Berkshire Hathaway Inc, Warren Buffett's insurance and investment company, reported a higher fourth-quarter profit, helped by improved results from investments and derivatives.

Operating profit nevertheless fell 40 percent, reflecting weak performance in several economically-sensitive businesses and the impact of a one-time year-earlier gain related to an aborted takeover.

Net worth per share, which measures asset minus liabilities and is a key metric for Buffett, rose 19.8 percent, rebounding from a 9.6 percent drop the prior year.

While near the 20.3 percent average since Buffett began running Berkshire in 1965, it lagged the 26.5 percent gain including dividends in the Standard & Poor's 500.

Berkshire has typically generated about half its results from insurance, including auto insurer Geico Corp and reinsurer General Re Corp.

It operates roughly 80 businesses that sell such things as carpeting, ice cream, paint, and underwear. Two weeks ago it bought Burlington Northern Santa Fe Corp, the second-largest U.S. railroad, in Buffett's largest takeover ever. That and a related stock split won Berkshire admission to the S&P 500.

In his annual letter to Berkshire shareholders, Buffett admitted that Berkshire's ability to outperform that benchmark has shrunk dramatically as the company has grown, an unpleasant trend that will continue. Huge sums forge their own anchor and our future advantage, if any, will be a small fraction of our historical edge, he wrote.

Quarterly net income rose to $3.06 billion, or $1,969 per Class A share, from $117 million, or $76, Berkshire said. Revenue rose 23 percent to $30.2 billion.

Excluding $1.03 billion of investment and derivative gains, operating profit fell 40 percent to $2.03 billion, or about $1.308 per share, from $3.37 billion, or $2,175.

On that basis, analysts on average expected $1,208 per share, according to Thomson Reuters I/B/E/S. Losses from investments and derivatives were $3.25 billion a year earlier.

Berkshire's book value rose 20 percent to $131.1 billion at year end from $109.27 billion at the end of 2008.

For all of 2009, profit rose 61 percent to $8.06 billion, or $5,193 per Class A share, from $4.99 billion, or $3,224. Revenue rose 4 percent to $112.49 billion.

(Reporting by Jonathan Stempel, editing by Vicki Allen)