Intermediate Financial Management (with Thomson One)

44 • Part 1 Fundamental Concepts
Which of the two stocks graphed in Figure 2-2 is less risky? Why?
How does one calculate the standard deviation?
Which is a better measure of risk if assets have different expected returns: (1) the standard
deviation or (2) the coefficient of variation? Why?
Explain the following statement: “Most investors are risk averse.”
How does risk aversion affect rates of return?
RISK IN A PORTFOLIO CONTEXT
In the preceding section, we considered the risk of assets held in isolation. Now
we analyze the risk of assets held in portfolios. As we shall see, an asset held as
part of a portfolio is less risky than the same asset held in isolation. Accordingly,
most financial assets are actually held as parts of portfolios. Banks, pension funds,
insurance companies, mutual funds, and other financial institutions are required
by law to hold diversified portfolios. Even individual investors—at least those
whose security holdings constitute a significant part of their total wealth—generally
hold portfolios, not the stock of only one firm. This being the case, from an
investor’s standpoint the fact that a particular stock goes up or down is not very
important; what is important is the return on his or her portfolio, and the portfolio’s
risk. Logically, then, the risk and return of an individual security should be analyzed
in terms of how that security affects the risk and return of the portfolio in
which it is held.
To illustrate, Pay Up Inc. is a collection agency that operates nationwide
through 37 offices. The company is not well known, its stock is not very liquid, its
earnings have fluctuated quite a bit in the past, and it doesn’t pay a dividend. All
this suggests that Pay Up is risky and that the required rate of return on its stock,
r, should be relatively high. However, Pay Up’s required rate of return in 2006,
and all other years, was quite low in relation to those of most other companies.
This indicates that investors regard Pay Up as being a low-risk company in spite
of its uncertain profits. The reason for this counterintuitive fact has to do with
diversification and its effect on risk. Pay Up’s earnings rise during recessions,
whereas most other companies’ earnings tend to decline when the economy
slumps. It’s like fire insurance—it pays off when other things go badly. Therefore,
adding Pay Up to a portfolio of “normal” stocks tends to stabilize returns on the
entire portfolio, thus making the portfolio less risky.
Portfolio Returns
The expected return on a portfolio, ˆr p , is simply the weighted average of the
expected returns on the individual assets in the portfolio, with the weights being
the fraction of the total portfolio invested in each asset:
ˆr p w 1 ˆr 1 w 2 ˆr 2 ... w n ˆr n
n
a wi rˆi
i1
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