- The market risk of a stock is measured by its beta coefficient, which is an index of
the stock’s relative volatility. Some benchmark betas follow:
b 0.5: Stock is only half as volatile, or risky, as an average stock.
b 1.0: Stock is of average risk.
b 2.0: Stock is twice as risky as an average stock.
- A portfolio consisting of low-beta securities will itself have a low beta, because the
beta of a portfolio is a weighted average of its individual securities’ betas:
. (3-7)
Here bpis the beta of the portfolio, and it shows how volatile the portfolio is in re-
lation to the market; wiis the fraction of the portfolio invested in the ith stock; and
biis the beta coefficient of the ith stock. For example, if an investor holds a
$100,000 portfolio consisting of $33,333.33 invested in each of three stocks, and if
each of the stocks has a beta of 0.7, then the portfolio’s beta will be bp0.7:
bp0.3333(0.7) 0.3333(0.7) 0.3333(0.7) 0.7.
Such a portfolio will be less risky than the market, so it should experience relatively
narrow price swings and have relatively small rate-of-return fluctuations. In terms
of Figure 3-9, the slope of its regression line would be 0.7, which is less than that
for a portfolio of average stocks.
Now suppose one of the existing stocks is sold and replaced by a stock with bi
2.0. This action will increase the beta of the portfolio from bp10.7 to bp2
1.13:
bp20.3333(0.7) 0.3333(0.7) 0.3333(2.0)
1.13.
Had a stock with bi0.2 been added, the portfolio beta would have declined from
0.7 to 0.53. Adding a low-beta stock, therefore, would reduce the risk of the port-
folio. Consequently, adding new stocks to a portfolio can change the riskiness of
that portfolio.
6.Since a stock’s beta coefficient determines how the stock affects the risk of a diversified port-
folio, beta is the most relevant measure of any stock’s risk.
Explain the following statement: “An asset held as part of a portfolio is generally
less risky than the same asset held in isolation.”
What is meant by perfect positive correlation, perfect negative correlation, and
zero correlation?
In general, can the risk of a portfolio be reduced to zero by increasing the num-
ber of stocks in the portfolio? Explain.
What is an average-risk stock? What will be its beta?
Why is beta the theoretically correct measure of a stock’s risk?
If you plotted the returns on a particular stock versus those on the Dow Jones In-
dex over the past five years, what would the slope of the regression line you ob-
tained indicate about the stock’s market risk?
a
n
i 1
wibi
bpw 1 b 1 w 2 b 2 wnbn
126 CHAPTER 3 Risk and Return
124 Risk and Return
