Diversification (finance)

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Diversification in finance involves spreading investments around into many types of investments, including stocks, mutual funds, bonds, and cash. Money can also be diversified into different mutual fund investment strategies, including growth funds, balanced funds, index funds, small cap, large cap, and sector-specific funds. Geographic diversification involves a mixture of domestic and international investments.

Diversification reduces the risk of a portfolio. It does not necessarily reduce the returns. This is why diversification is referred to as the only free lunch in finance.^{[citation needed]}

Diversification can be quantified as the intra-portfolio correlation. This is a statistical measurement from negative one to one that measures the degree to which the various assets in a portfolio can be expected to perform in a similar fashion or not.

Intra-portfolio correlation	Percent of diversifiable risk eliminated
1	0%
.75	12.5%
.50	25%
.25	37.5%
0	50%
-.25	62.5%
-.50	75%
-.75	87.5%
-1	100%

Portfolio balance occurs as the sum of all intra-portfolio correlations approaches negative one. Diversification is thus defined as the intra-portfolio correlation or, more specifically, the weighted average intra-portfolio correlation. Maximum diversification occurs when the intra-portfolio correlation is minimized. Intra-portfolio correlation may be an effective risk management measurement. The computation may be expressed as:

$Q = \frac{\sum_{i=1}^n\sum_{j=1}^n X_i X_j P_{ij}}{\sum_{i=1}^n\sum_{j=1}^n X_i X_j}$

Where Q is the intra-portfolio correlation, $X i$ is the fraction invested in asset i, $X j$ is the fraction invested in asset j, $P i j$ is the correlation between assets i and j, and n is the number of different assets.

Number of Stocks in Portfolio	Average Standard Deviation of Annual Portfolio Returns	Ratio of Portfolio Standard Deviation to Standard Deviation of a Single Stock
1	49.24%	1.00
2	37.36	.76
4	29.69	.60
6	26.64	.54
8	24.98	.51
10	23.93	.49
20	21.68	.44
30	20.87	.42
40	20.46	.42
50	20.20	.41
100	19.69	.40
200	19.42	.39
300	19.34	.39
400	19.29	.39
500	19.27	.39
1000	19.21	.39

^[1]

[edit] See also

[edit] References

^ These figures from Table 1 in M. Statman, "How Many Stocks Make a Diversified Portfolio?" Journal of Financial and Quantitative Analysis 22 (September 1987), pp. 353-64. They were derived from E. J. Elton and M. J. Gruber, "Risk Reduction and Portfolio Size: An Analytic Solution," Journal of Business 50 (October 1977), pp. 415-37. Taken from Ross, Westerfield, and Jordan, "Fundamentals of Corporate Finance" 7th Edition (2006-11-14), pp. 406.