(Adds Greenlight 2017 performance, Einhorn comments on tech, industrials, gold)
BOSTON, Jan 16 (Reuters) - Hedge fund manager David Einhorn told investors on Tuesday that he made a "large" bet on insurer Brighthouse Financial late last year, and had made money on General Motors but lost by shorting Amazon and Tesla.
Einhorn's Greenlight Capital bought into Brighthouse, MetLife's former U.S. retail life-insurance business, at an average cost of $57.92, according to a letter sent to clients and seen by Reuters. The stock is now trading at $63.90.
The fund manager said General Motors, which was his firm's biggest winner last year, remains "significantly under valued" given the automaker's "impressive fundamental performance."
But Einhorn also said he again lost money by betting that a group of fast-growing technology stocks, including Amazon, Netflix, and Tesla, would fall. "The biggest losers for the year were our short positions on the 'bubble basket'," Einhorn wrote.
Greenlight Capital, whose annualized 15.4 percent return over more than two decades make it one of the world's most closely watched hedge funds, posted only a modest return in 2017. The firm's 1.6 percent gain trailed the Standard & Poor's 500 21.8 percent gain and Einhorn said it was a tough year for so-called value investors like himself.
"While it feels like we have been running face first into the wind, we don't intend to capitulate and are sticking to our strategy of being long (on) misunderstood value and shorting 'not value'," he wrote.
Greenlight made money on German energy company Uniper and performance chemicals business Chemours, and took new stakes in offshore rigs operator Ensco and social media company Twitter.
Time Warner was bought again because Greenlight thinks the planned merger with AT&T will go through. And if it doesn't, "TWX has several strategic options to create value," said Einhorn.
Einhorn was candid about his losses, noting that his bet on pharmacy retailer Rite Aid, in which he invested at $7.45 a share, did not turn out the way he expected. He exited at $2.78 a share.
Greenlight is still betting that the price of gold will rise, but Einhorn said the firm lost money on the VanEck Vectors Gold Miners ETF and got out. "We don't need additional exposure to mining equities to express that view," he wrote.
Reporting by Svea Herbst-Bayliss; Editing by Chizu Nomiyama and Rosalba O'Brien