Ever since its acceptance of a 45 billion pound bailout in the depths of the financial crisis, Royal Bank of Scotland Group (NYSE:RBS) has been under majority government ownership. With the government stake at 81% today, many private investors are turned off by the current ownership structure.

But a BBC report earlier this month implies that share sales may begin sooner than previously thought. I'll take a look at what this would mean for RBS and its investors.

Reducing stakes
Bank bailouts are far from popular on either side of the Atlantic, but have been grudgingly implemented to prevent greater economic collapse. Currently, two major British banks remain partially owned by the government -- RBS at 81% and Lloyds Banking Group (NYSE:LYG) at 25%.

The government has been steadily reducing its stake in Lloyds, as the bank has returned to consistent profitability; something RBS has yet to do. Unlike the Lloyds stake, which has fallen from 39% to 25%, the RBS stake has remained essentially the same due to the lack of government share sales.

A new strategy
Reducing its RBS stake has always seemed to be a problem for the British government. On one hand, reducing its stake could be politically popular and help the image of the bank in private markets. On the other hand, RBS has not shown consistent profitability, and selling shares at current levels would mean incurring a loss for the UK Treasury.

But a BBC report says that UK Financial Investments, the government's vehicle for owning the shares, "has been approached about exploring a series of small stake sales to kick start the process."

Selling small stakes in RBS, probably to institutional investors first, would follow the same path as the Lloyds sales. Although the first RBS stake sales would almost certainly be done at a loss, once the markets realize that the government is serious in reducing its RBS stake, shares may rise in value like they did with the first Lloyds sales.

Confidence in the bank
Investors tend to dislike businesses that have inconsistent profits, large government ownership stakes, and few signs the government stake will be reduced. For now, RBS has all three -- but selling off some of the government stake could help with two of these three investment negatives.

By beginning share sales, the market would see that there is a plan to eventually return RBS to private control, and as sales continue, the government ownership stake would become less of an overhang.

Share price behavior at American International Group (NYSE:AIG) provides a fine example of how the market can react positively to the full liquidation of a government stake. Government ownership of AIG peaked at 92%, up from 79.9% after a conversion of preferred stock into common stock. AIG shares were trapped in the $20 and low $30 ranges as the stake was unwound. But after the last of these shares were sold to private investors, AIG moved higher, eventually hitting today's $50 range.

RBS won't necessarily repeat AIG's move, but it does serve as an example of the potential upside once a large government stake is fully eliminated. Although RBS may receive an initial boost as share sales begin, the AIG example would take significantly longer to play out in full as the government stake in RBS would need to be fully divested.

The bottom line
RBS still has its fair share of challenges ahead of it, and these share sales are far from complete. However, if UK Financial Investments chooses to act, it could kick off a process necessary to restoring market confidence in the bank.

This bank remains a long term investment, as changes in market sentiment take time -- as will any sell down in the government stake.

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Alexander MacLennan is long AIG warrants. This article is not an endorsement to buy or sell any security and does not constitute professional investment advice. Always do your own due diligence before buying or selling any security. The Motley Fool recommends American International Group. The Motley Fool owns shares of American International Group and has the following options: long January 2016 $30 calls on American International Group. 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.