CP

120 CHAPTER 3 Risk and Return

strong and badly when it is weak.^7 Thus, even very large portfolios end up with a

substantial amount of risk, but not as much risk as if all the money were invested in

only one stock.

To see more precisely how portfolio size affects portfolio risk, consider Figure 3-8,

which shows how portfolio risk is affected by forming larger and larger portfolios of ran-

domly selected New York Stock Exchange (NYSE) stocks. Standard deviations are plot-

ted for an average one-stock portfolio, a two-stock portfolio, and so on, up to a port-

folio consisting of all 2,000-plus common stocks that were listed on the NYSE at the

time the data were graphed. The graph illustrates that, in general, the riskiness of a port-

folio consisting of large-company stocks tends to decline and to approach some limit as

the size of the portfolio increases. According to data accumulated in recent years,  1 , the

standard deviation of a one-stock portfolio (or an average stock), is approximately 35

percent. A portfolio consisting of all stocks, which is called the market portfolio,would

have a standard deviation, M, of about 20.1 percent, which is shown as the horizontal

dashed line in Figure 3-8.

FIGURE 3-8 Effects of Portfolio Size on Portfolio Risk for Average Stocks

35

30

25

15

10

5

0

= 20.1

1 10 20 30 40 2,000+

Number of Stocks

in the Portfolio

σM

Portfolio's

Stand-

Alone

Risk:

Declines

as Stocks

Are Added

Portfolio's

Market Risk:

Remains Constant

Diversifiable Risk

Portfolio Risk, σ

(%)

p

Minimum Attainable Risk in a

Portfolio of Average Stocks

(^7) It is not too hard to find a few stocks that happened to have risen because of a particular set of circum-
stances in the past while most other stocks were declining, but it is much harder to find stocks that could
logically be expectedto go up in the future when other stocks are falling.
However, note that derivative securities (options) can be created with correlations that are close to
1.0 with stocks. Such derivatives can be bought and used as “portfolio insurance.”

118 Risk and Return