#### Don’t Forget Diversification by Gary Sanger, PhD, CFA

Diversification is one of the most fundamental yet misunderstood concepts in investment management. I will begin with a basic and hopefully intuitive discussion of the principles of diversification and the mechanics by which it works. Then, I will provide a more technical presentation for those interested. Throughout, I will use numeric examples to illustrate the principles involved. Finally, I will examine some typical historical data regarding diversification across asset classes (e.g., stocks, bonds, and cash).

Simply stated, diversification results when you spread your investable funds across different assets. By chance, some will do well when others do poorly, thus reducing the overall variability (i.e., risk) of your portfolio. There are numerous methods of achieving diversification. Naive diversification is done by simply randomly choosing a set of assets for your portfolio. The law of large numbers makes this work. If you have 30 randomly chosen stocks in your portfolio, some will go up when others go down, thus reducing overall portfolio risk. But we can do better. To maximize the benefits of diversification, we should look for assets that tend not to move together. We look for some assets that “zig” when others “zag.” We can reduce risk more efficiently this way (i.e., achieve the same level of risk reduction with fewer separate investments).

The key to efficient diversification involves the statistical concept of correlation. Correlation measures the degree to which two assets move together. The maximum correlation is 1.0, or 100%; in this case, the two assets always move up and down together (though possibly by different amounts) and no diversification is achieved. The minimum correlation is ?1.0, or ?100%; in this case, the two assets always move in the opposite direction and perfect diversification is achieved. For correlations between these extremes, the lower the correlation, the more diversification we achieve.

An Illustration

Consider the stocks in Table 1. Each stock has its typical ups and downs. Note that Stocks 2 and 3 have the same returns but in different years. Also note that Stocks 1 and 2 move together (positive correlation) whereas Stocks 1 and 3 move opposite one another (negative correlation).

Table 1. Stock Returns

 Year 1 Year 2 Year 3 Year 4 Stock 1 10% ?5% 15% ?8% Stock 2 12% ?7% 18% ?10% Stock 3 ?7% 12% ?10% 18%

Table 2 shows the values of two portfolios. Portfolio 1 assumes initial equal \$100,000 investments in Stocks 1 and 2, whereas Portfolio 2 assumes initial equal \$100,000 investments in Stocks 1 and 3. Both portfolios are rebalanced to 50% weights in each stock each year. I will comment on the significance of this below.

Table 2. Portfolio Values: \$200,000 Initial Investment

 Year 1 Year 2 Year 3 Year 4 Portfolio 1: Stocks 1 & 2 \$222,000 \$208,680 \$243,112 \$221,232 Portfolio 2: Stocks 1 & 3 \$205,000 \$210,125 @media (max-width: 600px){#admobil{display:none}#adpost{display:inline-block;width:300px !important;height:250px}}@media (min-width: 600px){#admobil{display:none}#adpost{display:inline-block;width:336px;height:280px}} \$218,530 \$227,271

First, note that Portfolio 1 is much more volatile than Portfolio 2. It fluctuates from a low of \$208,680 to a high of \$243,112. In contrast, Portfolio 2 climbs steadily in value. You would sleep much better at night with Portfolio 2. The lower volatility of Portfolio 2 is a direct result of the lower correlation between Stocks 1 and 3 relative to that of Stocks 1 and 2. Second, note that Portfolio 2 has a higher ending value than Portfolio 1 despite the fact that the stocks in each portfolio have the same period-by-period returns. This result is due to the annual rebalancing of the portfolios. In Portfolio 2, the negative correlation between the stocks, combined with rebalancing, causes more weight to be put into a stock after it has fallen and less weight after it has risen. Over time, this results in a higher ending portfolio value.

Typical Historical Correlations among Asset Classes

To get an idea of the correlations that can be expected for various asset classes, let’s examine historical correlations. Although correlations among assets can change over time, it is reasonable to consider recent history as representative of potential future results. Table 3 presents correlations for eight asset classes that might be considered in building a diversified portfolio. The asset class correlations were calculated by Morningstar for the period 1 January 2002 through 31 December 2006 (60 months). The following indices are represented by number in Table 3:

1. Three-month CD — cash equivalent
2. Lehman Brothers Global Aggregate* — global bonds
3. Lehman Brothers Aggregate Bond* — US bonds
4. MSCI EAFE Growth — Europe, Australasia, and Far East growth stocks
5. MSCI World ex US — global stocks excluding the United States
6. Russell 1000 Growth — US large-capitalization growth stocks
7. Russell 2000 Growth — US small-capitalization growth stocks
8. Russell Midcap Growth — US medium-capitalization growth stocks

Table 3. Historical Correlations among Asset Classes

(represented by indices)

1

2

3

4

5

6

7

8

1

1.0

2

?0.15

1.0

3

?0.04

0.72

1.0

4

0.10

0.13

?0.17

1.0

5

0.15

?0.35

?0.37

0.84

1.0

6

0.05

?0.23

?0.32

0.72

0.82

1.0

7

0.00

?0.13

?0.31

0.77

0.79

0.84

1.0

8