Relieved investors sent stocks sharply higher Tuesday after Russia pulled troops back from the border of Ukraine. The rally erased steep losses from Monday caused by fears of an escalating conflict.

KEEPING SCORE: The S&P 500 index was up 28 points, or 1.5 percent, at 1,873 as of 3:55 p.m. Eastern time Tuesday. It was the biggest gain for the benchmark index since October.

The Dow Jones industrial average rose 224 points, or 1.4 percent, to 16,392. The Nasdaq composite rose 74 points, or 1.7 percent, to 4,351.

RISING TIDE: The gains were extraordinarily broad. Five stocks rose for every one that fell on the New York Stock Exchange. All 10 industry sectors in the S&P 500 average rose.

RELIEF RALLY: The volatility comes after the S&P 500 closed at a record high on Friday, then posted its biggest decline in a month on Monday. That has left investors trying to figure out whether stocks are overvalued or whether they reflect an improving economy.

WHAT’S AN INVESTOR TO DO? “I think maybe you take a powder. Maybe take some positions off the table, and you hedge yourself a little but, for the chance that if it does go the other way and there is a downturn,” said Stephen J. Carl, head equity trader at The Williams Capital Group.

GOING FOR RISK: Bond and gold prices fell as traders moved money out of safe-play assets. The yield on the 10-year Treasury note rose to 2.68 percent from 2.60 percent late Monday. In another sign that investors were embracing risk, small-company stocks rose more sharply than the rest of the market. The Russell 2000 index of small stocks surged 33 points, or 2.9 percent, to 1,210.

ENERGY PRICES: Oil prices also fell as the immediate threat of economic sanctions on Russia, a major oil exporter, eased. Traders had also been worried about transportation disruptions in the Black Sea, a major transit point for oil.

WORLD MARKETS: Stock markets in Europe, including Moscow, and Asia recouped much of Monday’s losses. Indexes in France and Germany each rose 2.5 percent, and the FTSE 100 in Britain rose 1.7 percent.

THE SHACK PARES BACK: RadioShack Corp. plunged 48 cents, or 18 percent, to $2.24 after reporting a wider quarterly loss and saying it will close as many as 1,100 stores.

BUYBACK BOUNCE: Chipmaker Qualcomm rose $3.10, or 4 percent, to $76.73 after announcing a 20 percent increase in its quarterly dividend and adding $5 billion to its stock buyback program. Buybacks generally benefit shareholders because they increase the value of remaining shares.

PENNEY GAINS: J.C. Penney Co. rose 54 cents, or 7 percent, to $8.50 after Standard & Poor’s raised its outlook on the retailer’s debt, saying Penney’s performance “has begun to stabilize.” Last week Penney posted its first gain in two years at stores open at least a year.

DELTA TAKES OFF: Delta Air Lines rose $1.63, or 5 percent, to $34.22 after reporting strong February domestic demand and passenger revenue.