Few investors need an introduction to Berkshire Hathaway (BRK.A -0.76%) (BRK.B -0.69%). Warren Buffett, its leader, is one of the most recognized figures in finance, renowned around the globe.

There's a good reason for this fame: Berkshire Hathaway stock has been one of the best-performing investments in history, compounding value at market-beating rates for decades.

After a history-breaking run, it is fair to ask: Is Berkshire Hathaway stock still a buy today?

Nothing fundamental has changed

On the surface, Berkshire Hathaway is no longer the company it once was. In 1965, its sole asset was a textile manufacturing business. Then, in 1967, it purchased National Indemnity, its first of many insurance businesses it now owns. Under Buffett's direction, the holding company reallocated its insurance profits to other investments, over time owning large chunks of blue chip stocks like Coca-Cola and American Express. Berkshire Hathaway is now a behemoth conglomerate, owning stakes in more than 100 businesses, all adding up to a market cap of nearly $900 billion.

In other ways, however, very little has changed about the core of Berkshire Hathaway's business. The company still operates a number of insurance businesses, which throw off excess cash that can then be used to expand a growing portfolio of public and private investments. Warren Buffett is still at the helm, though he recently lost his investment partner, Charlie Munger, who died last year at the age of 99.

Sure, Berkshire is a lot bigger, but in many ways, investors are still buying into the same business model that historically made the company so successful.

Beware the law of large numbers

Berkshire Hathaway still operates the same business model that produced its long-term success, but that doesn't mean novel challenges haven't arisen. The biggest of these is, in many ways, beyond the company's control: The law of large numbers.

Investing millions of dollars is easier than investing billions. It is, after all, easier for a $100 million portfolio to double or triple in size than a $100 billion portfolio. Smaller figures allow an investor to target smaller, higher-growth opportunities. Ample liquidity is less of a concern, and essentially all potential investments can make a meaningful contribution to performance. But don't take my word for it -- take Buffett's, speaking to a reporter back in 1999:

"The highest rates of return I've ever achieved were in the 1950s. I killed the Dow. You ought to see the numbers. But I was investing peanuts then. It's a huge structural advantage not to have a lot of money. I think I could make you 50% a year on $1 million. No, I know I could. I guarantee that."

The law of large numbers has already come true for Berkshire Hathaway. In past decades, Buffett could deploy a few hundred million dollars into a high-growth investment and have a big effect on the company's bottom line. Now, such an investment would only be a drop in the bucket. Berkshire Hathaway's investing universe has, in many ways, been reduced to only the world's largest companies. It's no wonder that two of the planet's largest corporations, Amazon and Apple, are now major holdings of Berkshire Hathaway.

A limited investment universe has real effects. The company is still growing book value most years, despite its gargantuan size, but the rate of growth has slowed dramatically. Over the past three years, Berkshire Hathaway has only grown its book value by 17.3%, a figure it used to manage on an annual basis in previous decades.

Is Berkshire Hathaway stock still a buy?

A slowdown in book value growth hasn't prevented the market from boosting Berkshire's valuation. Currently, shares trade at their highest price-to-book multiple in over a decade. The last time shares traded at these levels was in 2008, just before the financial crisis.

BRK.B Book Value (Quarterly) Chart

BRK.B Book Value (Quarterly) data by YCharts

As Buffett is fond of reminding investors, your returns will be a direct function of the price you pay. Berkshire Hathaway is still a terrific business led by a legendary investor. Those with long time horizons shouldn't be afraid of taking a position. Buying shares even at their all-time highs has always proven prudent in the past. However, with an $850 billion market cap and a decade-high valuation multiple, don't expect the eye-popping returns of yesteryear.