Not putting all your eggs in one basket is the most basic principle of investing. It also may be the hardest to get right.

Investors have long been told by stockbrokers and financial planners that to have a properly diversified stock portfolio, you need shares in only 10 to 40 companies. Even the great investment analyst Benjamin Graham urged "adequate though not excessive diversification," which he defined as between 10 and about 30 securities.

As...