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and (2) after careful study of available information about the ¬nancial
markets, our independent application of logic and common sense.


The trouble is, the very names of asset classes”foreign stocks, small
stocks, emerging markets, venture capital”evoke varying emotions that
get in the way of rational evaluation by investors. A helpful starting point
with any asset class is to describe it quantitatively in order to move as far
as possible from the emotional to the intellectual.
To develop our Target Asset Allocation we need to quantify three criti-
cally important characteristics of every asset class:

1. Its expected return,
2. Its expected risk, and
3. Its expected correlations with every other asset class.

Why are these characteristics so important? Because they enable us
through diversi¬cation to accomplish our basic investment objective: the
highest net investment return our portfolio can achieve within whatever
limit of annual volatility we can accept.
The problem is that essentially riskless assets, such as U.S. Treasury
bills, provide the lowest long-term returns. And assets with the highest ex-
pected returns, such as start-up venture capital, are the most risky. The
risk/return chart in Figure 4.1 shows that the higher the expected rate of
return from an asset class is, the higher its volatility tends to be.
To some extent, diversi¬cation offers us a way to have our cake and
eat it too”to hold more higher-risk, higher-return assets without increas-
ing overall portfolio volatility. By assembling a portfolio of asset classes
that march to somewhat different drummers (that have a low correlation
with one another), we can increase our portfolio™s expected return at any
given level of expected volatility. What counts is the portfolio™s aggregate
volatility, not the volatility of each asset or each asset class.
To illustrate, let™s look at an imaginary portfolio of only two assets,
both having a high expected return of X%, both extremely volatile, but
with returns that move exactly opposite to one another”that is, with a
correlation of “1. This means when asset A goes up by X + Y%, asset B
returns X “ Y%, and vice versa. Although each asset is extremely
volatile, the aggregate volatility of the portfolio (assuming rebalancing
Characteristics of an Asset Class

Emerging Markets Stocks
Small Stocks
Large Stocks

High-Yield Bonds

Investment-Grade Bonds

Cash Equivalents


FIGURE 4.1 Risk/Return Chart

each year to 50:50) would be nil”and we would essentially earn X%
with no volatility.
Oh, if only two such assets existed! We can™t achieve this, but we can
get part way by combining asset classes whose annual returns are only
partly correlated.
How do we go about quantifying the three key assumptions for each
asset class? It™s hard. But if we don™t do it explicitly, we will end up doing it
implicitly and not even recognize what assumptions we are making. Let™s
discuss these three assumptions”expected return, risk, and correlation.

Wait a minute. As a member of the investment committee, am I
expected to come up with these assumptions?

No. For this we must rely on our adviser. But the next few paragraphs will
enable us to ask questions that will help us understand how our assump-
tions are being developed.

Expected Investment Return
By return, we mean the compound annual net return we expect over the
next 10 to 20 years. Why not the return we expect over the next year or
two? Because I don™t think anyone can forecast short-term results. Then,
how do we forecast long-term returns?

We can start by studying historical returns, placed in the context of
valuations now and at the beginning of the interval we are measuring.
Large U.S. stocks, for example, have about the most reliable historical data
of any asset class. Ibbotson Associates Yearbook2 goes back to 1926 in
providing the total investment return (including reinvested dividends) on
Standard & Poor™s 500 Index”a good index of the performance of large
U.S. stocks”and on other U.S. securities.
From 1926 through 2004, the S&P 500 compounded 10.4% per year.
That™s impressive, as it includes the Depression, World War II, and the ter-
rible investment climate of the 1970s. Does that mean we should expect
10% per year going forward?
Well, let™s say we have a 20-year time horizon. What is the range of the
S&P™s total annual returns over all 20-year intervals? We ¬nd it varies from
a low of 3% per year for the 1929“1948 interval to a high of 18% per year
for the recent interval of 1980“1999. On a real (in¬‚ation-adjusted) basis,
the range is from a low of 1.6% to a high of 13.6%.
A key question: Should we attribute equal predictive value to all years
of available historical data? Or should we say the world has changed mate-
rially since 19XX, and we should rely mainly on data since then? Remem-
ber, historical data for an asset class (or for a particular investment
manager) is no more useful than its predictive value, and that™s a judgment
we must make.
Also, we should consider adjusting our expectations relative to histori-
cal returns based on our view of whether stocks are priced dearly or
cheaply today. We should recognize, for example, that the phenomenal re-
turns on U.S. stocks for the last 20 years of the twentieth century re¬‚ect (1)
the fact that corporate earnings grew exceptionally fast over that interval
while (2) stock valuations zoomed from a price/earnings ratio of about 8 at
year-end 1979 to about 32 by year-end 1999.
As we study history, we might also consider the truism that total re-
turn must equal dividend yield plus the rate of earnings-per-share growth,
adjusted for change in the price/earnings ratio. Going forward from today,
what growth in long-term GDP (Gross Domestic Product) do we expect for
the U.S. economy”the combination of real GDP plus in¬‚ation? Given that
GDP growth, what growth rate do we expect in corporate earnings? In

Historical returns on the S&P 500 and certain other U.S. asset classes shown sub-
sequently in this chapter are taken or calculated from Ibbotson Associates™ Stocks,
Bonds, Bills and In¬‚ation Yearbook.
Characteristics of an Asset Class

other words, what change do we expect in corporate earnings as a percent-
age of GDP? Finally, what change, if any, do we expect in the market™s
price/earnings ratio?
In the ¬nal analysis, what should we select as our expected return for
large U.S. stocks? No, we can™t look to the gurus of Wall Street to tell us, be-
cause we will ¬nd an impressive guru who will support any expectation we
select. Recognize from the start that any return expectation we select will
almost surely be wrong! A bull™s-eye forecast would be phenomenal luck.
Should we therefore give up? No, because a well-thought-out expecta-
tion should get us in the ballpark. This is true of all asset classes, some of
which do not have clean historical data going back very far. We should ex-
amine whatever data exists and apply our common sense in projecting that
data into the future, and then . . . plan on some serious sensitivity tests.
Our purpose in this book is not to provide all the historical data and try
to apply it but rather to suggest the kinds of questions we should ask about
the relevance of that historical data to our expectations for the future.

Expected Risk
As discussed in Chapter 1, the best measure of risk is the volatility, or stan-
dard deviation, of returns. We can measure the volatility of returns of an
asset class historically. For example, over the 78 years 1926“2003 the total
return on the S&P 500 had a standard deviation of some 20 percentage
points. That means that if the average year™s return was 13%, and if future
returns should be the same, then in roughly two-thirds of the years the
S&P 500™s return should be about 13% ± 20 percentage points, or between
“7% and +33%, and about one-sixth of the years it should be below “7%,
and one-sixth of the years above +33%.
This example also suggests that in some 5% of the years, return should
be beyond two standard deviations, or 13% ± 40 percentage points. That
means below “27% and above +53%.
That™s history. But how do we forecast volatility? Do we project histori-
cal volatility from the last 78 years (some 20 percentage points), or from the
last 20 years (about 17 percentage points), or from some other interval?
Again, no one can give us the answer. We must apply our own common sense.
As might be predictable, cash equivalents have very little volatility,
investment-grade bonds have relatively low volatility, and stocks are ma-
terially more volatile than bonds.
In asset classes where there is little reliable historic information, how
do we assess expected volatility? It is not easy. But it is still worth doing.

Expected Correlation
Again, as indicated in Chapter 1, an understanding of correlations can lead
to the counterintuitive realization that it is better to make a portfolio less
risky by adding a small amount of a risky but uncorrelated security than by
adding a conservative but highly correlated security.
As we diversify, each additional asset class does incrementally less to
lower our aggregate volatility. Given that fact, then why do I advocate us-
ing as many asset classes as possible that have high expected returns?
Mainly because I don™t believe my own correlation estimates. I suspect that
some asset classes we now expect to be highly uncorrelated will become
more closely correlated over time, and vice versa. The larger the number of
diverse asset classes we invest in, and the less correlated their returns, the
more protected we are.
Our task, of course, is to make a reasonable assumption about the cor-
relation for each asset class with every other asset class. For example, if we
work with 15 asset classes, we will need a matrix of 105 correlations!
Where do we get them?
Historical correlation data is available for some asset classes, mainly
through consulting ¬rms at present. For certain asset classes, meaningful
correlation data does not exist. We must make a reasoned guess as we re-
late those asset classes to others for which correlation data is available. Il-
lustrated later in the chapter is a sample table of input assumptions for an
Ef¬cient Frontier, including a correlation matrix”but with only illustrative
assumptions, not necessarily ones you will want to use.
Do you get the idea we are dealing with some soft projections? You are
right. But with proper research and thought, those projections can be good
enough to help us develop reasonably optimal asset allocations.
After all our hard work, we must face the fact that our set of assump-
tions must be wrong. No one has a clear enough crystal ball to get even a
single assumption right. Should we therefore forget about these academic
prognostications? No! There are important ways to deal with this uncer-
tainty, which we shall address later in this chapter.


Well, what asset classes should we consider? All of them. Or at least all as-
set classes that we are competent”or can gain competency”to invest in.
Some of the more obvious asset classes include the following.
Asset Classes

Cash Equivalents
Cash equivalents (which, for short, we shall call “cash”) include Treasury
bills, short-term certi¬cates of deposit, money market mutual funds, and
short-term investment funds (STIFs)”investments that are usually
thought of as riskless, in that their maturity is so short we can hardly lose
any of our principal. If we venture outside of U.S. government securities,
we may take some credit risk, but for our purposes here let™s consider
cash as riskless.
If cash is riskless, then we should expect that cash has the lowest ex-
pected long-term return”and this has been true through the years. Over
the last 79 years, cash has barely returned 1 percentage point more than
the in¬‚ation rate. For certain intervals of years cash hasn™t even returned
the in¬‚ation rate, but over the 10 years 1995“2004 its return averaged
some 11/2 percentage points higher than in¬‚ation.
We might start our expectations with an estimate of the in¬‚ation rate
going forward and then decide what increment over that in¬‚ation rate cash
is likely to return.
And then ask ourselves: If over any long-term interval cash is likely to
provide the lowest return, why should we target any portion of our portfo-
lio to cash? Well, cash is a great tool for market timing, but I feel safe in as-
suming we are not blessed with the gift of prescience.
Many investors keep a portion in cash so that whenever they must
withdraw some money from their fund they can do so without having to
sell a longer-term security at a possibly inopportune time. Withdrawals,
however, occur repeatedly over time. Over the long term, a fund is un-
doubtedly better off keeping cash to zero and selling other securities when-
ever a withdrawal is needed”selling “just in time.” Sometimes, we™ll sell at
the bottom of the market and other times at the top. But over the long
term, we should be well ahead.
In any case, I favor a target allocation of 0% in cash.3

No matter how hard we try, it is dif¬cult to keep cash down to zero. Over the long
term, any amount of cash is a drag on portfolio return. One way to deal with this,
if our fund is large enough and if our cash balances are not too volatile, is to over-
lay our cash balances with very liquid index futures, such as S&P 500 futures. Such
futures “equitize” our cash, effectively converting it into an S&P 500 index fund.

Longer-Term Fixed Income
There are at least six distinct classes of bonds, and we should consider in-
cluding each:

Traditional investment-grade bonds

Long-duration bonds

Non-U.S. bonds from developed markets

High-yield bonds

Emerging markets debt

In¬‚ation-linked bonds

Traditional Bonds Traditional investment-grade bonds come in various
maturities, typically from one year to 30 years, and various levels of credit
risk, each having somewhat different long-term risk and return characteris-
tics. When talking of this asset class, we often talk in terms of the Lehman
Aggregate Bond Index, which attempts to include all investment-grade U.S.
¬xed income securities that are longer in maturity than cash equivalents.
Because the market values of bonds are more volatile than of cash, we
would expect a higher return from bonds, long term. In recent years, the
yield on U.S. bonds has tended to be a couple of percentage points higher
than on cash equivalents. Total returns on bonds during the 79 years
through 2004 averaged almost 3% over the in¬‚ation rate. Historically,
bonds have had a modest annual correlation with stocks.
It is dif¬cult to ¬nd an active manager of traditional investment-grade
U.S. bonds who can add as much as 1 percentage point of excess net return
above his benchmark. The other classes of bonds offer active managers the
opportunity to add a little more excess return above their benchmarks”if
the managers are among the best.

Long-Duration Bonds Unless we think interest rates are going to decline
(usually a gambler™s bet), why would we want to consider investing in
highly volatile long-duration bonds”much less as a replacement for tradi-
tional bonds? One possible reason is that the volatility of a long-duration
bond account can give us more protection against declining interest rates
than a traditional bond account, especially in a climate such as occurred in
the third quarter of 1998, when stock prices collapsed at the same time
that interest rates declined.
For this reason, long-duration bonds reduce our need to allocate as
large a percentage of our portfolio to ¬xed income, which historically has
provided a lower long-term rate of return than equity investments.
Asset Classes

Pension funds have a reason to be especially interested in long-term
bonds. We™ll discuss this in Chapter 10, “What™s Different About Pen-
sion Funds.”

Non-U.S. Bonds (Developed Countries) While the U.S. government and U.S.
corporations are the world™s largest issuers of public debt, government and
corporate bonds are sold to the public in all developed countries of the
world. That spells additional opportunity.
When fully hedged for foreign exchange risk, foreign bonds tend to
have a fairly high correlation with U.S. bonds. Knowledgeable global in-
vestors, however, can ¬nd ways to add value, because interest rate move-
ments across countries are certainly not in perfect synch.
A global bond portfolio that is not hedged provides more diversi¬ca-
tion bene¬t. The difference is volatility in foreign exchange values, which is
largely uncorrelated with the volatility in bonds and stocks.
Perhaps, rather than adding non-U.S. bonds from developed markets
as a separate asset class, the most practical approach may be to allow our
bond manager (or managers) to invest opportunistically anywhere in the
developed world that they believe will strengthen their long-term return.

High-Yield Bonds During the 1980s, high-yield bonds were introduced to
¬nance less creditworthy companies. Known for some years as junk bonds,
they are bonds with a high interest rate, with interest rates 1% to 4%
higher than investment-grade bonds, sometimes much higher yet for bonds
with the lowest credit rating. The higher interest rates are designed to com-
pensate investors for a small percentage of the issuers who statistically can
be predicted to default.
High-yield bonds provided investors with moderately higher long-
term returns than investment-grade bonds, and for the seven years
1992“1998 they did it with roughly the same volatility. Those, however,
were good economic times. During harder economic times, as in 1990
and 2000“2002, many issuers of high-yield bonds defaulted, and prices
of high-yield bonds tumbled.
Until recently, almost all high-yield bonds were issued by U.S. cor-
porations. Now, European companies have begun to issue high-yield
bonds also.

Emerging Markets Debt Some people consider debt issued in the developing
countries of the world simply another facet of high-yield bonds. There ap-
pears to be only a modest correlation, however, between high-yield bonds
and emerging markets debt, because their fundamentals are driven by some-

what different factors. Therefore, I tend to view them separately. Most
emerging markets debt consists of bonds of sovereign countries, but in-
creasingly, bonds of certain private corporations are becoming investable.
Notwithstanding a collapse in prices of emerging markets debt after
Russia defaulted on its bonds in August 1998, emerging markets debt over
the 10 years 1995“2004 delivered double-digit total returns. That™s com-
mon stock territory. If we can stand the volatility with a small portion of
our portfolio, I like emerging markets debt. I think it will provide relatively
strong returns long term, and returns that have a low correlation with
more traditional assets.

Inflation-Linked Bonds These are mainly government bonds that promise a
real return (above the in¬‚ation rate) until maturity. In¬‚ation-linked bonds
were ¬rst introduced by the United Kingdom in the early 1980s. The
United States introduced them in 1997, and they are known here as Trea-
sury In¬‚ation-Protected Securities (TIPS). Other countries that have issued
in¬‚ation-linked bonds include Sweden, Canada, France, Australia, and
New Zealand.
Investors who hold the bonds to maturity have a locked-in real return
of typically 1 to 4% or more, depending on their purchase price. Mean-
while the bonds ¬‚uctuate in value but not normally as much as traditional
bonds. One advantage is that they may be correlated slightly negatively
with traditional bonds”that is, when regular bond prices go up, prices of
in¬‚ation-linked bonds may tend to go down, and vice versa.

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