Morningstar Magazine - February/March 2014 - 43

Exhibit 1 Improving Total Portfolio Health
Asset-Only Approach
Value of Liabilities vs. Value of Assets

Time

Portfolio Health / Funding Costs

Time

Liability-Relative Approach
Value of Liabilities vs. Value of Assets

Portfolio Health / Funding Costs

Time

is, a portfolio containing both assets
and liabilities and is referred to as a "surplus
standard deviation."
Historical Analysis

Using the actual historical monthly returns of
our set of 20 asset classes, we can determine
the asset allocations that would have been
optimal in the past. Since we can each now
view the past with perfect hindsight, there is
no need to perform any type of resampling on
the historical data. Simply put, the past was
what it was. We are not suggesting with our
historical analysis that what has happened over
this 20-year historical period will happen again
in the future. We are simply providing
information about what would have been the
optimal portfolio given different asset-allocation approaches and potential liabilities.

Time

and non-U.S. commercial real estate. Second,
we have included at least one U.S. component
and one non-U.S. component for each of
the three broad asset classes included in the
study-stocks, bonds, and real estate.
Doing so enables us to investigate whether
liabilityrelative optimization leads to a greater
U.S. home bias than traditional asset-only
optimization. Third, we have split U.S. bonds,
which would often be represented by the
Barclays U.S. Aggregate Bond Index, into seven
subasset classes: short-term government,
short-term nongovernment, intermediate-term
government, intermediate-term nongovernment,
long-term government, long-term nongovernment, and mortgage-backed securities.
This granular representation allows us to study
the impact of liability-relative optimization
on the credit and duration characteristics of the
fixed-income allocations.
Optimizations

We use a single "liability model" in this
article: 50% TIPS, 30% nominal U.S. bonds,
10% equities, and 10% commercial real
estate. Our tool for comparing the efficient
asset allocations that result from the different

optimizations is an "efficient frontier area
graph." The graphs display the asset
allocations of the efficient frontier across the
entire risk spectrum. The vertical cross section
on the left side of the graph corresponds
with the minimum risk asset allocation,
while the vertical cross section on the right
side corresponds with the maximum return
asset allocation.
To allow for better comparison, the results
between the two optimization types are
contrasted using return as the reference point
on the horizontal axis, meaning that the optimal
allocation is included in the area chart given
that target return. For some very low return
targets, there are more efficient portfolios
(i.e., portfolios with a higher return for a given
level of risk). If such a portfolio exists, it is
the assumed allocation for that target return.
For the asset-only asset-allocation area graph,
risk is measured by the standard deviation
of the returns of the asset-only portfolios.
For the liability-relative asset-allocation area
graphs, risk is measured by the standard
deviation of returns of the total portfolio-that

The historical optimization results are included
in Exhibits 2 and 3. Exhibit 2 includes
the historical asset-only MVO optimization.
Exhibit 3 includes the results of the liabilityrelative optimization.
Visually, the two asset-allocation area
graphs share some similarities, although there
are considerable differences. Regardless
of the optimization approach, U.S. long
government bonds and U.S. real estate each
played large roles. This can be attributed to the
superior risk-adjusted returns of these
two asset classes over our historical test
period (1993-2012). With respect to the
liability-relative optimizations U.S. real estate
clearly had a dominant role, especially in the
more aggressive asset allocations. We also
see allocation to U.S. long government bonds.
If an investor has a high tolerance for risk
relative to the liability, the asset-only and
liability-relative optimizations led the investor
to increasingly similar asset allocations at
higher levels of risk. In practice, investors
during their preretirement wealth accumulation
periods rarely use liability-relative optimization
to develop their asset allocations. However,
when investors reach retirement and no longer

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