Last week’s stock rebound was so sharp you could carve your holiday turkey with it.

The Dow Jones Industrial Average plunged 890 points in seven trading days, then regained 736 points in the next three. At Friday’s close it was at 17804.80, less than 1% from its Dec. 5 record.

The snapback reflected investor confidence that the U.S. economic recovery is for real, that inflation will stay low and that Federal Reserve rate increases next year won’t end the bull market.

But the sudden rally may be hard to sustain. It was driven partly by the fact that many mutual funds have risen less than the big indexes. Some money managers are desperate to boost performance, so they won’t look bad compared with the S&P 500. Some are pumping available cash into stocks they think will rise faster than the market.

“If you are among the 85% of money managers behind the S&P 500, this is a chance to catch up,” said Jack Ablin, chief investment officer at BMO Private Bank, which oversees $68 billion in Chicago.

Because some of that investing is short-term, the danger is that managers could shift some money elsewhere early next year.

Something like that happened this year, when the Dow fell 7.3% in January and early February, before rebounding to a record high in April.

Mr. Ablin added that if the market keeps getting more expensive, he will consider trimming his own holdings in U.S. stocks, but not before next year. If he sold this year, he would face 2014 capital-gains taxes. He also would miss any late-year market gains.

Historically, late December is fantastic for stocks. In the last seven trading days, which is what remains this year, the Dow has risen 79% of the time since 1928, according to Bespoke Investment Group. Its average gain in that brief period is 1.4%, just about the entire average gain for the full month.

January also is normally strong, as retirement money flows into stocks. The 2014 weakness was due partly to bad weather, but also partly to money managers pulling back after playing catch-up in December.

The reason people are concerned is that U.S. stocks aren’t cheap, especially compared with those of Europe and the developing world.

After rising 30% in 2013, the S&P 500 is up 12% this year. It trades at 1.7 times its companies’ sales for the past 12 months. That is 20% above its historical median, Mr. Ablin calculates. Developing countries are at less than one times sales, 10% below their historical median. He hasn’t yet shifted money away from the U.S., but he is thinking about it.

Not everyone is concerned. For one thing, stocks soon recovered from their January slump in 2014. For another, stocks still are short of where they were Dec. 5, notes investment strategist Jason Pride at Glenmede Trust Co., which oversees $28 billion in Philadelphia.

Mr. Pride says the rebound had more to do with shifting views on the oil-price declines than with catch-up efforts.

People initially feared currency and debt markets could be destabilized. Then, helped by a Fed promise to be patient, they decided markets could withstand the shock and that cheaper oil would be positive.

“I don’t think it is necessarily performance-chasing into the year-end. It could be justified as people digest what lower oil prices mean,” Mr. Pride said.

That said, Mr. Pride agrees that high stock prices make it harder for the market to produce big returns. Like many, he projects stock gains similar to those of corporate earnings, although he adds that he wouldn’t be surprised if stocks surpassed expectations, as they did in 2013 and 2014.

“There is a good argument that these are the valuations you sit at in an economic expansion, and that valuations can even expand” as investors pile into a rising market, he said. In the past, stocks have become more expensive than they are now, although the higher they go, the riskier they get.

Now that the Federal Reserve has stopped making huge bond purchases to support markets and is preparing to raise short-term interest rates, stock swings could be even sharper in 2015, said Kristina Hooper, U.S. investment strategist at Allianz Global Investors, which oversees $488 billion.

“The stock market is taking two steps forward and one back, sometimes one and a half” steps back, Ms. Hooper said. “Our concern is that we are likely to see more volatility going forward, not less.”

It will be worse if the Fed shows signs of raising rates at midyear, Ms. Hooper said. Interest-rate futures suggest many investors expect rates to remain steady until the second half of the year, but Ms. Hooper believes the Fed will move at midyear, which could cause anxiety.

In addition, “there is the likelihood that the market could sell off a bit in January,” Ms. Hooper said. “We could see a revisiting of concerns about valuations.”

She isn’t expecting lasting damage, but she does expect single-digit percentage gains for major indexes in 2015, with some thrills and spills.

What the past few days have shown is that investors are hopeful about the economy and afraid of missing out on gains, but also afraid of being over-exposed if expensive U.S. stocks suddenly slump.

In 2014, that mix created temporary jitters, but nothing severe. Many money managers hope it will be no worse in 2015.