarter of 1996 included a $264-million gain from the sale of the property-casualty operations. This year's second-quarter results reflect Aetna's merger with US Healthcare, which was completed July 19, 1996. Excluding unusual items, operating earnings from continuing operations amounted to $205.8 million, or $1.27 a share, compared with $166.2 million, or $1.43, a year ago.