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Bodie’Kane’Marcus: II. Portfolio Theory Introduction © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition



uppose you believe that investments in This analysis quickly leads to other ques-

S stocks offer an expected rate of return of tions. For example, how should one measure
10% while the expected rate of return on the risk of an individual asset held as part of a
bonds is only 6%. Would you invest all of your diversified portfolio? You will probably be sur-
money in stocks? Probably not: putting all of prised at the answer. Once we have an accept-
your eggs in one basket in such a manner would able measure of risk, what precisely should be
violate even the most basic notion of diversifi- the relation between risk and return? And what
cation. But what is the optimal combination of is the minimally acceptable rate of return for
these two asset classes? And how will the op- an investment to be considered attractive?
portunity to invest in other asset classes”for These questions also are addressed in this Part
example, real estate, foreign stocks, precious of the text.
metals, and so on”affect your decision? In Finally, we come to one of the most con-
short, is there a “best” solution to your asset al- troversial topics in investment management,
location problem? the question of whether portfolio managers”
These questions are the focus of the first amateur or professional”can outperform sim-
chapters of Part II, which address what has ple investment strategies such as “buy a market
come to be known as Modern Portfolio Theory, index fund.” The evidence will at least make
or MPT. In large part, MPT addresses the ques- you pause before pursuing active strategies.
tion of “efficient diversification,” how to achieve You will come to appreciate how good ac-
the best trade-off between portfolio risk and tive managers must be to outperform their
reward. passive counterparts.

5 Risk and Return: Past and Prologue
6 Efficient Diversification
7 Capital Asset Pricing and Arbitrage Pricing Theory
8 The Efficient Market Hypothesis

Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition



> Use data on the past performance of stocks and bonds to
characterize the risk and return features of these

> Determine the expected return and risk of portfolios that are
constructed by combining risky assets with risk-free
investments in Treasury bills.

> Evaluate the performance of a passive strategy.

Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

Related Websites
These sites report current rates on U.S. and
international government bonds.
These websites list returns on various equity indexes.
These two sites are pages from the bond market
This site gives detailed analysis on index returns.
association. General information on a variety of bonds
Analysis of historical returns and comparisons to other
and strategies can be accessed online at no charge.
indexes are available. The site also reports on changes
Current information on rates is also available at
to the index.
This site contains current and historical information
This site contains information on virtually all available
on a variety of interest rates. Historical data can be
indexes. It also has a screening program that allows you
downloaded in spreadsheet format, which is available
to rank indexes by various return measures.
through the Federal Reserve Economic Database (FRED).

hat constitutes a satisfactory investment portfolio? Until the early 1970s, a

W reasonable answer would have been a bank savings account (a risk-free
asset) plus a risky portfolio of U.S. stocks. Nowadays, investors have access
to a vastly wider array of assets and may contemplate complex portfolio strategies
that may include foreign stocks and bonds, real estate, precious metals, and col-
lectibles. Even more complex strategies may include futures and options to insure
portfolios against unacceptable losses. How might such portfolios be constructed?
Clearly every individual security must be judged on its contributions to both the
expected return and the risk of the entire portfolio. These contributions must be eval-
uated in the context of the expected performance of the overall portfolio. To guide us
in forming reasonable expectations for portfolio performance, we will start this chap-
ter with an examination of various conventions for measuring and reporting rates of
return. Given these measures, we turn to the historical performance of several
broadly diversified investment portfolios. In doing so, we use a risk-free portfolio of
Treasury bills as a benchmark to evaluate the historical performance of diversified
stock and bond portfolios.
We then proceed to consider the trade-offs investors face when they practice the
simplest form of risk control: choosing the fraction of the portfolio invested in virtu-
ally risk-free money market securities versus risky securities such as stocks. We show
how to calculate the performance one may reasonably expect from various alloca-
tions between a risk-free asset and a risky portfolio and discuss the considerations
that determine the mix that would best suit different investors. With this background,
we can evaluate a passive strategy that will serve as a benchmark for the active
strategies considered in the next chapter.
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

132 Part TWO Portfolio Theory

A key measure of investors™ success is the rate at which their funds have grown during the in-
vestment period. The total holding-period return (HPR) of a share of stock depends on the
increase (or decrease) in the price of the share over the investment period as well as on any
dividend income the share has provided. The rate of return is defined as dollars earned over
Rate of return over a
the investment period (price appreciation as well as dividends) per dollar invested
given investment
Ending price Beginning price Cash dividend
Beginning price
This definition of the HPR assumes that the dividend is paid at the end of the holding pe-
riod. To the extent that dividends are received earlier, the definition ignores reinvestment in-
come between the receipt of the dividend and the end of the holding period. Recall also that
the percentage return from dividends is called the dividend yield, and so the dividend yield
plus the capital gains yield equals the HPR.
This definition of holding return is easy to modify for other types of investments. For ex-
ample, the HPR on a bond would be calculated using the same formula, except that the bond™s
interest or coupon payments would take the place of the stock™s dividend payments.

Suppose you are considering investing some of your money, now all invested in a bank ac-
count, in a stock market index fund. The price of a share in the fund is currently $100, and
5.1 EXAMPLE your time horizon is one year. You expect the cash dividend during the year to be $4, so your
expected dividend yield is 4%.
Your HPR will depend on the price one year from now. Suppose your best guess is that it will
be $110 per share. Then your capital gain will be $10, so your capital gains yield is $10/$100
.10, or 10%. The total holding period rate of return is the sum of the dividend yield plus the
capital gain yield, 4% 10% 14%.
$110 $100 $4
HPR .14, or 14%

Measuring Investment Returns over Multiple Periods
The holding period return is a simple and unambiguous measure of investment return over a
single period. But often you will be interested in average returns over longer periods of time.
For example, you might want to measure how well a mutual fund has performed over the pre-
ceding five-year period. In this case, return measurement is more ambiguous.
Consider, for example, a fund that starts with $1 million under management at the begin-
ning of the year. The fund receives additional funds to invest from new and existing share-
holders, and also receives requests for redemptions from existing shareholders. Its net cash
inflow can be positive or negative. Suppose its quarterly results are as given in Table 5.1 with
negative numbers reported in parentheses.
The story behind these numbers is that when the firm does well (i.e., reports a good HPR),
it attracts new funds; otherwise it may suffer a net outflow. For example, the 10% return in the
first quarter by itself increased assets under management by 0.10 $1 million $100,000;
it also elicited new investments of $100,000, thus bringing assets under management to
$1.2 million by the end of the quarter. An even better HPR in the second quarter elicited a
larger net inflow, and the second quarter ended with $2 million under management. However,
HPR in the third quarter was negative, and net inflows were negative.
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition

5 Risk and Return: Past and Prologue

1st 2nd 3rd 4th
TA B L E 5.1 Quarter Quarter Quarter Quarter
Quarterly cash flows
Assets under management 1.0 1.2 2.0 0.8
and rates of return
of a mutual fund at start of quarter ($ million)
Holding-period return (%) 10.0 25.0 (20.0) 25.0
Total assets before net inflows 1.1 1.5 1.6 1.0
Net inflow ($ million)* 0.1 0.5 (0.8) 0.0
Assets under management at 1.2 2.0 0.8 1.0
end of quarter ($ million)

New investment less redemptions and distributions, all assumed to occur at the end of each quarter.

How would we characterize fund performance over the year, given that the fund experi-
enced both cash inflows and outflows? There are several candidate measures of performance,
each with its own advantages and shortcomings. These are the arithmetic average, the geo-
metric average, and the dollar-weighted return. These measures may vary considerably, so it
is important to understand their differences.

Arithmetic average The arithmetic average of the quarterly returns is just the sum of arithmetic
the quarterly returns divided by the number of quarters; in the above example: (10 25 20 average
25)/4 10%. Since this statistic ignores compounding, it does not represent an equivalent, The sum of returns in
single quarterly rate for the year. The arithmetic average is useful, though, because it is the each period divided by
best forecast of performance in future quarters, using this particular sample of historic returns. the number of
(Whether the sample is large enough or representative enough to make accurate forecasts is,
of course, another question.)

Geometric average The geometric average of the quarterly returns is equal to the sin- geometric
gle per-period return that would give the same cumulative performance as the sequence of ac- average
tual returns. We calculate the geometric average by compounding the actual period-by-period The single per-period
returns and then finding the equivalent single per-period return. In this case, the geometric av- return that gives the
erage quarterly return, rG, is defined by: same cumulative
performance as the
(1 0.10) (1 0.25) (1 0.20) (1 0.25) (1 sequence of actual


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