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Updated to reflect additional information on buybacks and analyst ratings.



) -- In February,

Warren Buffett

made waves when he explained why an


(IBM) - Get International Business Machines Corporation Report

share lull would benefit his $10.3 billion stock holding. After

Wells Fargo

(WFC) - Get Wells Fargo & Company Report


Bank of America

(BRK.A) - Get Berkshire Hathaway Inc. Class A Report

passed Tuesday's

Federal Reserve

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stress tests, Buffett's point may also apply to his biggest bank investments.

In his annual letter, the investment guru detailed his math on how to gain on stock swoons and share repurchases, using his investment in IBM as an example. After Wells Fargo boosted its dividend 83% and indicated accelerated buybacks on the heels of stress test results, Buffett's largest bank holding may have a similar thesis, with a relevance to other

Berkshire Hathaway

(BRK.A) - Get Berkshire Hathaway Inc. Class A Report

investments in Bank of America,

American Express

(AXP) - Get American Express Company Report


U.S. Bancorp

(USB) - Get U.S. Bancorp Report


Warren Buffett

On Tuesday, Wells Fargo raised its quarterly dividend to 22 cents a share and indicated added buybacks to a 2011 program. Buffett owns 7.28% of Wells Fargo shares, worth $12.8 billion.

Other large Buffett investments in American Express and U.S. Bancorp also benefitted from capital return programs approved by the Federal Reserve. In buying back stock, banks will lower total outstanding shares thus boosting the proportion of earnings attributable to remaining shares.

American Express said it would launch a buyback program of $5 billion in shares and up its quarterly dividend to 20 cents, meanwhile U.S. Bancorp said it would hike its dividend by 56% and target $3.3 billion in buybacks. Buffett holds 13% of American Express shares worth over $8 billion, while he holds $2.14 billion in U.S. Bancorp shares, or 3.6% of the float.

Of the stress test results, Goldman Sachs analysts pointed to Wells Fargo, U.S. Bancorp and American Express as winners. "Based on today's results, we continue to believe WFC, JPM, and AXP are best positioned, while USB surprised the most to the upside," wrote Richard Ramsden. "Overall, the results came in mixed, with the strongest banks--AXP, JPM, USB, and WFC--announcing capital deployment above expectations," noted KBW analyst Fred Cannon about capital return programs.

That's where following Buffett's investment advice becomes key. In February, Buffett explained how shareholders can benefit from the


of companies with buyback programs. That may look like a contrarian strategy, especially if it were applied to the red-hot bank sector until the investment strategy is explained.

Following stress test results, the bank sector added to an over 17% surge in the

KBW Bank Index

(BKE) - Get Buckle, Inc. Report

, outperforming a near 8%

Dow Jones Industrial Average

rally in 2012. For more on the stress test results and what it means for banks, see

a complete list of stress test passes and fails


Here's how the buyback math that Buffett applied to IBM and may work for his bank investments.

In the letter to shareholders, Buffett said he hopes IBM's stock price "languishes throughout the five years" that the company engages in a $50 billion share repurchase program.

That's right: He wants the shares of a company in which he's investing to languish!

"When Berkshire buys stock in a company that is repurchasing shares, we hope for two events," Buffett explained. "First, we have the normal hope that earnings of the business will increase at a good clip for a long time to come; and second, we also hope that the stock underperforms in the market for a long time as well."

IBM has roughly 1.16 billion shares, 63.9 million of which are owned by Buffett in a 5.5% shareholding. Buffett expects the value of his investment to rise significantly as the company conducts its five-year, $50 billion share repurchase program.

If IBM shares languish at their current near record price of a little over $200, IBM will buy back 250 million shares, putting Buffett's stock ownership closer to 7%, as the company's share count shrinks to 910 million shares.

But if IBM shares continue to rise to say $300 a share, Buffet's stake would only be 6.5% on a share buyback of just 167 million shares.

Of course, the benefit of owning shares -- regardless of buyback programs -- is contingent on a company's earnings prospects, and that's where Buffett's strategy kicks in.

If IBM earns $20 billion in the year that its buyback expires, and its shares are still trading at $200, Buffett says that Berkshire's share of the earnings will be $100 million more than if shares trade at $300.

"At some later point our shares would be worth perhaps $1.5 billion more than if the "high-price" repurchase scenario had taken place," wrote Buffett of the impact to Berkshire's earnings.

"If you are going to be a net buyer of stocks in the future, either directly with your own money or indirectly (through your ownership of a company that is repurchasing shares), you are hurt when stocks rise. You benefit when stocks swoon," wrote Buffett.

That strategy also helped Buffett benefit from the tripling of Wells Fargo shares in the wake of the financial crisis, as other billionaire investors

threw in the towel

, only to miss the bank's 2012 rally. With Wells Fargo, American Express and U.S. Bancorp boosting their buyback ambitions to post-crisis records, Buffett is set to benefit as much as anyone from a post-stress rally at strongly capitalized banks.

As with IBM, Buffett is positioned to see his bank investments grow as companies like Wells outline new share buyback programs. Buffett can see his investment grow by simply waiting for company management to buy back shares, which management has indicated.

"In my early days I, too, rejoiced when the market rose. Then I read Chapter Eight of Ben Graham's

The Intelligent Investor

, the chapter dealing with how investors should view fluctuations in stock prices," wrote Buffett. "Immediately the scales fell from my eyes, and low prices became my friend. Picking up that book was one of the luckiest moments in my life."

Still, Buffett may hope for a continuation to a Bank of America stock rally to put his stock warrants "in the money" as he looks to convert a $5 billion August 2011 investment into common stock holdings sometime down the road.

In his annual letter, Buffett also praised the buyback strategy of JPMorgan Chief Executive Jamie Dimon. "One CEO who always stresses the price/value factor in repurchase decisions is Jamie Dimon at J.P. Morgan; I recommend that you read his annual letter," Buffett wrote. But a $8 billion 2011 stock buyback program

may have been ill timed

. In a third quarter conference call, Dimon said, "would have been wiser to wait," apologizing for the timing of the firm's share repurchases.

If current bank share prices are one day seen as overvalued, Tuesday's flurry of buyback plans may actually harm stock investors. Overall, the industry isn't as much of a screaming buy as it was in late 2011 or 2012, according to analyst price targets.

After many ratings changes on Wednesday, consensus analyst estimates for Wells Fargo, American Express and U.S. Bancorp of are near or below current trading prices, according to consensus estimates compiled by


. Meanwhile, as JPMorgan and Bank of America extend on over 30% and 57% year-to-date gain respectively, current share prices closing on consensus analyst price targets of $47.75 and $9.18 for the nation's two biggest banks.

For more on Berkshire Hathaway, here's how Buffett explained in his annual letter that

Berkshire Hathaway is positioned for growth in 2012 and beyond

. For more on risks to a bank rally after the stress tests, see

the other big tests that remain for the sector


-- Written by Antoine Gara in New York