One great historical case for Buffett was the Salad Oil Scandal. American Express stock plummeted because it had guaranteed loans backed by salad oil inventories that turned out to be fraudulent. It was facing a huge loss for the time, some were even afraid it might go out of business.
But Buffett went to lunch and saw customer after customer still using Amex cards to pay for their meals. He realized that the charge card part of Amex was still really valuable, and did the math on what the credit card business was worth and their maximum possible losses from their loans would be, and realized the stock was hugely undervalued and bought a ton.
Every business has remote risks of crazy bad things happening, it's why you diversify your portfolio if you are an active investor.
"Well if it's a belief, then isn't value investing just as much speculation as anything else?"
That's where the term Margin of Safety comes in. The financials of a company provide a delta, some min and max of where the company can go. When you plug in your estimates, and that delta's minimum is still less than the current price of the stock, esp by a significant margin, then you've picked a winner...more specifically, a winner over the next few years. Remember, plenty of events can occur between now and when your value is realized, and one of the other traits of a strong value investor is the ability to weather the storm. Oftentimes these companies with sufficient margin of safety will continue to fall in price before they rise again, one cannot time the market for the zenith nor the nadir of a stock's price.
Beyond that you spend time thinking about their business and what could go wrong. If there is something obvious to you they didn't disclose, that would tend to mean management is untrustworthy or incompetent, two other huge risks.
Buffett spends lots of hours reading reports away from CNN and computers and distractions. I'm sure he talks to Charlie and others regularly about things that concern him and gets different perspectives.
Leverage is only minor component of his late career success, and insurance float could never have gotten him broke. It's totally unlikely like a loan from your broker.
The reality is his late career is less impressive only in one way, annualized returns, and it's more impressive in virtually every other way. He started out with less than a million in investors money, and his 40% returns with the Buffett Partnership were probably with an average of $10M to $20M total.
Nowadays his public stock portfolio was $122B at year end 2016. That limits the stock market investments he can make to a tiny fraction of stocks. He's not going to buy hundreds of stocks, not even dozens. He wants to focus in his dozen or so best ideas. So he want to be able to put $10B to work in each and there are very few public companies with market caps and trading volumes large enough to allow him to do that. So problem #1 is that he went from a market of 5,000+ stocks he could choose from to maybe a few hundred, reduced opportunities that directly hurts his returns.
Worse, how can he accumulate $10B worth of a company before he's forced to publicly disclose his purchases. If he's forced to disclose prematurely, his future returns dwindle due to free-riders driving the purchase price up before he's done. That's big problem #2.
The fact that he's still beating the market carrying these heavy chains is more impressive to me than the fact he whipped it at 3x higher rates when he could buy anything he wanted.
While managing billions at minimal risk he is not making nearly 17% returns. He is doing OK but again your looking at a statistical outlier so you can't separate skill and luck as much as you might think.
His 40% returns were in the Buffett Partnerships, which ran for 12 years from mid 50s to late 60s, and aren't counted in Berkshires results.
Doubling the market return rate over 52 years is huge outperformance. For an investor it's roughly doubling every 3.5 years instead of 7.5 years.
Add in the fact he crushed the market by nearly 4x a year for an earlier 12 years and his immense skill is undeniable. He would be statistically implausible if the world had trillions of investors.
His annualized returns running the Buffett Partnerships with zero leverage were close to 40% per year for the dozen or so years they were operating.
And everyone compounds gains just by holding index funds for long periods. Buffett compounds them far faster because he has substantially higher returns than the market.