**Are you over diversified?**

A few decades ago, most investors (in conjunction with a broker) would assemble a portfolio by purchasing individual stock and bond issues. In the 1980s, it became more common to hand that task over to a professional money manager by investing in a mutual fund. Today, it's not uncommon for an investor to amass a substantial number of mutual funds. Some investors actively pick funds the way their grandparents picked stocks; others, via 401(k) plans or hyperactive brokers, end up with a large number of funds almost by accident.

Aside from the logistical problems and record-keeping headaches of tracking so many mutual funds, the following question arises: How many funds do you need to be adequately diversified, and, beyond that point, do you do yourself more harm than good? Is there such a thing as overdiversification?

The folks at *Morningstar Investor* took a look at that question recently, performing a couple of number-crunching studies. The first study examined how the number of funds you own affects the short-term volatility of your portfolio, as measured by standard deviation. Average standard deviations were calculated for the five-year performances of randomly selected one- to 30-fund portfolios. (We also performed these calculations for portfolios of individual stocks.) As shown in the graph on the left, only a moderate decrease in standard deviation was seen as portfolios increased in size from one fund to thirty. This contrasts sharply with the line for portfolios of individual stocks--which makes sense, given that the average fund holds more than 130 stocks. If we change the scale of the vertical axis, as we did for the graph on the right, we can see a similarly shaped curve for portfolios of funds: The greatest reduction in volatility comes from the first few funds. However, as you begin to add five, six, seven or more funds, you get less and less volatility reduction for each added fund. Eventually, the amount of volatility levels off, and including additional funds in a portfolio begins to have little or no effect on its standard deviation.

Most investors, however, are more concerned with the ending value of their investment than the standard deviation of their portfolio. After all, if you're investing for retirement, your biggest question is probably "how much will my portfolio be worth?" We performed a second study examining the range of expected final portfolio values for one- to 30-fund portfolios, assuming an initial investment of $10,000 and a five-year holding period. The following graph illustrates the range of returns (with a 95% confidence level) that resulted from each of these portfolios:

As expected, one-fund portfolios provided the highest potential ending portfolio value, as well as the lowest ending value. As we increased the number of funds in the portfolio, the range of final values narrowed. As we saw with portfolio volatility, this decrease was considerable as the first couple of funds were added, but it soon leveled off.

By themselves, these results suggest that if you want to hit it big with mutual funds, your chances of doing so are much higher with a fewer number of funds. If, however, you're more concerned about losing your shirt, or simply having your portfolio fall short of your goals, your strategy should be to own more funds. At a certain point, though, adding additional funds to a portfolio really doesn't affect it that much one way or the other. Once you get past 17 funds, additional funds don't change the expected range of returns.

*Questions:*

*The study by Morningstar finds little diversification benefit (in terms of standard deviation of the portfolio) from increasing the number of funds in your portfolio from one to thirty. How would you reconcile this with the evidence that increasing the number of stocks in your portfolio reduces the standard deviation significantly?**Why are the results different when you look at the end-of-period values instead of the standard deviations?**Should the number of funds you hold be affected by what kind of funds you buy? (Sector versus Diversified, Small versus Large, Concentrated versus Non-concentrated)*