Even if you find that you don't have a lot of overlap in individual stock names, you may still be overexposed to one or two sectors of the market.
As an example let's take technology, a sector that has received a lot of attention in the new century. Technology has been a wonderful long-term return story (most of us remember that it seemed like the only story in the late 1990s), so mutual fund managers have often spent a lot of money shopping in this industry. One of the reasons that the market's volatility was so painful for some of us in the last four years is that investors were generally more exposed to this sector than they had realized.
Growth funds, in particular, usually carried large tech weightings with lofty prices and even loftier earnings expectations. The average large-growth fund kept far more of its assets in technology stocks—37% in mid-2000—than in any other sector of the market. (In comparison, the S&P 500 Index had about 30% of its assets in tech stocks at the time.) Mid- and small-growth funds held even more of their assets, about 40%, in tech names. Many investors with multiple growth funds owned a lot more technology stocks than they realized. More recently, exposures to this sector have declined slightly as managers have hoped to find the next big thing in other industries.
The technology example may be overused, but that's partly because it was especially egregious. Keep in mind that at any given time there is likely to be a sector that grows to prominence among growth or value funds. It's a good idea to X-Ray your portfolio regularly to make sure that it hasn't gotten too skewed one way or another.
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