The start of the new year brings fresh optimism to many investors, and David Einhorn may be first among them this year. Einhorn's Greenlight Capital has suffered a string of setbacks in recent years, and the billionaire investment giant is no doubt looking for a way to start off 2018 strong.

Einhorn recently revealed to his investors in a quarterly letter that part of his plan to reinvigorate Greenlight Capital entails a new position in Twitter (TWTR), which he believes is undervalued compared to Facebook (FB).

New Position at $21.59

In his January 16 investor letter, Einhorn indicated that his fund "initiated a small position in Twitter at an average [price] of $21.59," according to a report by CNBC.  As of this writing, Twitter stock is trading for $24.16 per share.

Einhorn believes that "despite a massive user base and broad reach, Twitter has an enterprise value of about 2% of Facebook, the largest social media platform."

Greenlight's bet on Twitter is part of an attempt to outperform the firm's returns last year. In 2017, Greenlight brought in returns of just 1.6%, lagging behind rivals, as well as the broader market.

The average hedge fund rose by 6.5% over the same period, which was still far behind the growth of the S&P 500, which returned almost 22%, according to Bloomberg.

Greenlight's letter acknowledged the difficult position these returns had put its investors in, saying that "this must be frustrating to you, our partners. It is certainly frustrating to us." Einhorn said he hopes that Twitter's improvements to user experience will bring about a greater user base and, with it, more advertising possibilities and revenue growth.

New Stake in Brighthouse Financial

Besides Twitter, Einhorn's letter detailed several other new or altered positions going into 2018. Of these, one of the most significant is sure to be a position in Brighthouse Financial, Inc. (BHF), a life insurance company which spun out of MetLife last summer. Brighthouse has more than $220 billion in assets and is linked with fluctuations in the financial markets.

Greenlight believes, according to its letter, that analysts are too "laser focused" on the company's downside risks from a possible bear market, meaning they are "too pessimistic" about the company's share quality.

Einhorn also revealed to investors that he had taken on new positions in Ensco PlC, as well as a repurchased stake in Time Warner in response to the decline in stock price after the U.S. government opposed its sale to AT&T, Inc. "We think that the Department of Justice has a weak anti-trust case and the merger is likely to go through," Einhorn wrote in the letter.