Morningstar Magazine - June/July 2018 - 70

Strategies

20
0

0
10
20
30
Average
Improvement
in
Asset-Allocation
Fit
EXHIBIT 4
(Equity %)

A Custom Glide Path A retirement plan can create its own glide path based on its
participants' recommended asset allocation.

Individual Participant
Moderate
Morningstar Index:

Conservative

Custom

Equity Exposure
100%
75

50

Average Misﬁt (%)

Conservative
Moderate
Custom

12.2
9.6
5.7

25
0

20
Age

30

40

50

60

70

80

Source: Morningstar.

Quantifying and Contrasting the Benefit of
Different QDIA Options

In E X H I B IT 3 , we used the retirement-managedaccounts engine to arrive at an individualized
asset-allocation recommendation for 10
hypothetical participants as represented by the
blue bubbles. In this case, looking at a
conservative target-date glide path, we can
quantify the average absolute distance
an idealized asset allocation is from the targetdate-fund glide path in question-thus
quantifying the goodness of fit. This process can
be used to compare the goodness of fit of a
wide range of funds and fund families for a given
retirement plan.
demonstrates another potential use
of this type of technique: the creation of a
"best fit" glide path that is customized to a given
retirement plan.

trade-off between a higher-priced investment
solution that fits its participants better
versus a lower-priced investment solution that
does not fit as well?
To answer this question, we need an approach
that can quantify the trade-off between
the difference in fees and the degree to which
a given solution better fits the plan demographics.
Utility theory provides a framework for evaluating
these types of trade-offs and ultimately
determining a cost hurdle that makes the
investor indifferent to two asset-allocation options,
as well as the cost hurdle that makes a
plan sponsor indifferent between competing
QDIA options.

EXHIBIT 4

Incorporating Fees-Utility-Based Framework

So far, we have avoided the complicating subject
of fees. Presumably, if the options all cost
the same, the plan sponsor would always choose
retirement managed accounts-because
each participant would receive an individualized
recommendation. In the real world, the best-fit
option may not always be the least expensive.
How should a plan sponsor balance the

70

Morningstar June/July 2018

Harry Markowitz established the mean-variance
optimization framework, which requires three sets
of inputs: returns, standard deviations, and
pair-wise correlations for the assets in question.
For a given investor, the optimal asset allocation
is the one that maximizes the investor's utility,
where utility is the expected return on the portfolio
minus a calibrated penalty for risk in which
the calibration factor is the implied risk-aversion
coefficient for the participant. Having the ideal
asset allocation results in zero utility loss,
by definition, because it represents the utilitymaximizing asset allocation. An important

assumption that we are making is that with an
individualized retirement managed account
that uses the known information about
a participant, the participant will be assigned to
the ideal asset allocation-his or her personal
utility-maximizing asset allocation.
When we apply this framework, the Morningstar
retirement-managed-accounts engine
solves for the optimal stock/bond asset allocation,
and we treat it as the ideal utility-maximizing
target asset allocation. We can couple
this with capital market assumptions and then
solve for the implied risk-aversion coefficient
that would make the recommended stock/bond
asset allocation the utility-maximizing mix.
Then, using the implied risk-aversion coefficient for
the participant, we can calculate the utility
of the corresponding age-based asset allocation
of the solution in question. Unless the
asset allocation of both the recommended and
alternative solutions are identical, the utility
of the solution being evaluated will be
somewhat lower, allowing us to calculate the
decrease in utility for each participant, which is
equivalent to the fee differential that
would make an investor indifferent to the two
competing solutions.
When a plan moves to a one-size-fits-all mode,
such as a family of target-date funds, most
if not all participants will experience some loss
in utility relative to an ideal, individualized
recommendation. One can calculate the expected
loss in utility for an individual participant,
which, in turn, can be aggregated to calculate the
total expected loss in utility for the entire
plan. This enables plan sponsors to leverage a
widely used technique from economics and
mathematically compare different potential QDIA
options. For example, plan sponsors can
compare the gain in utility associated with the
incremental higher fee of managed accounts
to determine if managed accounts justify
the higher fee. Additionally, plan sponsors can
determine which glide path minimizes expected
utility loss given an individualized assessment
of every plan participant. Likewise, one
can quantify the expected utility differential
between an off-the-shelf glide path versus
a potential custom glide path. Another application
Table of Contents for the Digital Edition of Morningstar Magazine - June/July 2018
