CHAPEL HILL, N.C. (MarketWatch) — If you own more than five to 10 stocks, you may own too many.

I know this flies in the face of conventional wisdom that portfolios with fewer than a couple dozen stocks are not well-diversified. But if you have information or insight about a handful of companies, it may make more sense to construct your portfolio out of them rather than to invest in the 50 or so stocks that some statisticians tell us is needed to be adequately diversified.

These thoughts are occasioned by the recent resignation of two board directors at Sequoia Fund SEQUX, -1.48% , which is managed by proteges of Warren Buffett and sports one of the best long-term records of any actively managed mutual fund. The directors’ resignation was in reaction to the fund’s outsized investment in just one stock: Valeant Pharmaceuticals US:VRX.

At one point this summer, for example, over 30% of this fund’s assets were invested in that company’s stock. So when the stock plummeted, the fund plunged: Over the past three months, the fund lost 25.6% versus a 2.4% loss for the S&P 500 SPX, -2.37% according to Morningstar.

It’s easy to criticize the fund’s managers for their apparent arrogance and chutzpah, and many have already done so. At the same time, however, Sequoia’s big bet on Valeant is part of a long tradition of big bets from legendary managers.

Perhaps the most famous of such wagers was from Benjamin Graham, the father of fundamental analysis who championed investing in a diversified basket of so-called value stocks — those selling at deep discounts relative to their net assets. The bulk of Graham’s long-term above-market performance came from violating both of those rules — by investing over 20% of his fund in Geico, the Government Employees Insurance Co.

In the mid-1970s, in what appears eerily similar to Valeant’s recent plunge, Geico ran into trouble and its stock plunged from more than $60 to only $2.10. Buffett, who was Graham’s protege, thought Wall Street was wrong and snatched up the insurance company’s shares at the low prices. By the mid-1980s, Geico’s stock was trading for more than $70.

Years later, reflecting on this experience and others like it, Buffett defended under-diversified portfolios as the rational choice of “know-something” investors, in contrast to “know-nothing” investors who should construct widely diversified portfolios. In his 1993 letter to Berkshire Hathaway shareholders, he wrote:

“If you are a know-something investor, able to understand business economics and to find five to 10 sensibly priced companies that possess important long-term competitive advantages, conventional diversification makes no sense for you. It is apt simply to hurt your results and increase your risk. I cannot understand why an investor of that sort elects to put money into a business that is his 20th favorite rather than simply adding that money to his top choices — the businesses he understands best and that present the least risk, along with the greatest profit potential.”

Academic research provides support for Buffett’s argument. One study, which appeared in the prestigious Journal of Finance a decade ago, found that less-diversified mutual funds had better performance, on average, than the actively managed funds that were most diversified. To be sure, the less-diversified funds were riskier than the most diversified ones; but even on a risk-adjusted basis, they still came out ahead.

In pointing this out, of course, I run the big danger of encouraging “know-nothing” investors to construct the under-diversified portfolios that are appropriate only for “know-something” investors. Marcin Kacperczyk, one of the academic study’s authors and a professor of finance at Imperial College in London, told me earlier this week that it’s human nature for each of us to think we’re above average.

Most of us are not, of course. If you had any doubt, consider a landmark study conducted more than a decade ago by Terrance Odean, a finance professor at the University of California, Berkeley. Upon analyzing the trading performance of more than 66,000 accounts at a major discount-brokerage firm, he found that, far more often than not, the stocks we sell turn out to perform better than the stocks we buy as their replacements. (See the chart at the top of this column.)

Our default assumption should be that we don’t know how to pick stocks, and that therefore we should invest in an index fund.

But, Kacperczyk told me, it would be going too far to conclude that no one has stock-picking abilities. So be careful when drawing investment lessons from the Sequoia Fund’s recent woes. Their huge Valeant stake might be evidence of its managers’ foolish overconfidence — or the brilliance of having the courage of their well-found convictions.

Click here to inquire about subscriptions to the Hulbert Sentiment Indexes.