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The average monthly return on Disney over the 59 months was “0.07%. The standard
deviation in monthly returns was 9.33% and the variance in returns was 86.96%.2 To
convert monthly values to annualized ones:
Annualized Standard Deviation = 9.33% *√12 = 32.31%
Annualized Variance = 86.96% * 12 = 1043.55%
Without making comparisons to the standard deviations in stock returns of other
companies, we cannot really draw any conclusions about the relative risk of Disney by
just looking at its standard deviation.

optvar.xls is a dataset on the web that summarizes standard deviations and
variances of stocks in various sectors in the United States.

˜: 3.2. Upside and Downside Risk

2 The variance is percent squared. In other words, if you stated the standard deviation of 9.96% in decimal
terms, it would be 0.0996 but the variance of 99.15% would be 0.009915 in decimal terms.

You are looking at the historical standard deviations over the last 5 years on two
investments. Both have standard deviations of 35% in returns during the period, but one
had a return of -10% during the period, whereas the other had a return of +40% during
the period. Would you view them as equally risky?
a. Yes
b. No
Why do we not differentiate between “upside risk” and “downside risk” in finance?

In Practice: Estimating only downside risk
The variance of a return distribution measures the deviation of actual returns from
the expected return. In estimating the variance, we consider not only actual returns that
fall below the average return (downside risk) but also those that lie above it (upside risk).
As investors, it is the downside that we generally consider as risk. There is an alternative
measure called the semi-variance that considers only downside risk. To estimate the
semi-variance, we calculate the deviations of actual returns from the average return only
if the actual return is less than the expected return; we ignore actual returns that are
higher than the average return.
t= n
(R t "Average Return)2
Semi-variance = #

n = number of periods where actual return < Average return
With a normal distribution, the semi-variance will generate a value identical to the
variance, but for any non-symmetric distribution, the semi-variance will yield different
values than the variance. In general, a stock that generates small positive returns in most
periods but very large negative returns in a few periods will have a semi-variance that is
much higher than the variance.

II. Rewarded and Unrewarded Risk
Risk, as we have defined it in the previous section, arises from the deviation of
actual returns from expected returns. This deviation, however, can occur for any number
of reasons, and these reasons can be classified into two categories - those that are specific
to the investment being considered (called firm specific risks) and those that apply across
most or all investments (market risks).

The Components of Risk
When a firm makes an investment, in a new asset or a project, the return on that
investment can be affected by several variables, most of which are not under the direct
control of the firm. Some of the risk comes directly from the investment, a portion from
competition, some from shifts in the industry, some from changes in exchange rates and
some from macroeconomic factors. A portion of this risk, however, will be eliminated by
the firm itself over the course of multiple investments and another portion by investors as
they hold diversified portfolios.
The first source of risk is project-specific;
Project Risk: This is risk that affects
an individual project may have higher or lower
only the project under consideration, and
cashflows than expected, either because the firm
may arise from factors specific to the
misestimated the cashflows for that project or
project or estimation error.
because of factors specific to that project. When
firms take a large number of similar projects, it
can be argued that much of this risk should be diversified away in the normal course of
business. For instance, Disney, while considering making a new movie, exposes itself to
estimation error - it may under or over estimate the cost and time of making the movie,
and may also err in its estimates of revenues from both theatrical release and the sale of
merchandise. Since Disney releases several movies a year, it can be argued that some or
much of this risk should be diversifiable across movies produced during the course of the
The second source of risk is Competitive Risk: This is the unanticipated
competitive risk, whereby the earnings effect on the cashflows in a project of competitor
and cashflows on a project are affected actions - these effects can be positive or negative.
(positively or negatively) by the actions
of competitors. While a good project analysis will build in the expected reactions of
competitors into estimates of profit margins and growth, the actual actions taken by
competitors may differ from these expectations. In most cases, this component of risk

will affect more than one project, and is therefore more difficult to diversify away in the
normal course of business by the firm. Disney, for instance, in its analysis of revenues
from its Disney retail store division may err in its assessments of the strength and
strategies of competitors like Toys™R™Us and WalMart. While Disney cannot diversify
away its competitive risk, stockholders in Disney can, if they are willing to hold stock in
the competitors.4
The third source of risk is industry-specific risk ““ those factors that impact the
earnings and cashflows of a specific industry. There are three sources of industry-specific
risk. The first is technology risk, which reflects the effects of technologies that change or
evolve in ways different from those expected when a project was originally analyzed. The
second source is legal risk, which reflects the effect of changing laws and regulations.
The third is commodity risk, which reflects
Industry-Specific Risk: These are unanticipated
the effects of price changes in commodities
effects on project cashflows of industry-wide
and services that are used or produced
shifts in technology, changes in laws or in the
disproportionately by a specific industry. price of a commodity.
Disney, for instance, in assessing the
prospects of its broadcasting division
(ABC) is likely to be exposed to all three risks; to technology risk, as the lines between
television entertainment and the internet are increasing blurred by companies like
Microsoft, to legal risk, as the laws governing broadcasting change and to commodity
risk, as the costs of making new television programs change over time. A firm cannot
diversify away its industry-specific risk without diversifying across industries, either with
new projects or through acquisitions. Stockholders in the firm should be able to diversify
away industry-specific risk by holding portfolios of stocks from different industries.
International Risk: This is the additional
uncertainty created in cashflows of projects by
unanticipated changes in exchange rates and by
3 To provide an illustration, Disney released Treasure Planet, an animated movie,markets. which cost $140
political risk in foreign in 2002,
million to make and resulted in a $98 million write-off. A few months later, Finding Nemo, another
animated Disney movie made hundreds of millions of dollars and became one of the biggest hits of 2003.
4 Firms could conceivably diversify away competitive risk by acquiring their existing competitors. Doing
so would expose them to attacks under the anti-trust law, however and would not eliminate the risk from as
yet unannounced competitors.

The fourth source of risk is international risk. A firm faces this type of risk when
it generates revenues or has costs outside its domestic market. In such cases, the earnings
and cashflows will be affected by unexpected exchange rate movements or by political
developments. Disney, for instance, was clearly exposed to this risk with its 33% stake in
EuroDisney, the theme park it developed outside Paris. Some of this risk may be
diversified away by the firm in the normal course of business by investing in projects in
different countries whose currencies may not all move in the same direction. Citibank and
McDonalds, for instance, operate in many different countries and are much less exposed
to international risk than was Wal-Mart in 1994, when its foreign operations were
restricted primarily to Mexico. Companies can also reduce their exposure to the exchange
rate component of this risk by borrowing in the local currency to fund projects; for
instance, by borrowing money in pesos to invest in Mexico. Investors should be able to
reduce their exposure to international risk by diversifying globally.
The final source of risk is market risk: macroeconomic factors that affect
essentially all companies and all projects, to varying degrees. For example, changes in
interest rates will affect the value of projects already taken and those yet to be taken both
directly, through the discount rates, and indirectly, through the cashflows. Other factors
that affect all investments include the term structure (the difference between short and
long term rates), the risk preferences of
Market Risk: Market risk refers to the
investors (as investors become more risk unanticipated changes in project cashflows
averse, more risky investments will lose value), created by changes in interest rates, inflation
rates and the economy that affect all firms,
inflation, and economic growth. While expected
though to differing degrees.
values of all these variables enter into project
analysis, unexpected changes in these variables will affect the values of these
investments. Neither investors nor firms can diversify away this risk since all risky
investments bear some exposure to this risk.

˜: 3.3. Risk is in the eyes of the beholder
A privately owned firm will generally end up with a higher discount rate for a project
than would an otherwise similar publicly traded firm with diversified investors.
a. True
b. False

Does this provide a rationale for why a private firm may be acquired by a publicly traded

Why Diversification Reduces or Eliminates Firm-Specific Risk
Why do we distinguish between the different types of risk? Risk that affect one of
a few firms, i.e., firm specific risk, can be reduced or even eliminated by investors as they
hold more diverse portfolios due to two reasons.
The first is that each investment in a
• Diversification: This is the process of
holding many investments in a
diversified portfolio is a much smaller
portfolio, either across the same asset
percentage of that portfolio. Thus, any risk
class (eg. stocks) or across asset
that increases or reduces the value of only that classes (real estate, bonds etc.
investment or a small group of investments
will have only a small impact on the overall portfolio.
The second is that the effects of firm-specific actions on the prices of individual

assets in a portfolio can be either positive or negative for each asset for any
period. Thus, in large portfolios, it can be reasonably argued that this risk will
average out to be zero and thus not impact the overall value of the portfolio.
In contrast, risk that affects most of all assets in the market will continue to persist even
in large and diversified portfolios. For instance, other things being equal, an increase in
interest rates will lower the values of most assets in a portfolio. Figure 3.5 summarizes
the different components of risk and the actions that can be taken by the firm and its
investors to reduce or eliminate this risk.

Figure 3.5: A Break Down of Risk

may be stronger
or weaker than Exchange rate
anticipated and Political
Projects may
Interest rate,
do better or
Entire Sector Inflation &
worse than
may be affected news about
by action economy

Firm-specific Market

Actions/Risk that Actions/Risk that
Affects few Affects many
affect only one affect all investments
firms firms
Firm can Investing in lots Acquiring Diversifying Diversifying Cannot affect
reduce by of projects competitors across sectors across countries

Investors Diversifying across domestic stocks Diversifying globally Diversifying across
can asset classes
mitigate by

While the intuition for diversification reducing risk is simple, the benefits of
diversification can also be shown statistically. In the last section, we introduced standard
deviation as the measure of risk in an investment and calculated the standard deviation
for an individual stock (Disney). When you combine two investments that do not move
together in a portfolio, the standard deviation of that portfolio can be lower than the
standard deviation of the individual stocks in the portfolio. To see how the magic of
diversification works, consider a portfolio of two assets. Asset A has an expected return
of µA and a variance in returns of σ2A, while asset B has an expected return of µB and a
variance in returns of σ2B. The correlation in returns between the two assets, which
measures how the assets move together, is ρAB.5 The expected returns and variance of a
two-asset portfolio can be written as a function of these inputs and the proportion of the
portfolio going to each asset.
µportfolio = wA µA + (1 - wA) µB
σ2portfolio = wA2 σ2A + (1 - wA)2 σ2B + 2 wA wB ρ‘’ σA σB

5 The correlation is a number between “1 and +1. If the correlation is “1, the two stocks move in lock step
but in opposite directions. If the correlation is +1, the two stocks move together in synch.

wA = Proportion of the portfolio in asset A
The last term in the variance formulation is sometimes written in terms of the covariance
in returns between the two assets, which is
σAB = ρ‘’ σA σB
The savings that accrue from diversification are a function of the correlation coefficient.
Other things remaining equal, the higher the correlation in returns between the two assets,
the smaller are the potential benefits from diversification. The following example
illustrates the savings from diversification.

Illustration 3.2: Variance of a portfolio: Disney and Aracruz
In illustration 3.1, we computed the average return and standard deviation of


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