LONDON -- When sentiment turns, a previously unpopular share can rise sharply. Here I have found three FTSE 100 shares that, with a fair wind, could do just that in 2013.

Tullow Oil
Shares of oil explorer Tullow Oil (LSE:TLW) have fallen almost 20% in the last year. That's a big fall for a FTSE 100 company, especially when you consider that we are in a bull market.

On Wednesday, the company reported its 2012 results. Sales rose just 2%, while earnings per share (EPS) fell 5%. Its dividend held at $0.69 per share.

Tullow has long been one of the most successful oil exploration companies on the market. 2013 will see the company drill key wells onshore in Kenya and Ethiopia. If Tullow can continue its recent drill success rate in this acreage, these prospects could prove to be transformational for the company in 2013.

Lloyds Banking Group
I believe that Lloyds Banking Group (LSE:LLOY) (NYSE:LYG) will provide further evidence of its recovery with its 2012 results on 1 March.

Lloyds' profits have been hit hard by Payment Protection Insurance compensation claims. However, little further provision for these costs is likely. 2013 could be the year that banking analysts put more emphasis on Lloyds' profit potential.

The bank is forecast to report 3.9 pence of EPS for 2013. Further good news on asset impairments could see this estimate revised sharply upwards. Investors need a share price of 63 pence to break even. At the very least, I expect the shares to trade higher than that by the time Lloyds announces 2013 interims. Today, the shares can be bought for 55 pence.

Aggreko
Glasgow-headquartered Aggreko (LSE:AGK) is a supplier of temporary power equipment worldwide. The company's generators are used in football stadiums, hospitals, and industry. It has enjoyed tremendous growth in recent years. Between 2007 and 2011, revenues increased nearly threefold. EPS rose from 20 pence to 96.1 pence.

However, a recent trading statement from the company has damaged its market rating. Aggreko is now expected to report EPS growth of just 5.3% for 2012, to be followed by a small decline in 2013. If its markets can pick up, the shares could win back the premium rating that they enjoyed in 2012. That would equate to a rise of nearly 40% from today's price.

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David O'Hara owns shares in Lloyds Banking Group but none of the other shares mentioned. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.