The stock market is off to a great start under the new administration but President Trump's own social media company isn't riding the rally.

Shares of Trump Media & Technology Group, majority owned by Trump, sank 11% Tuesday and were 3% lower at $34.47 early Wednesday. Ahead of last year's election the stock was seen as a proxy for the chances of a Trump victory -- it has struggled for direction since the outcome became clear in November.

Now that he's back in the White House, it looks as if investors are unsure what the future holds for the stock.

The Truth Social parent's shares, trading under the ticker DJT, plunged 11% Tuesday - the first trading day after Trump's inauguration. Heading into Wednesday's trading, the stock has fallen 31% from a recent peak of $51.51 the week before the election.

The shares appeared to rely on the buzz and momentum created by Trump's campaign and subsequent victory, rather than trading based on fundamentals. Now that the dust has settled investors have other, more tangible, ways to play the president's second term.

On Tuesday, investors instead focused on Trump's executive orders and the sectors that might benefit from his early policy decisions. For example, Oracle stock was one of the S&P 500's biggest risers as the software company was included in a joint venture with the White House, OpenAI and SoftBank. The venture will invest up to $500 billion in artificial intelligence infrastructure in the U.S.

Trump's backing of traditional auto makers in his inauguration speech and removal of an electric-vehicle mandate gave investors cause boost General Motors and Ford stocks.

In among all of that, DJT has been left behind. Truth Social has undoubtedly grown in importance -- the president used it to fire four government officials from the Biden administration. It could even become the place for some important policy announcements in the months ahead.

But that may not be enough to reinvigorate the stock.