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Why Diversification Makes Sense
by Jonathan Berk
Associate Professor, Haas School of Business
U.C. Berkeley
Guest Columnist for Grubman Financial Consulting
January 2007
Why does diversification make sense for the average investor, that is, why is it always better for an investor to invest his or her money in a portfolio of many stocks rather than in a single stock? The folk wisdom is that it is because it is never a good idea to put all your eggs in one basket or in this case put all your hopes on a single stock. Although this folk wisdom is correct, it is not the full story. For example, suppose an investor would like to get a very high return that he believes a particular stock offers, but that a large portfolio of stocks would not offer. In this case, might it not make sense for this investor to forgo the portfolio and instead invest in the single stock? The answer is no.
To understand why it never makes sense to invest in an individual stock, we first need to explore the relation between the risk of an investment and its return. How do you measure the risk of an investment? One measure of risk that many people use is the volatility or standard deviation of the return on the investment --- a measure of how much the realized return over a particular interval is likely to depart from its expected or average return.
Using quarterly data gathered over the last 80 years, Figure 1, plots the historical average return versus the volatility of six large portfolios of different investment types --- short term government bonds, corporate bonds, a collection of stocks from all over the world, stocks in the S&P 500 index, mid-cap stocks and small stocks. There is a very clear linear pattern: The portfolios with higher volatility have rewarded investors with higher average returns to compensate them for the risk they are taking.
Figure 1 The Historical Tradeoff Between Risk and Return in Large Portfolios, 1926-2006. Also included is a mid-cap portfolio composed of the 10% of U.S. stocks whose size is just below the median of all U.S. stocks, and a world portfolio of large stocks from North America, Europe, and Asia (source: CRSP, Morgan Stanley Capital International and Global Financial Data). Note the general increasing relationship between historical volatility and average return for these large portfolios.
Figure 1 suggests the following simple idea: investments with higher volatility should have higher average returns. Indeed, looking at Figure 1 it is tempting to draw a line through the portfolios and conclude that all investments should lie on or near this line - that is, average returns should rise proportionately with volatility. This conclusion appears to be approximately true for the large portfolios we have looked at so far. Is it true for other investments as well, for instance, individual stocks?
Figure 2: Historical Volatility and Return for Individual Stocks, by Size, Updated Quarterly, 1926-2006. Unlike the case for large portfolios, there is no precise relationship between volatility and average return for individual stocks. The 50 largest stocks in the sample are shown in (green) yellow, the 100 smallest are shown red and the rest are in blue.
Unfortunately, it isn't. To see why, let's add individual stocks to the same plot. Figure 2 adds the average return and volatility of the 500 largest stocks over the last 80 years.1 There is no clear relationship between average return and volatility of individual stocks! Even more importantly, individual stocks all fall below the line. That is, individual stocks are a raw deal --- comparing an individual stock to a portfolio with same level of volatility, the portfolio always has a higher average return. So it does not make sense to invest in an individual stock when you can invest in a portfolio of stocks.
What if you wanted to get a very high return and are comfortable taking on a lot of volatility? For example, say you wanted to invest in the single stock in the plot with the highest average return (which is marked on Figure 2). Might this make sense because there is no portfolio that has a higher average return than this stock? This is the same question we started out with. The answer is that even though there is no portfolio of stocks that has an average return as high as the stock, an investor can always construct a portfolio out of existing portfolios that has the same average return as the individual stocks by combining the existing portfolios with a riskless investment. To demonstrate, assume that instead of investing in the individual stock the investor instead bought the S&P500 portfolio on margin, that is, borrowed some of the money to make the investment. By leveraging in this way, he can increase the average return of his investment to the average return of the individual stock. What happens to the volatility of this position? It increases linearly, that is, the leveraged portfolio plots on the blue line! So it will have a lower volatility than the individual stock, that is, it is a better investment because it has the expected return as the stock but a lower volatility. Hence, even in this case it does not make sense to invest in a single stock.
The historical results plotted in Figure 2 might appear puzzling. After all, the portfolios plotted on the line are made up of individual stocks. How can all the individual stocks plot below the line while a portfolio of the same stocks plots on the line? The answer to this question is the reason diversifying makes sense. Some of the variation in individual stocks in a portfolio cancels with each other --- when one stock goes up another might go down, so in aggregate the portfolio has far less variation than the individual stocks within it. I will return to this idea in a future column, but before I do, in my next column I will address another common reason people give for not diversifying --- that they like a particular stock and believe is it is under priced.
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1Each point represents the returns from 1926 to 2004 of investing in the Nth largest stock traded in the U.S. (updated quarterly) for N = 1 to 500.
