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many stocks we hold.
Figure 6.1 illustrates these concepts. When all risk is firm-specific, as in Figure 6.1A, di-
versification can reduce risk to low levels. With all risk sources independent, and with invest-
ment spread across many securities, exposure to any particular source of risk is negligible.
market risk, This is just an application of the law of averages. The reduction of risk to very low levels be-
systematic risk, cause of independent risk sources is sometimes called the insurance principle.
nondiversifiable When common sources of risk affect all firms, however, even extensive diversification can-
risk not eliminate risk. In Figure 6.1B, portfolio standard deviation falls as the number of securities
increases, but it is not reduced to zero. The risk that remains even after diversification is called
Risk factors common
market risk, risk that is attributable to marketwide risk sources. Other names are systematic
to the whole economy.




F I G U R E 6.1 σ σ
Portfolio risk as
a function of the
number of stocks
in the portfolio

Unique risk




Market risk


n n
A: Firm-specific risk only B: Market and unique risk
Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




171
6 Efficient Diversification


risk or nondiversifiable risk. The risk that can be eliminated by diversification is called unique risk,
unique risk, firm-specific risk, nonsystematic risk, or diversifiable risk. firm-specific risk,
This analysis is borne out by empirical studies. Figure 6.2 shows the effect of portfolio di- nonsystematic
versification, using data on NYSE stocks. The figure shows the average standard deviations risk, diversifiable
of equally weighted portfolios constructed by selecting stocks at random as a function of the risk
number of stocks in the portfolio. On average, portfolio risk does fall with diversification, but Risk that can be
the power of diversification to reduce risk is limited by common sources of risk. The box eliminated by
on the following page highlights the dangers of neglecting diversification and points out that diversification.
such neglect is widespread.

6.2 ASSET ALLOCATION WITH TWO RISKY ASSETS
In the last chapter we examined the simplest asset allocation decision, that involving the
choice of how much of the portfolio to place in risk-free money market securities versus in a
risky portfolio. We simply assumed that the risky portfolio comprised a stock and a bond fund
in given proportions. Of course, investors need to decide on the proportion of their portfolios
to allocate to the stock versus the bond market. This, too, is an asset allocation decision. As the
box on page 173 emphasizes, most investment professionals recognize that the asset alloca-
tion decision must take precedence over the choice of particular stocks or mutual funds.
We examined capital allocation between risky and risk-free assets in the last chapter. We
turn now to asset allocation between two risky assets, which we will continue to assume are
two mutual funds, one a bond fund and the other a stock fund. After we understand the prop-
erties of portfolios formed by mixing two risky assets, we will reintroduce the choice of the
third, risk-free portfolio. This will allow us to complete the basic problem of asset allocation
across the three key asset classes: stocks, bonds, and risk-free money market securities. Once
you understand this case, it will be easy to see how portfolios of many risky securities might
best be constructed.


Covariance and Correlation
Because we now envision forming a risky portfolio from two risky assets, we need to under-
stand how the uncertainties of asset returns interact. It turns out that the key determinant of
portfolio risk is the extent to which the returns on the two assets tend to vary either in tandem



F I G U R E 6.2
Average portfolio standard deviation (%)




Risk compared to a one-stock portfolio




Portfolio risk
decreases as
100%
50 diversification
increases
40
75%
Source: Meir Statman,
30 “How Many Stocks Make a
50% Diversified Portfolio?”
20 40% Journal of Financial and
Quantitative Analysis 22,
10
September 1987.
0 0
0 2 4 6 8 10 12 14 16 18 20 100 200 300 400 500 600 700 800 900
1,000
Number of stocks in portfolio
Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




Dangers of Not Diversifying Hit Investors
people think their company is safer than a stock mutual
Enron, Tech Bubble
fund, when the data show that the opposite is true,”
Are Wake-Up Calls says John Rekenthaler, president of Morningstar™s on-
Mutual-fund firms and financial planners have droned line-advice unit.
on about the topic for years. But suddenly, it™s at the While some companies will match employees™
epicenter of lawsuits, congressional hearings and pres- 401(k) contributions exclusively in company stock, in-
idential reform proposals. vestors can almost always diversify a large portion of
Diversification”that most basic of investing princi- their 401(k)”namely, the part they contribute them-
ples”has returned with a vengeance. During the late selves. Half or more of the assets in a typical 401(k)
1990s, many people scoffed at being diversified, be- portfolio are contributed by employees themselves, so
cause the idea of investing in a mix of stocks, bonds diversifying this portion of their portfolio can make a
and other financial assets meant missing out on some significant difference in reducing overall investing risk.
of the soaring gains of tech stocks. But in picking an investing alternative to buying your
But with the collapse of the tech bubble and now employer™s stock, some choices are more useful than
the fall of Enron Corp. wiping out the 401(k) holdings others. For example, investors should take into account
of many current and retired Enron employees, the dan- the type of company they work for when diversifying.
gers of overloading a portfolio with one stock”or even Workers at small technology companies”the type of
with a group of similar stocks”has hit home for many stock often held by growth funds”might find better di-
investors. versification with a fund focusing on large undervalued
The pitfalls of holding too much of one company™s companies. Conversely, an auto-company worker might
stock aren™t limited to Enron. Since the beginning of want to put more money in funds that specialize
2000, nearly one of every five U.S. stocks has fallen by in smaller companies that are less tied to economic
two-thirds or more, while only 1% of diversified stock cycles.
mutual funds have swooned as much, according to re-
search firm Morningstar Inc.
While not immune from losses, mutual funds tend SOURCE: Abridged from Aaron Luccheth and Theo Francis,
to weather storms better, because they spread their “Dangers of Not Diversifying Hit Investors,” The Wall Street Journal,
bets over dozens or hundreds of companies. “Most February 15, 2002.




or in opposition. Portfolio risk depends on the correlation between the returns of the assets in
the portfolio. We can see why using a simple scenario analysis.
Suppose there are three possible scenarios for the economy: a recession, normal growth,
and a boom. The performance of stock funds tends to follow the performance of the broad
economy. So suppose that in a recession, the stock fund will have a rate of return of 11%, in
a normal period it will have a rate of return of 13%, and in a boom period it will have a rate of
return of 27%. In contrast, bond funds often do better when the economy is weak. This is be-
cause interest rates fall in a recession, which means that bond prices rise. Suppose that a bond
fund will provide a rate of return of 16% in a recession, 6% in a normal period, and 4% in a
boom. These assumptions and the probabilities of each scenario are summarized in Spread-
sheet 6.1.
The expected return on each fund equals the probability-weighted average of the out-
comes in the three scenarios. The last row of Spreadsheet 6.1 shows that the expected return
of the stock fund is 10%, and that of the bond fund is 6%. As we discussed in the last chapter,
the variance is the probability-weighted average across all scenarios of the squared deviation
between the actual return of the fund and its expected return; the standard deviation is the
square root of the variance. These values are computed in Spreadsheet 6.2.
What about the risk and return characteristics of a portfolio made up from the stock and
bond funds? The portfolio return is the weighted average of the returns on each fund with
weights equal to the proportion of the portfolio invested in each fund. Suppose we form a
172
Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




First Take Care of Asset-Allocation Needs
Once you have settled on your asset-allocation mix,
If you want to build a top-performing mutual-fund port-
decide what sort of stock, bond, and money-market
folio, you should start by hunting for top-performing
funds you want to own. This is particularly critical for
funds, right?
the stock portion of your portfolio. One way to damp
Wrong.
the price swings in your stock portfolio is to spread your
Too many investors gamely set out to find top-notch
money among large, small, and foreign stocks.
funds without first settling on an overall portfolio strat-
You could diversify even further by making sure that,
egy. Result? These investors wind up with a mishmash
when investing in U.S. large- and small-company
of funds that don™t add up to a decent portfolio. . . .
stocks, you own both growth stocks with rapidly in-
. . . So what should you do? With more than 11,000
creasing sales or earnings and also beaten-down value
stock, bond, and money-market funds to choose from,
stocks that are inexpensive compared with corporate
you couldn™t possibly analyze all the funds available. In-
assets or earnings.
stead, to make sense of the bewildering array of funds
Similarly, among foreign stocks, you could get addi-
available, you should start by deciding what basic mix
tional diversification by investing in both developed for-
of stock, bond, and money-market funds you want to
eign markets such as France, Germany, and Japan,
hold. This is what experts call your “asset allocation.”
and also emerging markets like Argentina, Brazil, and
This asset allocation has a major influence on your
Malaysia.
portfolio™s performance. The more you have in stocks,
the higher your likely long-run return.
But with the higher potential return from stocks
come sharper short-term swings in a portfolio™s value.
Source: Abridged from Jonathan Clements, “It Pays for You to Take
As a result, you may want to include a healthy dose of
Care of Asset-Allocation Needs before Latching onto Fads,” The Wall
bond and money-market funds, especially if you are a Street Journal, April 6, 1998. Reprinted by permission of Dow Jones &
conservative investor or you will need to tap your port- Company, Inc. via Copyright Clearance Center, Inc. © 1998 Dow
folio for cash in the near future. Jones & Company, Inc. All Rights Reserved Worldwide.




portfolio with 60% invested in the stock fund and 40% in the bond fund. Then the portfolio
return in each scenario is the weighted average of the returns on the two funds. For example
Portfolio return in recession 0.60 ( 11%) 0.40 16% 0.20%
which appears in cell C5 of Spreadsheet 6.3.
Spreadsheet 6.3 shows the rate of return of the portfolio in each scenario, as well as the
portfolio™s expected return, variance, and standard deviation. Notice that while the portfolio™s
expected return is just the average of the expected return of the two assets, the standard devi-
ation is actually less than that of either asset.



S P R E A D S H E E T 6.1
Capital market expectations for the stock and bond funds


A B C D E F
Stock Fund Bond Fund
1
Scenario Probability Rate of Return Col. B Col. C Rate of Return Col. B Col. E
2
Recession 0.3 11 3.3 16 4.8
3
Normal 0.4 13 5.2 6 2.4
4
Boom 0.3 27 8.1 4 1.2
5
SUM: SUM:
Expected or Mean Return: 10.0 6.0
6




173
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Essentials of Investments, Companies, 2003
Fifth Edition




174 Part TWO Portfolio Theory



S P R E A D S H E E T 6.2

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