Despite the current pullback, Standard & Poor's 500-stock index has returned a solid 12% over the past year. Not every stock in the index has gained, of course. Many, in fact, have lost ground. Are any of those stocks worth buying? To find out, we sifted through the index's losers over the past 12 months and sorted out those that our favorite stock fund managers have recently acquired, as well as those that are favorably rated by Wall Street analysts. We settled on five companies. All are contrarian bets and come with above-average risk, and all will require some (or maybe a lot of) patience and grit.

Avon Products

Share price: $11.32

One-year return: -43.7%

Why the stock is down: It's a long story. The cosmetic company's stock (AVP) was a Wall Street darling in the 1990s, but it stumbled in the mid aughts after a series of management missteps. As its business declined, Avon attempted corporate restructurings in 2005 and 2009 that ultimately didn't help. And in 2008, Avon began an internal investigation into bribery allegations in China; the U.S. government began its own investigation in 2011. Then, in 2012, just as new chief executive Sheri McCoy stepped in, Avon's board of directors rejected a $24.75-per-share buyout offer from Coty (COTY), the fragrance firm. Avon's stock--$20 when Coty made its offer--has since fallen by more than 40%. It recently dipped lower after Avon's chief financial officer announced that she was leaving.

Why we like it: McCoy is making strides toward righting the ship: She cut the dividend by 75%, leaving more cash to plow back into the firm, and launched a $400 million cost-cutting program that included pulling out of countries such as South Korea and Vietnam, where Avon wasn't performing well. She also resolved the China bribery allegations--without admitting any wrongdoing, Avon paid a $135 million settlement. Wall Street analysts expect operating earnings to fall 22% this year, but they see profits rebounding 18% in 2015. The stock looks cheap, selling at 13 times estimated earnings for the next four quarters. That's well below the average price-earnings ratio of 17 for three of Avon's major competitors--Coty, Estee Lauder (EL) and Nu Skin Enterprises (NUS).

Who bought it recently: Mark Finn at T. Rowe Price Value (TRVLX), who says he is positive on Avon, "as current management works through mismanagement issues of the past and focuses on improving the financial and operational condition of the firm."

Carmax

Share price: $45.06

One-year return: -5.1%

Why the stock is down: Stock in the no-haggle seller of used cars doubled between June 2012 and December 2013. But growth is beginning to slow at CarMax (KMX), and that could be a drag on the share price.

Why we like it: As consumer spending increases, so will car buying. CarMax is the biggest seller of used cars in the country, and its transparent sales style--in addition to the absence of haggling, customers stick with one sales agent from the moment they walk in the door to the moment they drive away in their newly purchased car--gets results. But the firm has plenty of other revenue drivers, too. It sells new cars in more than 120 locations, it has a financing arm (CarMax Auto Finance), and its wholesale-auction division is the third largest in the U.S. Analysts expect earnings per share to climb 13% in the fiscal year that ends next February and 10% in the year that ends in February 2016.

Who bought it recently: Chuck Akre, manager of Akre Focus (AKREX), a member of the Kiplinger 25, a collection of our favorite no-load funds; the managers behind Primecap Odyssey Growth(POGRX).

eBay

Share price: $50.24

One-year return: -6.9%

Why the stock is down: The online auction site has changed the way many people buy and sell almost everything, from paper clips to collectible cars. Its foreign sites are growing rapidly--overseas sales generate more revenue for eBay (EBAY) than do sales in the U.S. But this business is mature, and that repels the growth investors that eBay used to attract. The exciting part of the eBay story now lies in online payments. But PayPal, which eBay acquired in 2002, faces competition from, among others, Apple (AAPL) and possibly Facebook (FB), which hired PayPal's president earlier this year.

Why we like it: PayPal. The digital wallet system is the best-known and most established in the country, which means it is well-positioned to withstand growing competition. The number of transactions has grown 25% annualized for the past five years, three times faster than the online retail market, according to research firm Forrester. Buy the stock now, ahead of eBay's planned spin-off of PayPal at the end of 2015.

Who bought it recently: The managers at Dodge & Cox Stock (DODGX), a member of the Kiplinger 25; the team behind Primecap Odyssey Growth (POGRX).

Starbucks

Share price: $72.38

One-year return: -4.9%

Why the stock is down: It's taking a breather. Starbucks (SBUX) had been as hot as a steaming cup of java, nearly doubling between July 2012 and November 2013, when it topped $81.

Why we like it: S&P Capital IQ analyst Efraim Levy, who rates the stock a "buy," expects sales to increase a hefty 11% in the fiscal year that ends in September 2015. Overall, analysts see earnings jumping 19% for the year. Given that kind of growth, Starbucks's P/E of 24, based on estimated year-ahead earnings, is reasonable.

Who bought it recently: Will Danoff, manager of Fidelity Contrafund (FCNTX).

Western Union

Share price: $15.84

One-year return: -11.8%

Why the stock is down: Western Union (WU), the world's biggest electronic mover of money, faced a number of challenges over the past year, including a subpoena relating to a 2013 investigation into fraud-related money transfers, and news that Wal-Mart Stores (WMT) is launching a money-transfer business.

Why we like it: Western Union's network is extensive--it boasts some 500,000 agents in 200 countries--posing a high barrier to potential challengers. Plus, although the company was founded in 1851, it's far from old-fashioned. Western Union is building up its business in bank-account and debit- and credit-card-funded transfers, and these kinds of transactions are growing quickly (the number rose by 65% in 2013, according to Morningstar). Finally, the stock's dividend yield of 2.9% is nearly a full percentage point better than that of the broad market.

Who bought it recently: Mark Finn, manager of T. Rowe Price Value (TRVLX), who likes to buy large companies trading at bargain prices. "We used the short-term weakness to add to our stake, as we believe the market is underestimating the value of Western Union's network," he says.

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Nellie S. Huang is Senior Associate Editor at Kiplinger's Personal Finance magazine.