Introduction to Corporate Finance

6: The Trade-Off Between Risk and Return

a below-average year. What would have happened if we had formed a portfolio by investing some of our

money in Coca-Cola and the rest in ADM?

The green bar in Figure 6.7 plots the return on an equally weighted (50% invested in each stock)

portfolio of Coca-Cola and ADM. In the years in which Coca-Cola and ADM moved together, our

portfolio return was quite volatile, just as the individual stock returns were volatile. For example, our

portfolio return in 2007 was very high because both stocks did well that year, and in 2008, the portfolio

performed poorly because both stocks performed poorly. However, in some other years the excellent

performance of one stock was partially offset by the sub-par performance of the other, and the portfolio’s

results were close to the average return of 10.5% (2004 and 2010 are good examples of this pattern). In

other words, the portfolio’s return does not deviate as far or as often from the average as the individual

stock returns do. As a result, the standard deviation for the portfolio is just 19.1%, less than the standard

deviation of either Coca-Cola or ADM.

Now extend that logic to portfolios containing more than two securities. Figure 6.8 indicates that the

standard deviation of a portfolio falls as the number of securities in the portfolio rises. The dot in the upper-

left corner of the graph represents a portfolio invested entirely in one randomly selected share. As previously

noted, the typical share has a standard deviation of about 55%. Next, move down and to the right to the dot

which represents a portfolio containing an equal share of two randomly selected securities. The standard

deviation of this portfolio is considerably lower. Continuing down and to the right, we continue to add

randomly selected securities, one at a time, and the resulting portfolio standard deviation declines. However,

eventually, adding more securities to the portfolio does little to reduce the portfolio’s standard deviation.

FIGURE 6.8 THE RELATIONSHIP BETWEEN PORTFOLIO STANDARD DEVIATION AND

THE NUMBER OF SHARES IN THE PORTFOLIO

The standard deviation of a portfolio tends to decline as more securities are added to the portfolio. The standard deviation
declines rapidly as securities are first added to the portfolio. However, at some point, adding more securities to the portfolio
does little to reduce the standard deviation. The risk that diversification eliminates is called unsystematic risk. The risk that
remains, even in a well-diversified portfolio, is called systematic risk.

Number of securities

Portfolio standard deviation

0%

10%

20%

30%

40%

50%

60%

0 1 2 3 4 5 6 7 8 9 10

systematic

risk

unsystematic

risk

A portfolio contains two

investments, one that is

quite volatile and one that

is relatively stable. Does the

standard deviation of the

portfolio’s returns fall between

the standard deviations of the

returns of the two investments

in the portfolio?

thinking cap

question