Morningstar Magazine - June/July 2018 - 59

EXHIBIT 1

reason we don't use a holdings-based approach.
A factor-based model allows us to better
decompose risk and return into sources related
to market exposure, style, and security selection
in the same model.

1.0

Market Risk Dominates On an absolute basis, market exposure is by far the largest
driver of risk within a given target-date fund.
Average Contributions to Time-Series Variance for Target-Date-Fund Vintages

Market

Style

Selection
100%

Also, returns-based style exposures reflect
a historical "average" over the 0.8
estimation period,
and these averages may differ from current
style weights if the portfolio manager has recently
0.6
made significant changes to the underlying
portfolio exposures. Therefore, we believe this
0.4
approach is more useful for historical
benchmarking purposes rather than reflecting the
current risks of a target-date fund.
0.2
To better capture the various style
0.0exposures
that exist across target-date series, our regression
model expands on the five factors introduced
by Fama and French (1993), which are
market, small, value, term (or duration), and
quality. To estimate the market (or equity) exposure,
we include both a market variable as well
as a (linear) market interaction variable to capture
potential changes in equity allocations over
the regression period (to capture the glide path).
Our estimated style return factors were
value, small, international equity, emergingmarkets equity, REITs, commodities, high yield,
duration, TIPS, and international bonds.
The final return component, selection, is
the intercept of the regression plus the residual
term. The intercept is often called alpha
because it represents the average of the portion
of returns not explained by the independent
variables (the equity and style exposures in this
regression). A variety of items drive the
selection return component, such as market timing,
the implementation of investments (for
example, whether it is an actively managed
investment), more exotic styles not captured in
factor regression (like illiquidity), and others.
The factor-regression model does a relatively
good job describing the historical return series,
with an average adjusted R-squared of
approximately 98% across the target-date funds
included in the analysis. The period for the
analysis was the 36 months ending Dec. 31,
2016. We used a short estimation period to capture

80
60
40
20
0
2050

2045

2040

2035

2030

2025

2020

2015

Retirement

Source: Morningstar.

the more recent exposures of the funds as
well as increase the opportunity set of target-date
series. There were a total of 438 unique
target-date mutual funds and 47 fund series with
data from Morningstar Direct. Considerably
more target-date series exist (such as collective
trusts); however, we focused on mutual fund
series in this study.
Decompositions of Variance

We used the factor model to decompose the
variance of target-date-fund returns and,
thus, better understand their risks. To do this, we
decomposed the variance of the returns
on each fund based on the three components:
market, style, and selection. We averaged
the contributions of the time-series variances
within each target-date-fund vintage. Additional
details regarding this model can be found
in Blanchett and Kaplan (2018), the paper upon
which this article is based.
E X H I BIT 1 shows the results, which suggest that
market exposure is by far the most important driver
of risk within a given target-date fund on an
absolute basis. This finding is not surprising, given
the past research of Brinson, Hood, and Beebower
(1986), Ibbotson and Kaplan (2000), and others.

On an absolute basis, the equity decision will
drive considerably more risk than style or selection
decisions given the pure risks associated with
investing in equities. The market-risk contribution
decreases as target-date funds become more
conservative closer to retirement.
While information on the absolute risks associated
with target-date-fund vintages is interesting,
it does not really provide any context as to
how the relative risks differ within a given vintage.
For example, if all target-date funds had
the same glide path, the time-series variance
decompositions shown in EXHIBIT 1 would
still suggest that market risk is the largest risk
driver for the funds, despite the fact that all of the
actual return differences would come from
other factors. Therefore, we are more interested
in the cross-sectional variation in returns given
the differences (and similarities) among
target-date-fund providers; this should provide
some context regarding what will likely drive the
series performance differences.
To do this, we first calculate the log-compound
annual return for the three components of
log-excess return. Because compound log-returns
are averages, the log-compound annual return

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59


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