Hedge fund titan David Tepper, founder and president of Appaloosa Management, told CNBC on Tuesday he's still bullish on stocks and investors shouldn't worry about the Federal Reserve tapering its massive bond-buying program.
"There better be a true [Fed] taper or else you might be back into the last half of 1999," Tepper said in a "Squawk Box" interview. "So like guys that are short, they better have a shovel to get themselves out of the grave."
"If the Fed doesn't taper back, we're going to get into this hyper-drive market," he explained. "It's a backwards argument. To keep the markets going up at a steady pace the Fed has to taper back."
He thinks a natural path will develop for the Fed to exit its accommodative stance.
Tepper, whose Appaloosa delivered an after-fee annual return of 30 percent in 2012, joking compared the reason for being in stocks to the ending of the movie "My Cousin Vinny"—saying the evidence is overwhelming. The fund manager said that "the economy is getting better, autos are better, housing's better it continues to improve, they can't find enough people to work in housing, that's the only thing holding it back right now."
By his calculations, he said there's $400 billion in the economy looking for a place to go—and stocks are one of those places. Tepper said he's nervous to be short anything because there's so much unallocated cash.
The last time Tepper was on CNBC, he said stocks were cheap, and on "Squawk" Tuesday he said he still feels that way.
He referenced a blog by the New York Fed talking about valuations. He said the post showed "when the equity risk premium is high historically, you get better returns after that." He continued, "So we're at one of the highest all-time risk premiums in history."
Tepper's Short Hills, N.J.-based Appaloosa has about $18 billion under management, and he topped Institutional Investor's Alpha magazine's 12th annual "Rich List"—earning $2.2 billion last year.
His appearance on "Squawk" in September of 2010 sparked what was dubbed "The Tepper Rally" after he said the Fed's asset-purchase program virtually guaranteed strength in stocks. Since then, the Dow Jones Industrial Average and the S&P 500 have each gained about 45 percent.
Tepper said he still has a position in Apple and it should perform with the market. He suggested the tech giant's stock could resume its uptrend if the next new product is revolutionary or evolutionary.
He said his biggest holding is still Citigroup, yet he holds a small position in another big bank, JPMorgan Chase. Once considered one of Wall Street's best-run banks, JPMorgan is now facing calls to split the chairman and the CEO roles currently held by Jamie Dimon.
Tepper didn't want to comment directly on the JPMorgan situation, but said he generally favors those jobs as separate from one another.
As for the economy, he said it has characteristics of an early stage recovery and it doesn't matter whether the Fed's easy monetary policy has helped or not. "The private sector of the economy, what we care most about seems to be in pretty good shape," he said.
Once the government's fight over mandatory spending cuts have been resolved, "it's going to be a really interesting second half of the year," Tepper added.
"The deficit over the next six months is shrinking massively ... because of tax increases, because of budget cuts," he said. Growth, as well as "Fannie Mae paying back money to the government, and also Freddie Mac soon to pay back money to the government" have also been helpful factors, Tepper said.
In Japan, he said, the stock market there could rise even more as the central bank there moves to flood markets with massive monetary stimulus.