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mum protection for the economic scenarios where we need protection
most and (2) enable us to reduce materially the size of our allocation to
lower-expected-return assets.8
For pension funds, bonds serve a further crucial purpose, which we
shall cover in our ¬nal chapter, “What™s Different About Pension Funds?”

Another approach is to use interest-rate futures combined with market-neutral pro-
grams”programs that have little or no correlation with other investments in our
portfolio. This approach is called Portable Alpha and will be covered in Chapter 5.

This discussion, however, focuses only on one aspect of asset allocation.
Let™s now describe a tool that can be immensely helpful as we approach that
all-important decision about our fund™s Policy Asset Allocation”a tool
known as the “Ef¬cient Frontier.”

The Efficient Frontier
The Ef¬cient Frontier is a computer-generated single portfolio that will
give us the highest expected return for any given level of expected volatility
(the expected standard deviation of annual returns from the portfolio™s av-
erage return). An Ef¬cient Frontier looks like Figure 4.2.
Point A represents a particular portfolio of asset classes that has an ex-
pected volatility of 10% per year. No portfolio of asset classes with the
same expected volatility will give an expected return higher than point A.
Every point on the curve”the “Ef¬cient Frontier””represents a different
portfolio of asset classes that provides the highest expected return at that
level of volatility.
You can see from this graph that at the lowest level of volatility we can
increase the expected rate of return rapidly with little increase in the ex-
pected portfolio volatility. But the higher the expected rate of return, the
more portfolio volatility we must take on to increase still further our ex-


Expected Return


8% 10% 12% 14%
Expected Volatility

FIGURE 4.2 An Ef¬cient Frontier
Putting It All Together

pected rate of return. At some point, we can increase portfolio volatility al-
most without gaining any incremental expected return.
As we consider alternative asset allocations, we should have two

1. We want to move the Ef¬cient Frontier line as high as possible. As
shown by Figure 4.3, the larger the number of diverse asset classes we
include in the optimizer the higher the Ef¬cient Frontier line is likely to
be”and the higher the expected return we can get at any given volatil-
ity level. Note how limited is a portfolio based only on U.S. stocks,
high-grade bonds, and cash equivalents. Note also that all 10 asset
classes in Figure 4.3 are liquid asset classes. The Ef¬cient Frontier
would be higher yet if illiquid asset classes were added.
The Ef¬cient Frontiers in Figure 4.3 would be different, of course,
under different assumptions. But under virtually all reasonable as-
sumptions, the Ef¬cient Frontier based on a larger number of diverse
asset classes would be materially higher than an Ef¬cient Frontier
based on fewer asset classes. Figure 4.4 compares a well-diversi¬ed
portfolio with that of an actual endowment fund. It illustrates the ad-
vantage of diversi¬cation under a range of different assumptions.
2. After moving the Ef¬cient Frontier as high as we can, we then want to
develop a Policy Asset Allocation that will get us as close as possible to
the Ef¬cient Frontier line at our chosen volatility constraint.

------10 Asset Classes: Add inflation-linked bonds, emerging
markets debt, and market neutral programs
Expected Return

“ “ “ “ “7 Asset Classes: Add non-U.S. stocks, emerging
markets stocks, REITs, and high-yield bonds
_______3 Asset Classes: U.S. stocks, bonds, and cash
5% 7% 9% 11% 13% 15% 17%
Expected Volatility

FIGURE 4.3 Alternative Portfolios
The more diverse asset classes we use in our model, the higher the Ef¬cient Frontier.

Increase in Expected Return, B vs. A



Portfolio B “ An alternative portfolio
Portfolio A “ The actual portfolio of an endowment fund
Each represents a different set of assumptions.
“1.50% “1.00% “.50% .00%
Decrease in Expected Volatility, B vs. A

FIGURE 4.4 Sensitivity Tests
Under 13 sets of assumptions, Portfolio B (a more diversi¬ed portfolio) provides
materially higher expected return and lower volatility than Portfolio A (the current
portfolio of an actual endowment fund). The assumptions are combinations of
those used by ¬ve different consultants.

As our adviser inputs his assumptions for the return, volatility, and
correlations of each asset class (see the illustration of input assumptions in
Table 4.2), he should also enter certain constraints. With no constraints,
the optimizer might hypothetically tell us the most ef¬cient portfolio con-
sists of only emerging markets stocks, emerging markets debt, and arbi-
trage programs!
We wouldn™t want more than X% of our portfolio subject to the com-
mon factors that periodically infect prices in the emerging markets. And we
doubt that we could get more than Y% of our portfolio into quality arbitrage
programs. We should go through each of our asset classes and ask ourselves if
we need a constraint for that asset class or for any combination of asset
classes. We also might consider a requirement to have at least Z% of the port-
folio in a particular asset class, such as U.S. stocks. We should limit such con-
straints and requirements, however, to only those cases where we have a
compelling reason. Each such constraint will lower the Ef¬cient Frontier line.
Because any set of assumptions must be wrong, we want our adviser
to run extensive sensitivity tests by calculating Ef¬cient Frontiers based on
a range of assumptions. That way we will eventually home in on asset al-
locations that are robust”that are least sensitive to a range of reasonable
Putting It All Together

assumptions. If there is one set of asset allocations that seems optimal,
what changes in assumptions will make the portfolio suboptimal? What
other asset allocations are just about as good but not as sensitive to
changes in assumptions?
This is all very technical. As a committee member, what is my role in
this Ef¬cient Frontier process?
As committee members, we want to be sure our adviser is using an
Ef¬cient Frontier model. We can ask questions about how he arrived at
his assumptions and why he set constraint levels where he did. We can
ask what alternative sets of assumptions he used and what alternative
asset allocations seemed about as good as others under his different
Use of Ef¬cient Frontier models entails a lot of effort. Many invest-
ment funds decide their Policy Asset Allocations without going through the
Ef¬cient Frontier exercise. But their asset allocations imply certain assump-
tions for the return, volatility, and correlation of each asset class, and the
committee hasn™t identi¬ed what those assumptions are.

An Even Better Approach to Efficient Frontier
Standard Ef¬cient Frontier computer models give us the most probable re-
sult of any particular asset allocation. A more sophisticated Ef¬cient Fron-
tier model, called an Asset/Liability study, uses a Monte Carlo system of
500 or more simulations to give us the range of expected results from each
asset allocation”the probability, for example, that in X years time, asset
allocation would provide a return higher than Y% (our minimum thresh-
old of pain).
Asset/Liability studies are particularly important for pension funds, as
the present value of pension liabilities ¬‚uctuates each year as interest rates
¬‚uctuate. We will discuss this in more detail in Chapter 10.
But a Monte Carlo simulation can also be useful to endowment funds
and foundations. Such simulations can analyze the trade-offs among (a)
the highest expected rate of return, (b) the probability of the sponsor suf-
fering reduced income from the endowment fund, and (c) the probability
of the endowment fund not maintaining its purchasing power (not keeping
up with in¬‚ation) through the years.
A Monte Carlo approach, of course, is more expensive and more
complex than the standard Ef¬cient Frontier model. For many endow-
ment funds and foundations, the standard Ef¬cient Frontier model may
be adequate.

TABLE 4.2 Sample Input: Long-Term Assumptions for Ef¬cient Frontier

Common Stocks Fixed Income Other Assets
Expected Expected
Compound Annual U.S. 25- High- Emerging Core Private
Annual Standard Large Small Emerging Cash U.S. Non-U.S. Year Yield Mkt. Real Aggressive Timberland Private Energy Distressed Arbitrage
Return Deviation U.S. U.S. Non-U.S. Markets Equiv. Bonds Bonds Zeros Bonds Debt Estate RE Funds Energy Funds Securities Programs

Common Stocks
Large U.S.
stocks 7.5% 16% 1.00 .70 .60 .40 “.10 .20 .10 .20 .50 .40 .30 .20 .00 .00 .50 .50 .25
Small U.S.
stocks 8.5 19 .70 1.00 .50 .40 “.10 .10 .10 .10 .60 .50 .30 .20 .00 .00 .70 .70 .10
markets 7.5 19 .60 .50 1.00 .40 .00 .10 .10 .10 .30 .20 .20 .10 .00 .00 .50 .50 .10
stocks 9.5 30 .40 .40 .40 1.00 .00 .10 .10 .10 .20 .50 .20 .00 .20 .20 .10 .10 .00
Fixed Income
U.S. cash
equivalents 5.0 3 “.10 “.10 .00 .00 1.00 .20 .10 .20 .00 .00 .20 .20 .00 .00 .00 .00 .10
U.S. high-
bonds 6.0 8 .20 .10 .10 .10 .20 1.00 .80 .80 .40 .40 .00 .10 .10 .00 .20 .10 .10
markets 6.0 10 .10 .10 .10 .10 .10 .80 1.00 .80 .40 .40 .00 .00 .10 .00 .10 .00 .10
bonds 6.0 32 .20 .10 .10 .10 .20 .80 .80 1.00 .40 .40 .00 .10 .10 .00 .20 .10 .10
bonds 7.5 12 .50 .60 .30 .20 .00 .40 .40 .40 1.00 .40 .10 .00 .10 .10 .10 .30 .00
debt 8.0 20 .40 .50 .20 .50 .00 .40 .40 .40 .40 1.00 .00 .00 .10 .10 .10 .10 .00
Other Assets
Core real
estate 7.5 10 .30 .30 .20 .20 .20 .00 .00 .00 .10 .00 1.00 .80 .00 .00 .20 .20 .00
real estate 9.0 15 .20 .20 .10 .00 .20 .10 .00 .10 .00 .00 .80 1.00 .00 .00 .20 .20 .00
funds 9.0 15 .00 .00 .00 .20 .00 .10 .10 .10 .10 .10 .00 .00 1.00 .30 “.10 “.10 .00
properties 9.0 20 .00 .00 .00 .20 .00 .00 .00 .00 .10 .10 .00 .00 .30 1.00 “.10 “.10 .30
funds* 10.0 25 .50 .70 .50 .10 .00 .20 .10 .20 .10 .10 .20 .20 “.10 “.10 1.00 .30 .00
securities 9.0 20 .50 .70 .50 .10 .00 .10 .00 .10 .30 .10 .20 .20 “.10 “.10 .30 1.00 .00
programs 9.2 11 .25 .10 .10 .00 .10 .10 .10 .10 .00 .00 .00 .00 .00 .00 .00 .00 1.00

*Includes venture capital, LBO funds, and buy-in funds, both U.S. and non-U.S. Some of these subclasses may not be highly correlated with one another, so it might be advantageous to treat them separately.

A Secondary Benefit of Diversification
Gaining the bene¬ts of diversi¬cation is what this chapter is all about.
Everyone understands that diversi¬cation reduces the aggregate volatility
of our portfolio. Fewer people recognize that, in addition, diversi¬cation
can actually add a little to our expected return! How?
The Ef¬cient Frontier model lets us use our expected returns, standard
deviations, and correlations for each asset class to project our portfolio™s
expected return and standard deviation over the next 10 years. We shall
see that the expected volatility of the portfolio can be materially lower
than the weighted average volatilities of each of the asset classes, and the
expected return of the portfolio can be slightly higher.
Table 4.3 shows a portfolio with an extremely volatile allocation to
very long duration bonds. Don™t get hung up on the particular assumptions
of expected return and expected standard deviation for each asset class.
Note instead, at the bottom of the table, the weighted average expected
standard deviation is 21.0% whereas the expected standard deviation for
the overall portfolio, thanks to diversi¬cation, is only 12.5%.
Note also that the weighted average expected return from our 13 asset
classes is 8.3%, whereas the expected return on the overall portfolio is
9.6%.9 That™s real diversi¬cation bene¬t!
Of course, our assumptions are wrong. No such assumptions can be
right. But change them as we will, the expected volatility and return for the
overall portfolio will still be dramatically better than the weighted average
volatility and return of our 13 individual asset classes.

A Drawback of Diversification
The kind of broadly diversi¬ed portfolio this chapter is leading us to
should provide strong long-term returns. But over shorter intervals it may
be greatly out of step with results of our peer investment funds, which typ-
ically invest predominantly in large U.S. stocks. In 1997“1998, for exam-
ple, the only strong asset class was large U.S. stocks, which returned over
30%, while returns on a broadly diversi¬ed portfolio would have been in
the lower teens. If we are to invest con¬dently in a broadly diversi¬ed port-
folio, we must avoid undue concern about returns achieved by our peers.

The calculation assumes that the portfolio will be annually rebalanced to this Pol-
icy Asset Allocation. Rebalancing can add a little to the expected return of the over-
all portfolio.
In Short

TABLE 4.3 Illustration of Diversi¬cation Bene¬t
Expected Expected
Percent Compound Standard
Allocation Asset Class Return Deviation

15% Large U.S. stocks 8.0% 17%
11% Small U.S. stocks 8.5 19
12% Non-U.S. stocks, developed markets 8.0 19
8% Emerging markets stocks 9.5 30
15% 25-year zero-coupon bonds 6.6 32
2.5% High-yield bonds 8.0 12
3.5% Emerging markets debt 8.2 20
7.5% Value-added real estate 9.0 15
2.5% Timberland funds 9.0 15
2% Private energy properties 9.0 20
9% Private equity funds 9.3 25
4% Distressed securities 9.0 11
8% Arbitrage programs 9.2 11
Weighted average 8.3% 21.0%
Overall portfolio 9.6 12.5

Returns on a broadly diversi¬ed portfolio in the ¬rst few years of the
twenty-¬rst century could have enabled a broadly diversi¬ed portfolio to
materially outperform typical peer portfolios over longer intervals includ-
ing 1997“1998.


We should familiarize ourselves with the full range of asset classes in

which our portfolio might invest. This range far exceeds traditional
ones of domestic stocks, bonds, and cash.
To the extent we make use of all the attractive asset classes we can,

such diversi¬cation can meaningfully reduce our portfolio™s volatility
and can even ratchet up our expected return.
Use of an Ef¬cient Frontier model can help us develop an asset alloca-

tion that is likely to give us the best return at any given level of risk.

Alternative Asset Classes

hen we talk about investing, we all too quickly think of stocks and
W bonds. We fail to think about many other kinds of viable”and valu-
able”alternative asset classes.
An alternative asset class might be considered any asset class that our
decision makers have not considered before. For some, any stocks but the
largest, most prestigious U.S. stocks might be an alternative asset class. For
purposes of this chapter, however, we shall de¬ne alternative asset classes as
anything other than marketable stocks, bonds, and cash equivalents.
Under that de¬nition, the Commonfund Benchmark Study found in a
survey of 563 U.S. educational endowment funds that 23% of their aggre-
gate assets in ¬scal 2000 was allocated to alternative investments.
We shall divide this chapter between two kinds of alternative assets”
(a) liquid investments, ones that are often lumped together under the catch-
all term “hedge funds,” and (b) illiquid investments.

As an investment committee member, do I have to know all about
these arcane alternative investments?

No, but I should at least be familiar with what they are so that I can recog-
nize them if our adviser recommends an investment in one of them. We
have included discussion about each of these kinds of investments in this
chapter also as a reference whenever one of these investments comes up for
discussion at an investment committee meeting.


A valuable addition to most portfolios can be market neutral asset
classes”ones that have little or no correlation with stocks and bonds. They


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