Diversifying one’s portfolio is conventional investment wisdom. The wise investor spreads his investments among domestic stocks, foreign stocks, bonds, commodities and other assets. Even within an asset class, it’s important to diversify the individual holdings to lower risk. For stocks, the question becomes: How many stocks should you hold? Five? 50? 500? And if some diversification is good, is more better?
Let’s look at diversification conceptually, and then test those concepts with some real numbers. Suppose the only stock you own is Home Depot. Your portfolio is subject to two kinds of risk. The first is called “systematic risk,” or market risk. The value of your Home Depot stock will rise and fall as market participants change their opinions about the value of stocks generally, often over issues that have no direct bearing on Home Depot. Diversification of your stock portfolio does not address this market risk.
Company-specific risk, on the other hand, reflects investors’ perceptions of the importance of changes in Home Depot’s business fortunes. These changes will be reflected in a rising or falling Home Depot stock price independent of whether the market generally is going up or down. The goal of diversification is to minimize this company-specific risk.
The investment profession commonly quantifies risk using data on the degree to which a stock’s price moves up and down, called “volatility.” Thus, a stock whose price is likely to move up or down 20 percent over the course of a month is considered to be much riskier than one that typically moves up or down 5 percent. Volatility risk is ordinarily expressed in terms of the “standard deviation of returns,” or simply, “standard deviation.”
As measured using Morningstar’s Principia database, Home Depot’s standard deviation over the past three years was about 20. Assuming Home Depot’s average monthly return (stated on an annualized basis) during that period was 10 percent, then in two out of three months the range of returns would have been between -10 percent and +30 percent. Compared with other stocks, Home Depot has been a pretty risky stock to own.
Adding another stock to the portfolio can reduce a portfolio’s overall volatility, even if the second stock is riskier than Home Depot. Although that seems contrary to common sense, it occurs because the new stock tends to move differently from Home Depot, zigging when Home Depot zags. Adding giant insurer American International Group to your portfolio, for example, would lower the portfolio volatility to 16; despite the fact AIG standing alone has a standard deviation of 22, higher than that of Home Depot.
Adding more stocks to your portfolio will lead to further decreases in its overall standard deviation, provided the stock’s prices move at least somewhat differently than those of the stocks you already hold. But with each stock you add, it becomes increasingly difficult to find stocks that respond differently to market conditions than those already in your portfolio. Improvements in portfolio risk, as exhibited by declines in the standard deviation, eventually become insignificant.
Here are some results from Morningstar’s Principia database for some well-known stocks, which, for simplicity, we’ll call One through Twenty. First, a portfolio of five stocks held in equal amounts showing their individual standard deviations (SD) and the portfolio standard deviation:
Stock Stock SD
One 20.30
Two 19.00
Three 12.40
Four 15.10
Five 12.20
Portfolio SD: 9.36
The portfolio standard deviation for a widely held S&P 500 index fund for the same period was 7.82. Our portfolio of five stocks, while still quite concentrated, has less risk than any of its components, although it’s still somewhat more risky than an S&P 500 index fund.
Now let’s add the rest of our stocks, five at a time, and check the standard deviation at each step (each step includes all the stocks in the prior steps):
Stocks Portfolio SD
One through Ten 8.16
One through Fifteen 7.35
One through Twenty 7.17
As expected, the reduction in portfolio standard deviation becomes smaller with each group of five stocks we add.
Much academic work supports the conclusion that, by the time you’ve added the twentieth stock to your portfolio, you’ve exhausted the benefits of further portfolio diversification as a way of reducing company-specific risk. In the book Modern Portfolio Theory and Investment Analysis, Elton and Gruber illustrate how going from one stock to 20 typically reduces portfolio volatility by about 30 percent, while adding another 980 stocks to bring the portfolio to 1,000 reduces the volatility further by less than 1 percent.
Managing a 20-stock portfolio is pretty much a full time job for a professional. Each additional stock requires the same amount of time to research and analyze, so while the amount of time required to manage the portfolio grows as the number of stocks grow, the effect of that effort is diluted by smaller and smaller position sizes.
For the average self-directed investor, the maximum benefit of diversification is probably reached by the time the portfolio reaches 10 stocks. In our example, the 10-stock portfolio had a standard deviation only slightly greater than the S&P 500 index fund. It’s better to carefully review and analyze 10 stocks than to be overwhelmed by 40 or 50.
David Raub has 16 years’ experience as a registered investment adviser. He is co-owner of Raub Brock Capital Management in Larkspur. You can reach him at draub@northbaybiz.com.
