Imagine if I told you Warren Buffett has lost $1 billion and he's excited about it. Would you think he was crazy? Would you think I was crazy?

Well, it turns out it's true, and it can teach us all a valuable lesson about how we look at stocks.

The market laggard
In 2011, through Berkshire Hathaway (NYSE:BRK-A)(NYSE:BRK-B), Warren Buffett amassed a massive position in IBM (NYSE:IBM), buying 64 million shares at a cost of $10.9 billion, for a 5.5% ownership stake in the technology giant. And by the end of the year, Berkshire's position was already worth $895 million more than what it cost.

Since 2011 Buffett has selectively added to the position, and by the end of September this year Berkshire's stake had grown to 70.5 million shares, at a cost of roughly $12.1 billion, with a market value of $13.4 billion.

However those on-paper gains didn't last long, as IBM's posting of abysmal third quarter results sent the stock plummeting, and now Buffett's stake in the company is worth nearly $1 billion less than what it cost to purchase it.

This has been a trend since Berkshire began accumulating a stake in IBM in the first quarter of 2011, as IBM has seen its stock trail the broader market dramatically, especially since the middle of last year:

IBM Chart

Source: IBM data by YCharts

But it turns out, Buffett is likely thrilled about this reality, and he himself can tell you why.

Excited and delighted
When Buffett discussed Berkshire's IBM stake in the 2011 Letter to Shareholders he said:

Today, IBM has 1.16 billion shares outstanding, of which we own about 63.9 million or 5.5%. Naturally, what happens to the company's earnings over the next five years is of enormous importance to us. Beyond that, the company will likely spend $50 billion or so in those years to repurchase shares. Our quiz for the day: What should a long-term shareholder, such as Berkshire, cheer for during that period?

I won't keep you in suspense. We should wish for IBM's stock price to languish throughout the five years.

How on earth could he be excited about such a scenario as he watched nearly $12 billion, in his words, "languish?"

Without diving into the math, he goes on to say since IBM outlined an aggressive plan to buy back its own shares, then it would naturally make sense for him to desire those shares to be cheap, because then IBM would buy more of them, meaning Buffett's ownership stake in the firm would grow to an even higher amount.

Remember Buffett looks at every investment he makes as an investment in a business, not simply a number on a screen. In the case of IBM, it posted a net income of $15.9 billion in 2011, and Berkshire's ownership stake stood at 5.5%.

Although it never showed up in Berkshire's financial statements, Buffett understands as a result, it would be right to claim Berkshire's share of IBM's total income stood at $875 million.

So what does this have to do with Buffett being excited about IBM stock performing abysmally?

Consider for a moment that while Buffett has increased Berkshire's position in IBM by roughly 10%, its ownership stake has grown by 30% because the company has doled out a staggering $54.5 billion to repurchase shares since the end of 2011:

Source: Company SEC Filings. 

So knowing Berkshire's ownership stake is up to 7.1%, what has this meant to the portion of IBM's earnings it can rightfully claim based on its ownership?

While we don't have the full year results yet for IBM, we do know its income from continuing operations is down 4% through the first nine months of the year, so for the sake of example, let's say that persists and its total income for the full year falls 5%, from $16.5 billion in 2013 to $15.7 billion in 2014.

And using that as an estimated amount, you can see the total IBM earnings attributable to Berkshire has risen 28% since 2011:

Source: Company Investor Relations 

In other words, while the market may suggest Buffett's stake in IBM is worth $1 billion less than what he paid for it, in his eyes, he's made over $4 billion from his investment in IBM. And that doesn't even include the more than $800 million worth of dividends Berkshire has received since it first took its stake in IBM in 2011.

Buffett's closing thoughts
Buffett concluded his remarks in 2011 by noting:

Charlie and I don't expect to win many of you over to our way of thinking – we've observed enough human behavior to know the futility of that – but we do want you to be aware of our personal calculus ... In the end, the success of our IBM investment will be determined primarily by its future earnings. But an important secondary factor will be how many shares the company purchases with the substantial sums it is likely to devote to this activity.

When you consider the mass market sell-off is exactly what Buffett hoped for, and it's only resulted in Berkshire having a larger ownership stake in a company he declared as one of four "excellent businesses" that "are run by managers who are both talented and shareholder-oriented," it's hard to suggest he isn't happy with the outcome.