What we've learned about portfolio construction from the first decade of hedge funds.

Rarely has the development of a diversified
portfolio, which combines traditional assets and hedge fund strategies
in a way that should meet a taxable investor's objectives for both
return and risk, been more important to investors than it is today. In
a world of modest returns on financial assets and an ever closer
correlations between different markets around the globe, the search for
uncorrelated returns has become intense.

This article is divided into two parts and builds on
the insights from our previous articles on performance and risk1,2 in
hedge fund strategies [Financial Advisor, March 2005 and May 2005]. The
first part will develop a general asset allocation framework that
begins by examining only traditional assets. Particular emphasis is
placed on the realization that return distributions are not normally
distributed, and that loss of wealth over a period of time may be more
of a concern to an investor than the volatility of returns from period
to period. We also introduce hedge fund strategies toward the end of
Part I to examine the improvement an investor may be able to achieve by
including such strategies. In Part II, we will delve deeper into the
process to select specific hedge funds to populate one of the hedge
fund strategies identified in part I. While we will emphasize the use
of quantitative tools to assist in the construction of the portfolio,
we acknowledge from practice that portfolio construction is more of an
art than it is a science.

Part I

The Investor's Objective

In any given investment program the first and
perhaps most important step is to determine the investment goal.
Remember that this is not a one-size-fits-all exercise. While
investment goals and objectives are personal, key considerations are
common to most investors. These include a desired rate of return;
quantifying the "pain" associated with economic loss; investment time
horizon; liquidity requirements; and the investor's tax status. Each of
these key considerations must be reviewed, understood and defined
before portfolio design can begin.

For our portfolio construction exercise, we assume the investor:

must pay taxes on the investment portfolio;

has a five-year investment horizon;

will have grave concerns if there is a loss of
portfolio assets of greater than 10% over any time period within the
five-year period;

must be confident that 60% of the value of the portfolio can be liquidated at any time;

requires a 7% to 9% compound return after taxes and fees;

is willing to consider some limited investment in
hedge funds, if a good case can be made and appropriate funds can be
found.

Portfolio construction is largely an art, but as
with any art there are valuable tools of the trade. These include the
use of optimization and stress testing. Key elements of each of these
tools are return distributions and how returns vary over time with each
other, i.e., correlations. As we pointed out in prior articles,3
serious problems are associated with each of these tools. In developing
the portfolio for the hypothetical investor, we will show how these
problems may be addressed to arrive at a solution that has a greater
likelihood of meeting the investor's expectation.

The Analysis

To begin the analysis, we start with performance
data for six traditional asset classes where the asset returns have
been adjusted for ETF (exchange-traded fund) or mutual fund fees for
each asset class. All returns were estimated on an after-tax basis,
assuming 15% capital gains and dividend taxes and a 40% effective tax
rate on current income. A two- to three-year holding period was assumed
for calculating capital gains. The data was collected from January 1,
1990, through December 31, 2003. Figure 1 shows the average annualized
returns and standard deviations of the data used.

To illustrate problems associated with portfolio
optimization using historical mean returns and standard deviations, we
developed an efficient frontier6 using the traditional assets in shown
in Table 1 and the associated correlations. There were no constraints
placed on any of the assets, meaning that the investor could choose any
investment option and weight that investment between 0 and 100%.
Shorting and leverage, however, were not permitted in this exercise.
This efficient frontier is shown in Figure 2 and the associated asset
mix for varying returns in Figure 3.

What Does The Efficient Frontier Suggest?

For starters, it becomes apparent that the high end
of the 7% to 9% after-tax return objective may be difficult to achieve.
To obtain a portfolio with returns of greater than 8% would require an
equity investment in excess of 75%. If that were the case, the standard
deviation of the portfolio would be 11%. This level of risk would imply
that in any given year the portfolio could realize a return of +19% to
-3% two-thirds of the time.7 Furthermore, it is possible that the
returns could range between a gain of 30% and -14% with 95%
probability. Perhaps a "reasonable" portfolio would be one with 60%
S&P and 40% Municipals that has a return of 7.7% and a standard
deviation of 9.0%. A two-standard-deviation downside return would be a
loss of 10.3% with this portfolio. This result would appear to be close
to the low side of the investor's objective. Overall, it does not
appear that the investor's objective can be fully met with traditional
assets. Before we go searching for other assets, however, we will
stress test this solution to see how well the portfolio offering a
return of 7.7% meets other criteria set up by the investor.

The Problem With Traditional Mean-Variance Optimization

As we noted in the earlier articles, mean-variance
optimization is based on the assumption that asset returns are normally
distributed. Figures 4, 5 and 6 show that this is not a good
assumption, even for traditional assets. These charts provide the
histogram of the returns for the Lehman Aggregate Bonds, S&P 500
Equities and Municipal Bonds, and a normal distribution curve that has
the same mean and standard deviation. The exhibits also show the
probability distribution that is the "best fit" for the returns. The
best-fit curves are obviously a much better representation of the
return distribution than the normal curve, when compared to the
histograms. It should be noted that the best-fit curves are negatively
skewed, and have "fat tails."8 The problem with a distribution with fat
tails is the element of surprise. In looking at the exhibits, one may
wonder if the distributions are really that much different. Keeping in
mind that the returns shown are monthly returns, there is 2.5%
probability of a loss of greater than 2.1% for Municipals if the normal
curve is used but a loss of greater than 2.5% if the "best-fit"
distribution is used, or almost 20% greater. The increase in possible
losses for the S&P 500 and the Lehman Aggregate Bonds are 15% and
18% respectively. Thus while the distributions do not appear
dramatically different, if losses are a concern, the difference is
relatively large.

Another constraint with mean-variance optimization
is that it is a single period optimization. Our investor's goal,
however, has a five-year objective and includes not realizing a loss of
10% at any time within the five years. We developed a Monte Carlo9
simulation to test the 7.7% optimized portfolio and evaluate how the
optimized portfolio might perform over the five-year period, with
return patterns that are the best-fit distributions. The simulation
consisted of 1,000 iterations over a random 60-month period. The
portfolio is rebalanced monthly. The simulation preserved the
correlations of the returns and used the best-fit distributions. The
results of the simulation are shown in Figure 7.

One statistic that was captured by the simulation
was the maximum drawdown in any 60-month period. This drawdown could
have been the result of several months of poor performance and was
independent of the calendar, e.g., it could have been over the
year-end. The average of the maximum drawdown over the 1,000 iterations
was 16.6%, but there was one 60-month period out of the 1,000 that had
a drawdown of almost 50%. This is clearly outside of the investor's
objectives. It is interesting to note that the average compound return
was 7.1%-below the investor's objective and less than would have been
expected from the mean-variance optimization, which is a result of the
negative skewness described above and shown in Figures 4, 5 and 6. This
suggests that this portfolio was doomed to disappoint the investor
because it is highly likely to have never returned the expected 7.7%.
The portfolio had negative skewness (greater downside events) and
slight positive excess kurtosis (fat tails indicating performance
events that are outside normal expectations).

Can We Improve The Results?

While the traditional asset portfolio may meet some
of the investor's goals, the drawdown is too large and the returns will
be at the low end of the range. Thus, it would appear to be desirable
to look for other strategies, including hedge funds, which have low
correlations to traditional assets in order to develop a portfolio that
will be more consistent with the investor's objectives.

Hedge funds diversify overall portfolio risk by
generating returns that for the most part have low correlations to
traditional equity and bond indexes. However, before adding other,
noncorrelated strategies like hedge funds to the mix, it is worth
examining a more robust approach to building a more "efficient"
portfolio.

The major objections of traditional mean-variance
optimization techniques include the assumption that returns are
normally distributed and are best viewed as a one-year probabilistic
outcome. To incorporate more realistic factors, we use a simulation
model and optimize the asset mix to minimize the average maximum
drawdown at a given level of return. Figure 8 shows the results of this
optimization approach when we set the target return to 7.1%, which was
the result of the simulation of the original mean-variance
optimization. There were no constraints placed on any asset class for
this optimization.

Even though the compound return is still 7.1%, the
asset allocation indicated has characteristics that are more in line
with the investor's objective. The average maximum drawdown is 11.1%.
The largest drawdown recorded over the 1,000 iterations of the
five-year period is only 30.8%, or almost 20 percentage points less
than the portfolio created using mean-variance optimization. On
average, we are much closer to the investor's objective of no drawdown
in excess of 10%, but must improve because there is still a 5% chance
that the portfolio will have a drawdown greater than 19.3%. The
portfolio has less negative skewness (smaller downside potential with
only slightly larger fat tails). The resulting asset mix changed
significantly, and is mostly comprised of municipals and emerging
market equities and large-cap stocks. As a result of this shift, the
standard deviation of the portfolio is reduced to 7.2%. Clearly, this
illustrates how the use of more representative distributions, which do
not appear dramatically different from normal distributions, can affect
the compositions of the optimum portfolios and can lead to portfolios
that are more responsive to the investor's objective.

Why is the allocation to municipals so high? For a taxable investor,
municipals offer the best risk-weighted, after-tax return. This high
allocation to municipals would be quite different for a nontaxable
entity like a pension fund. Other assets, like emerging markets equity,
help diversify and add return so that the portfolio is closer to
achieving the investor's objective.

Adding Hedge Funds To The Mix

While we are closer to the investor's drawdown
objective, it has not been met and returns are on the low side. If we
include alternative strategies, like hedge funds, it may be possible to
improve the results. The first question we will analyze is which hedge
fund strategies are most complementary.

Keep in mind that the investor exhibited some concern about the use of
hedge funds, but indicated some willingness to include them at a modest
level. The investor's objective also included a requirement to be able
to liquidate 60% of the portfolio at any time. Since most hedge funds
have limited liquidity13, we will include hedge funds in the
optimization process but limit the allocation to 25% of the total and
limit the maximum investment to any one strategy to 10% or less. We
also will set the target return to 8%, the mid-range of the objective,
and optimize to minimize the average maximum drawdown over the
five-year period. The allocation and relevant statistics are shown in
Figure 9.

At the 8% average compound return over the five-year
period, the average maximum drawdown is reduced to 6.3%, which is well
within the investor's objective. The maximum drawdown (19.1%) is still
somewhat above the 10% objective but there is only a 5% chance that the
maximum drawdown will be greater than 10.9%. Thus, it is likely that
this portfolio is close enough to the investor's objective to be
acceptable.

Conclusion For Part I

Actual re-turns are not normally distributed.

While differences between best-fit distributions
and normal distributions appear small, the differences in performance,
drawdowns and portfolio allocations can be large.

The use of simulations using best-fit
distributions can identify potential areas of investor concern and
provide a better method to evaluate the likelihood of meeting the
investor's objectives.

Optimization, combined with simulations, provides
a means to select portfolio allocations that can come closer to meeting
investor expectations.

The inclusion of hedge funds provides an opportunity
to increase returns and reduce risk to the investor. In comparing
Figure 9 to Figure 7 (the simulated results of the optimal portfolio
developed through mean-variance optimization), higher returns are
apparent with significantly lower drawdowns and volatility.

It also is apparent that for the taxable investor, municipals play an important role.

The taxable investor may need an unconventional
asset allocation, but by adding uncorrelated assets like hedge funds,
an investor can achieve better potential results.

Part II

Identification Of Specific Hedge Funds

The hedge fund strategies indicated in Figure 9
include Managed Futures, Event Driven, Long/Short Equity and Macro
Funds. No hedge fund strategy is greater than 10%, and the total hedge
fund allocation is 25%.

Which hedge funds should one consider?

The first step in identifying hedge funds is to use
screening criteria to reduce the field of well over 7,000 funds
contained in hedge fund databases.
The screens used are designed to identify those
funds that appear to have characteristics that suggest they:

have the financial ability to retain staff;

are viable businesses that will remain in existence;

have indications of a risk management process that controls drawdowns and are risk/return efficient;

have returns that are reasonable, but not
necessarily in excess of the investor's objectives for the portfolio;

have product descriptions that suggest a well thought out process and a viable investment philosophy;

are available to U.S. taxpaying investors.

The screens identify around 20 to 30 funds in each
strategy. This is a reasonable number to start the qualitative due
diligence process. Added to this field are funds suggested by the
investor, and others that have been previously evaluated, but may not
be in databases.

Phone calls are made to the marketing contact to
determine if the funds are open, and to get a description of the
investment process, investment staff background and other basic
information to determine if further review is warranted. This step
usually eliminates a third of the identified funds.

Marketing presentations, due diligence questionnaires, fund
prospectuses, financial statements and subscription agreements are
obtained from the remaining funds and are thoroughly reviewed. Internet
searches, including the SEC's records, are also conducted to determine
if there is any relevant information to assist in the decision process.
Information obtained from this document review can provide reason to
eliminate half or more of the remaining candidates.

The next step is to have telephone interviews with
investment staff to develop a greater understanding of the research
process, portfolio construction, and risk management discipline
employed by the funds. The most promising prospects are then visited
for an onsite review.

The onsite visits are used to expand the understanding of the
investment and risk management activities, inspect the facilities and
confirm their existence and to evaluate the interaction of the staff to
determine how well they work together and the likelihood of defections
of major players. Frequently, discussions with the receptionist or new
hires can be as insightful as those with the managing partners.

Selection Of Specific Funds

We now have built a file for each strategy that
includes monthly performance net of fees and taxes, volatility measures
and a correlation matrix, which describes in one number how each fund's
performance varies relative to all other funds.16 A portfolio built
with funds that exhibit low correlations to each other is ideal, as
performance for the overall portfolio will be more predictable over
time with fewer painful surprises.

The remaining candidates for each strategy are evaluated to determine which ones make the "best" strategy portfolio.

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