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returns on Disney between January 1999 and December 2003. While Aracruz is a
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Brazilian stock, it has been listed and traded in the U.S. market over the same period.
Using the same 60 months of data on Aracruz, we computed the average return and
standard deviation on its returns over the same period:
Average Monthly Return - 0.07% 2.57%
Standard Deviation in Monthly Returns 9.33% 12.62%
Over the period (1999-2003), Aracruz was a much more attractive investment than
Disney but it was also much more volatile. We computed the correlation between the two
stocks over the 60-month period to be 0.2665. Consider now a portfolio that is invested
90% in Disney and 10% in the Aracruz ADR. The variance and the standard deviation of
the portfolio can be computed as follows:
Variance of portfolio = wDis2 Пѓ2Dis + (1 - wDis)2 Пѓ2Ara + 2 wDis wAra ПЃDis,Ara ПѓDis ПѓAra
= (.9)2(.0933)2+(.1)2(.1262)2+ 2 (.9)(.1)(.2665)(.0933)(.1262)
= .007767

6 Like most foreign stocks, Aracruz has a listing for depository receipts or ADRs on the U.S. exchanges.
Effectively, a bank buys shares of Aracruz in Brazil and issues dollar denominated shares in the United
States to interested investors. AracruzвЂ™s ADR price tracks the price of the local listing while reflecting
exchange rate changes.
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.007767 = .0881 or 8.81%
Standard Deviation of Portfolio =
The portfolio is less risky than either of the two stocks that go into it. In figure 3.6, we
graph the standard deviation in the portfolio as a function of the proportion of the
!
portfolio invested in Disney:

Figure 3.6: Standard Deviation of Portfolio

14.00%

12.00%

10.00%
Standard deviation of portfolio

8.00%

6.00%

4.00%

2.00%

0.00%
100% 90.0% 80.0% 70.0% 60.0% 50.0% 40.0% 30.0% 20.0% 10.0% 0.0%
Proportion invested in Disney

As the proportion of the portfolio invested in Aracruz shifts towards 100%, the standard
deviation of the portfolio converges on the standard deviation of Aracruz.

Identifying the Marginal Investor
The marginal investor in a firm is the investor who is most likely to be trading at
the margin and therefore has the most influence on the pricing of its equity. In some
cases, this may be a large institutional investor, but institutional investors themselves can
differ in several ways. The institution may be a taxable mutual fund or a tax-exempt
pension fund, may be domestically or internationally diversified, and vary on investment
philosophy. In some cases, the marginal investors may be individuals, and here again
there can be wide differences depending upon how diversified these individuals are, and
what their investment objectives may be. In still other cases, the marginal investors may
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be insiders in the firm who own a significant portion of the equity of the firm and are
involved in the management of the firm.
While it is difficult to identify the marginal investor in a firm, we would begin by
breaking down the percent of the firmвЂ™s stock held by individuals, institutions and
insiders in the firm. This information, which is available widely for US stocks, can then
be analyzed to yield the following conclusions:
If the firm has relatively small institutional holdings but substantial holdings by
вЂў
wealthy individual investors, the marginal investor is an individual investor with a
significant equity holding in the firm. In this case, we have to consider how
diversified that individual investorвЂ™s portfolio is to assess project risk. If the
individual investor is not diversified, this firm may have to be treated like a
private firm, and the cost of equity has to include a premium for all risk, rather
than just non-diversifiable risk. If on the other hand, the individual investor is a
wealthy individual with significant stakes in a large number of firms, a large
portion of the risk may be diversifiable.
If the firm has small institutional holdings and small insider holdings, its stock is
вЂў
held by large numbers of individual investors with small equity holdings. In this
case, the marginal investor is an individual investor, with a portfolio that may be
only partially diversified. For instance, phone and utility stocks in the United
States, at least until recently, had holdings dispersed among thousands of
individual investors, who held the stocks for their high dividends. This preference
for dividends meant, however, that these investors diversified across only those
sectors where firms paid high dividends.
If the firm has significant institutional holdings and small insider holdings, the
вЂў
marginal investor is almost always a diversified, institutional investor. In fact, we
the top 15 or 20 largest stockholders in the firms, and then categorizing them by
tax status (mutual funds versus pension funds), investment objective (growth or
value) and globalization (domestic versus international).
If the firm has significant institutional holdings and large insider holdings, the
вЂў
choice for marginal investor becomes a little more complicated. Often, in these
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scenarios, the large insider is the founder or original owner for the firm, and often,
this investor continues to be involved in the top management of firm. Microsoft
and Dell are good examples, with Bill Gates and Michael Dell being the largest
stockholders in the firms. In most of these cases, however, the insider owner
seldom trades the stock, and his or her wealth is determined by the level of the
stock price, which is determined by institutional investors trading the stock. We
would argue that the institutional investor is the marginal investor in these firms
as well, though the leading stockholder will influence the final decision.
Thus, by examining the percent of stock held by different groups, and the largest
investors in a firm, we should have a sense of who the marginal investor in the firm is,
and how best to assess and risk in corporate financial analysis.

Illustration 3.3: Identifying the Marginal Investor

Who are the marginal investors in Disney, Aracruz and Deutsche Bank? We begin
to answer this question by examining whether iinsiders own a significant portion of the
equity in the firm and are involved in the top management of the firm. Although no such
investors exist at Disney and Deutsche Bank, the voting shares in Aracruz are closely
held by its incumbent managers. In Table 8.4, we examine the proportion of stock held in
each of the firms by individuals and institutions, with the institutional holding broken
down further into mutual fund and other institutional holdings.
Table 3.1: Investors in Disney, Aracruz and Deutsche Bank
Disney Deutsche Bank Aracruz (non-voting)
Mutual Funds 31% 16% 29%
Other 42% 58% 26%
Institutional
Investors
Individuals 27% 26% 45%
Source: Value Line, Morningstar

All three companies are widely held by institutional investors. To break down the
institutional investment, we examined the ten largest investors in each firm at the end of
2002 in Table 8.5, with the percent of the firmвЂ™s stock held by each (in brackets).
Table 3.2: Largest Stockholders in Disney, Aracruz and Deutsche Bank

Disney Deutsche Bank Aracruz - Preferred
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Barclays Global (3.40%) Allianz (4.81%) Safra (10.74%)
State Street (3.10%) La Caixa (3.85%) BNDES (6.34%)
Fidelity (3.01%) Capital Research (1.35%) Scudder Kemper (1.03%)
Citigroup (3.00%) Fidelity (0.50%) BNP Paribas (0.56%)
Southeastern Asset (2.36%) Frankfurt Trust (0.43%) Barclays Global (0.29%)
State Farm Mutual (2.06%) Aviva (0.37%) Vanguard Group (0.18%)
Vanguard Group (1.93%) Daxex (0.31%) Banco Itau (0.12%)
JP Morgan Chase (1.83%) Unifonds (0.29%) Van Eck Associates
(0.12%)
Mellon Bank (1.64%) Fidelity (0.28%) Pactual (0.11%)
Lord Abbet & Co(1.58%) UBS Funds (0.21%) Banco Bradesco (0.07%)
Source: Bloomberg

The ten largest investors in Disney are all institutional investors, suggesting that we are
on safe grounds assuming that the marginal investor in Disney is likely to be both
institutional and diversified. The largest single investor in Deutsche Bank is Allianz, the
German insurance giant, reflecting again the cross-holding corporate governance
structure favored by German corporations. However, the investors below Allianz are all
institutional investors, and about half of them are non-German. Here again, we can safely
assume that the marginal investor is likely to be institutional and broadly diversified
across at least European equities rather than just German stocks. The common shares in
Aracruz, where the voting rights reside, is held by a handful of controlling stockholders,
but trading in this stock is light.7 The two largest holders of preferred shares in Aracruz,
Safra and BNDES, are also holders of common stock and do not trade on their substantial
holdings. The remaining shares are held largely by institutional investors and many of
them are from outside Brazil. While there is a clear danger here that the company will be
run for the benefit of the voting shareholders, the price of the voting stock is closely
linked to the price of the preferred shares. Self-interest alone should induce the voting
shareholders to consider the investors in the preferred shares as the marginal investors in
the company.

Why is the marginal investor assumed to be diversified?
The argument that investors can reduce their exposure to risk by diversifying can
be easily made, but risk and return models in finance go further. They argue that the

7 Three stockholders, VCP, Safra and Grupo Lorentzen hold 28% each of the voting shares.
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marginal investor, who sets prices for investments, is well diversified; thus, the only risk
that will be priced in the risk as perceived by that investor. The justification that can be
offered is a simple one. The risk in an investment will always be perceived to be higher
for an undiversified investor than to a diversified one, since the latter does not consider
any firm-specific risk while the former does. If both investors have the same perceptions
about future earnings and cashflows on an asset, the diversified investor will be willing to
pay a higher price for that asset because of his or her risk perceptions. Consequently, the
asset, over time, will end up being held by diversified investors.
While this argument is a powerful one for stocks and other assets, which are
traded in small units and are liquid, it is less so for investments that are large and illiquid.
Real estate in most countries is still held by investors who are undiversified and have the
bulk of their wealth tied up in these investments. The benefits of diversification are
strong enough, however, that securities such as real estate investment trusts and
mortgage-backed bonds were created to allow investors to invest in real estate and stay
diversified at the same time.
Note that diversification does not require investors to give up their pursuit of
higher returns. Investors can be diversified and try to beat the market at the same time,
For instance, investors who believe that they can do better than the market by buying
stocks trading at low PE ratios can still diversify by holding low PE stocks in a number of
different sectors at the same time.

в˜ћ: 3.4. Management Quality and Risk
A well managed firm is less risky than a firm that is badly managed.
a. True
b. False

In Practice: Who should diversify? The Firm or Investors?
As we noted in the last section, the exposure to each type of risk can be mitigated
by either the firm or by investors in the firm. The question of who should do it can be
answered fairly easily by comparing the costs faced by each. As a general rule, a firm
should embark on actions that reduce risk only if it is cheaper for it to do so than it is for
its investors. With a publicly traded firm, it will usually be much cheaper for investors to
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diversify away risk than it is for the firm. Consider, for instance, risk that affects an entire
sector. A firm can reduce its exposure to this risk by either acquiring other firms, paying
large premiums over the market price, or by investing large amounts in businesses where
it does not have any expertise. Investors in the firm, on the other hand, can accomplish
the same by expanding their portfolios to include stocks in other sectors or even more
simply by holding diversified mutual funds. Since the cost of diversifying for investors is
very low, firms should try to diversify away risk only if the cost is minimal or if the risk
reduction is a side benefit from an action with a different objective. One example would
be project risk. Since Disney is in the business of making movies, the risk reduction that
comes from making lots of movies is essentially costless.
The choice is more complicated for private businesses. The owners of these
businesses often have the bulk of their wealth invested in these businesses and they can
either try to take money out of the businesses and invest it elsewhere or they can diversify
their businesses. In fact, many family businesses in Latin America and Asia became
conglomerates as they expanded, partly because they wanted to spread their risks.

III. Measuring Market Risk
While most risk and return models in use in corporate finance agree on the first
two step of this process, i.e., that risk comes from the distribution of actual returns around
the expected return and that risk should be measured from the perspective of a marginal
investor who is well diversified, they part ways on how to measure the non-diversifiable
or market risk. In this section, we will provide a sense of how each of the four basic
models - the capital asset pricing model (CAPM), the arbitrage pricing model (APM) and
the multi-factor model - approaches the issue of measuring market risk.

A. The Capital Asset Pricing Model
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