Saving for retirement while having more nights with
peaceful sleep: Comparison of lifecycle and lifestyle

strategies from expected utility perspective

Rosita P. Changa, David Huntera, Qianqiu Liua,*, Helen Saarb

aShidler College of Business, University of Hawaii at Manoa, 2404 Maile Way, Honolulu, HI 96822, USA
bUdvar-Hazy School of Business, Dixie State University, 225 South 700 East, St. George, UT 84770, USA

Abstract

We evaluate the fit of target-date funds (TDFs) as the main retirement savings instrument for the
utility-maximizing investor who becomes more risk averse as she gets older. Using bootstrapping
simulations, we show that TDFs can provide higher expected utility than the alternative lifestyle
strategies. With loss aversion incorporated in the model, we still find that the optimal lifecycle strategy
over time leads to higher expected utility than the best lifestyle strategy. Therefore, TDFs are
preferable to the utility-maximizing investor. However, lifecycle strategies are not one-size-fits-all
solution and investor’s risk tolerance has to be considered when selecting TDF funds. © 2014
Academy of Financial Services. All rights reserved.

Jel classification: G11; G23; D14

Keywords: Target-date funds; Life cycle investing; Retirement saving

1. Introduction

Since being endorsed by the Department of Labor, target-date funds (TDFs) have grown
in both size and popularity.1 According to the Investment Company Institute (2013), at the
end of 2012 the total assets of TDFs were $481 billion, which is about 9.5% of the total assets
of defined contribution plans. This represents a significant increase since 2007, when TDFs
only had a 4.2% share of defined contribution plans. With this growing market share, it is

* Corresponding author. Tel.: �1-808-956-8736; fax: �1-808-956-9887.
E-mail address: qianqiu@hawaii.edu (Q. Liu)

Financial Services Review 23 (2014) 169–188

1057-0810/14/$ – see front matter © 2014 Academy of Financial Services. All rights reserved.



important to verify the central tenet of TDFs: investors should gradually diminish the
importance of risky assets in their retirement portfolio returns over time. Moreover, it is
essential to establish if the current variety of TDF offerings satisfy the risk preferences of all
individual investors. If not, individual investors and financial advisors need to be aware of
this, so that they can evaluate how to alter the portfolios properly to match their risk profiles
and maximize their utilities.

TDFs are distinguishable by both the target retirement date and a glide path, which is
defined as the specific strategy that decreases the portfolio’s risky asset allocation throughout
its accumulation period.2 Instead of TDFs, an investor could alternatively invest in lifestyle
funds that hold equity allocations fixed over time. The superiority of decreasing equity
allocations over holding them fixed has been questioned for a long time, even before the
emergence of TDFs. Many financial planners have advocated that the equity weighting in an
individual investor’s portfolio should be inversely related to the investor’s age. The most
common rule of thumb is that the percentage of wealth invested in stocks should be equal to
100 minus the investor’s age (Ameriks and Zeldes, 2004). Following this rule an investor
who is 45 years old should have no more than 55% of her wealth invested in stocks.
Academic literature refers to this idea as the lifecycle investment hypothesis (Bakshi and
Chen, 1994).

Although financial planners seem to generally agree with decreasing risky allocations over
time, the academic support for this argument has been less straightforward. We do know that
stocks are not as risky over a long investment horizon (Bali, Demirtas, Levy, and Wolf, 2009;
Malkiel, 2011), and that stocks are essential to accumulate funds for different financial goals
(Samuelson, 1989; Dynan, Skinner, and Zeldes, 2002). We also know that younger employ-
ees are endowed with future labor income that will help them recover from potential
investment losses if they earn poor returns from risky investments, and likewise, that all
investors have desire to attain high terminal values at the end of their investment horizon
(Bodie, Merton, and Samuelson, 1992; Jagannathan and Kocherlakota, 1996). Our findings
add one more reason to this list: as an investor’s risk aversion increases with age, the equity
allocation in her portfolio needs to decrease to remain optimal for the utility-maximizing
investor.

An investor’s risk aversion is directly related to her utility, which represents the satisfac-
tion that the investor gets from her consumption of goods or services. Unlike returns on
investments or the terminal wealth, utility takes into account the cost of reaching monetary
goals; such as an investor’s sleepless nights that are attributable to taking too much risk.
Keeping too much wealth in risky assets when the investor’s risk tolerance is low might lead
to lower expected utility despite the potential large dollar amount that could be earned by
doing so.

Experts in different fields, such as psychology, economics, finance, and management,
among others, have conducted research on demographics of individual risk aversion with
data from many countries. They have determined an individual’s risk aversion with: analysis
of actual holdings of risky assets (see, for instance, Morin and Suarez, 1983; Bakshi and
Chen, 1994; Pålsson, 1996; Agnew, Balduzzi, and Sundén, 2003; and Gibson, Michayluk,
and Van de Venter, 2013); experimental studies looking at the participant’s choice between
risky alternatives, and studies that involve monitoring brain activity during decision-making

170 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



that involves risk (Deakin, Aitken, Robbins, and Bahakian, 2004; Lee, Leung, Fox, and Gao,
2007). In general, these studies support the lifecycle risk aversion hypothesis. Specifically,
they provide evidence that the Arrow-Pratt measure of relative risk aversion increases with
age, and older investors hold lower proportion of risky assets in their total wealth.3

In this article we use expected utility over different accumulation periods to compare
differences between lifecycle and lifestyle strategies whereas assuming that investors are
utility maximizers.4 We run simulations with a range of portfolio weights on stocks and
bonds for both lifecycle and lifestyle strategies, with a range of representative investors with
different risk aversion characteristics. Our investigation includes portfolio strategies that are
more common among the funds offered by fund families and the best performing strategies.
We find that for the investor whose risk aversion increases as she gets older, the lifecycle
portfolio strategies lead to higher expected utility than strategies that keep equity allocation
fixed over the whole accumulation period. Prior studies in the field of behavioral finance have
concluded that investors have different attitude towards downside risk and are more sensitive
to the negative changes to their wealth (Kahneman and Tversky, 1979). We therefore
incorporate the concept of loss aversion into the expected utility model. The results find
further evidence that an investment strategy that decreases the weight of risky assets in the
portfolio as the target retirement date nears, leads to higher expected utility than that of the
best lifestyle strategy and is, therefore, preferable to the utility-maximizing investor.

It is also important to remember that not all TDFs with the same target date are the same.
Balduzzi and Reuter (2012) find increased heterogeneity among the TDFs offered in the
market and conclude that this differentiation can lead to varying levels of performance and
risk. Idzorek (2009) stresses that it is important to look beyond the target date and evaluate
the fund strategy in terms of investors’ risk preference and risk capacity. The Morningstar
Industry Survey (2009) reports that in 2008 the equity allocations for 2010 TDFs range from
26% to 72%. Because of this wide difference in glide paths, we consider a variety of lifecycle
strategies, including different glide path lengths, gentle and steep descent glide paths (also
referred to as glide paths with kink), as well as aggressive and conservative glide paths in our
analysis.

As the popularity of TDFs increases, there is an emerging research on this topic in recent
years. Studies have been both critical of the lifecycle model as well as finding support for the
suitability of TDF strategy. The main focus in most of these studies has been on the
accumulated wealth by the target retirement year and the appropriateness of the asset
allocation (see, for instance, Bodie and Treussard, 2007; Schleef and Eisinger, 2007; Basu
and Drew, 2009; Branch and Qiu, 2011). Spitzer and Singh (2008, 2011) analyze the
performance of lifecycle strategies both during accumulation period and during retirement,
and find that TDF strategies underperform the lifestyle strategies and are not as safe as
implied. Liu, Chang, De Jong, and Robinson (2011) evaluate the performance of the two
lifecycle funds with gentle and steep descent glide paths and seven lifestyle funds throughout
accumulation and withdrawal phases examining the total accumulated wealth at the retire-
ment date. They conclude that lifecycle strategies are beneficial to the investor, especially
during the withdrawal phase. Pang and Warshawsky (2011) find that lifecycle strategies are
less risky than comparable balanced strategies and are proper for investors who wish to
protect their accumulated funds. Recent article by Lipton and Kish (2011) finds that lifecycle

171R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



strategies fail to reach the benchmarks, and there is little uniformity in allocation and timing
among the TDF families. Pfau (2010, 2011) studies the utility from retirement savings by
using standard constant relative risk-aversion utility function. He focuses on four different
lifecycle strategies and compares them to 11 lifestyle strategies, and finds that investors with
moderate risk aversion will reach higher expected utility from investing their retirement
savings in TDF strategy than fixed asset allocation strategy. This article extends the existing
literature by incorporating investor’s increasing risk aversion and loss aversion into the
expected utility framework introduced in Pfau (2010, 2011). We also include in our analysis
a wider range of real-world lifecycle and lifestyle strategies and examine the lifecycle
strategy with the highest expected utility in theory from bootstrapping simulations. Our
results suggest that for the representative investor there always exists a TDF strategy that
generates higher lifetime utility than those from the conventional lifestyle strategies. We also
find that TDFs are not one-size-fits-all solution. Although many TDF strategies already exist
in the market, they may not be optimal to utility-maximizing investors. Investors who are less
risk tolerant need a TDF strategy that starts at lower levels of equity in the portfolio.
Financial advisers and plan sponsors should take into account the risk tolerance profiles of
individual investors to make sure the chosen TDF strategy is a good fit.

2. Data and methodology

2.1. Mean-variance utility model

The objective of this article is to evaluate the accumulation period utility of investors with
similar, but uniquely different perceptions about risk from different portfolio strategies. Our
first analysis assumes that the investor’s risk aversion increases as she gets older. In the
second model we also assume that the investor becomes more risk averse as she experiences
losses. Based on these assumptions we look at how the change in risk aversion over the
accumulation period and the portfolio composition affect the investor’s expected utility.
More specifically, do lifecycle strategies yield higher expected utility compared with lifestyle
strategies for the utility-maximizing investor who becomes more risk averse as she gets
older?

We use the expected utility in the accumulation period to compare the differences between
lifecycle and lifestyle strategies for a representative investor who becomes less risk tolerant
as she gets older. At any month t, we express the utility of the representative investor using
the mean-variance model adopted by Friend and Blume (1975):

Ut � E�Rp,t� �
1

2
At�p,t

2 (1)

Where Rp,t,�p,t are the return and variance of the portfolio that the investor holds, and At

is Arrow and Pratt’s measure of relative risk aversion at month t.5 This mean-variance model
can be motivated by assuming quadratic utility for arbitrary distributions, or assuming that
the return of the risky portfolio is normally distributed for arbitrary preferences (Huang and

172 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



Litzenberger, 1988). We calculate monthly utilities for the representative investor with
different scales of risk aversion.

Many articles have studied the value of the risk aversion coefficient using theoretical
models and experimental frameworks, resulting in a wide range of results. The majority of
the studies conclude that the value of a relative risk aversion coefficient is somewhere
between 0 and 5, and 2 to 4 for a typical investor. For example, Friend and Blume (1975)
estimate that a coefficient of relative risk aversion is about 2 assuming stock returns are the
only stochastic component of wealth. Grossman and Shiller (1981) find the coefficient of
relative risk aversion has to be at least 4 to explain the variability in stock prices. Pålsson
(1996) finds the range for the coefficient of relative risk aversion is between 2 and 4.

In our analysis we assume that for the representative investor the risk aversion level starts
from zero to 2 at the beginning of the accumulation period, and ends between 4 and 6 at the
target retirement year.6 The expected utility for all these different risk aversion ranges is
calculated for the finite number of portfolio strategies based on equity/bond mix. The
expected utility for the whole accumulation period (e.g., 40 years from age 25 to age 65) is
defined as the present value of all monthly expected utilities:

E�U� � �
t�1

T

�t�E(Rp,t) �
1

2
At�p,t

2 � (2)

Where � is the discount factor, T is the length of accumulation period in months, and t
stands for a specific month. We use a discount factor of 0.99.7

In this expected utility model we assume the investor’s relative risk aversion increases
over her lifetime. We assume that the change in risk aversion is linear, but for robustness we
also examine cases where the investor’s risk aversion stays constant for a certain period (e.g.,
first 10 years) and starts increasing closer to the target retirement year.

2.2. Mean-variance utility model with loss aversion

Behavioral finance studies have shown that investors are loss averse, meaning they are more
sensitive to the negative changes to their wealth than gains (Thaler, Tversky, Kahneman, and
Schwartz, 1997). In the case of loss aversion, utility function is steeper for losses than gains. In
the second model we incorporate the concept of loss aversion into the original mean-variance
utility model. We add to the expected utility function the loss aversion coefficient, �, which
increases the investor’s risk aversion when the prior period’s portfolio return was negative. The
value of the loss aversion coefficient, �, is determined based on the realized portfolio return in the
previous month. Following Tversky and Kahneman (1992), we assume this parameter to be equal
to 2.25 when the portfolio return was negative in the previous month.

With the loss aversion coefficient the accumulation period expected utility function is
expressed as follows,

E�U� � �
t�1

T

�t�E(Rp,t) �
1

2
At�t�p,t

2 � (3)

173R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



Where

�t � � 1 when Rp,t�1
s � 0

2.25 when Rp,t�1
s � 0 (4)

RS
p,t-1 stands for the portfolio return for the month t � 1. If during the previous month the

portfolio return was negative, the investor’s risk aversion will increase 2.25 times next
month. In the case of a positive portfolio return, the investor’s risk aversion does not deviate
from the regular risk aversion that the investor normally has.

2.3. Return data and simulation

Expected portfolio return is calculated based on the portfolio mix for each strategy at the
respective accumulation period. The lifecycle portfolios follow different glide path strategies
that are characterized by the beginning equity allocation, ending equity allocation, and the
time point when the equity allocation starts to decrease in the portfolio (e.g., for the first 10
years the weight of equity is kept at the maximum creating a kink in the glide path). Based
on these parameters, the portfolio allocations of lifecycle strategies change each year by
decreasing the equity in equal increments but stay the same within the year.8 Lifestyle
strategies keep the equity allocation constant over the entire accumulation period. The
monthly mean return of the portfolio for each strategy is calculated as follows:

E�Rp,t� � wbond,t � R� bond � weq,t � R� eq (5)

Where wbond,t and weq,t are the weights on bond and equity in the portfolio at month t,
respectively. R� bond is the mean return of the bond and R� eq is the mean return of diversified
equity portfolio. The portfolio variance for each strategy is calculated for each period as
follows:

�t
2�Rp,t� � wbond,t

2 �� bond
2 � weq,t

2 �� eq
2 � 2wbond,tweq,t�� bond�� eq	bond,eq (6)

Where 	 is the correlation between the returns of the equity portfolio and the returns of
the fixed income portfolio. In the simulations we use a diversified equity portfolio for equity
allocation with 45% invested in the S&P 500 Index, 30% invested in the Russell 2000 Index,
and 25% invested in the MSCI EAFE Index, following Liu, Chang, De Jong, and Robinson
(2009). For the fixed income holding we use a 10-year U.S. Treasury bond. The monthly
return data for equity indices and Treasury bonds is retrieved from CRSP and Datastream.
The sample period is from January 1970 to December 2010. Table 1 shows the descriptive
statistics for the three equity indices: the S&P 500 Index, the Russell 2000 Index, and the
MSCI EAFE Index, the 10 year U.S. Treasury Bonds, and the diversified equity portfolio.

2.4. TDFs and their glide paths

The glide path of the TDF is characterized by two attributes: length of the glide path and
change in the asset allocation over the fund lifetime. As Balduzzi and Reuter (2012) note, the
fund families try to differentiate themselves from other TDFs there are many different glide

174 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



paths and asset allocation strategies in the market. Table 2 summarizes the characteristics of
glide paths offered by fund families collected from the prospectus of individual TDFs as of
September 2012.

As of September 2012, there were 230 TDFs with 45 fund families sponsoring these
funds. Most TDFs are founded 40 years before the target year with five year increments. The
most common beginning equity level among the TDFs offered currently in the market is 90%
equity. The highest level of beginning equity in the glide path is 100%. On average the TDFs
reach the level of 40% to 45% equity by the target year. The minimum level of equity at the
target year is 20%. The most common combination is the glide path from 90% equity
allocation 40 years before the target year and 50% equity at target year. Five fund families
follow this glide path strategy with their TDFs. The next most common combinations are
90% to 40%, 90% to 30%, and 90% to 20% equity. Among the more conservative strategies

Table 1 Descriptive statistics for monthly returns for assets used in simulated strategies for the period from
January 1970 to December 2010

10-year T-bond S&P 500 Russell 2000 MSCI EAFE Diversified
equity portfolio

Mean 0.00689 0.00896 0.00908 0.00755 0.00864
Median 0.00595 0.01202 0.01308 0.00978 0.01187
Standard deviation 0.02357 0.04555 0.06392 0.05018 0.04417
Sample variance 0.00056 0.00207 0.00409 0.00252 0.00195
Kurtosis 1.17384 1.97282 4.29705 1.08029 3.55604
Skewness 0.35503 �0.48217 �0.03284 �0.34430 �0.60492
Minimum �0.06682 �0.21580 �0.30615 �0.20239 �0.22394
Maximum 0.09999 0.16811 0.39515 0.17874 0.21885

Table 2 Summary statistics for the glide paths of TDFs offered by the mutual fund families

Percentage of equity Year of the
kink before
target year

Length of the glide path in
years

40 years before
target year

At target
year

Before target
year

After target
year

Mean 91 42 30 43 19
Median 90 45 30 40 20
Mode 90 45 25 40 10
Min 80 20 10 40 0
Max 100 60 35 50 40
Market leaders
Fidelity 90 20 N/A 45 0
Vanguard 90 50 25 50 5
T. Rowe Price 90 45 25 45 40
Percentage of TDFs with

Kink in the glide path 57%
Continue past target year 66%

Glide path longer than 40 years before target year 41%
Number of fund families 45
Number of funds 230

175R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



the common combination is from 80% to 40%, 80% to 30%, and 80% to 20% equity. Among
the TDF families, 57% have a kink in their glide path, meaning that they keep the equity at
the maximum level for the first five to 30 years. Most commonly the glide path is flat for the
first 10 years and starts decreasing after 10 years. TDFs that continue the glide path after the
target year are called “through” TDFs. On average the glide path continues 19 years past the
target year and 66% of TDFs are “through” TDFs.

Given there is a wide range of glide path strategies used by actual TDFs in the market-
place, we calculate the expected utility over the accumulation period for different glide paths.
Each glide path can be characterized by its beginning equity level, ending equity level, and
the steepness of the glide path or the presence of the kink in the glide path. We analyze glide
paths that begin with equity allocation from 100% to 50% and end with the equity allocation
from 70% to 0%. In addition we assume the glide path can be flat in the beginning of the
accumulation period for 10, 20, or even 30 years, creating a kink into the glide path. Given
the different combinations between the beginning and ending equity and the kink in the glide
path, we analyze well over 900 different portfolio strategies. We simulate 1,000 bootstrap
samples for each portfolio strategy. In this article, we present the results for the more
common strategies used by the fund families as well as the best performing strategy. For the
base case we examine the representative investor who starts saving for retirement in the
beginning of her professional career and has at least 40 years to accumulate funds to support
her retirement years. In our results we present the expected utility for the following seven
common lifecycle strategies: 90% to 50%, 90% to 40%, 90% to 30%, 90% to 20%, 80% to
40%, 80% to 30%, and 80% to 20%. For comparison we also present results from the best
performing lifecycle and lifestyle strategies.

3. Empirical results

3.1. Expected utility for the representative investor with different accumulation periods

We first consider the case of a young investor who has at least 40 years to save up for her
retirement and calculate the total accumulation period expected utility following Eq. (1) for
a wide range of different portfolio strategies; both lifestyle and lifecycle. Table 3 summarizes
the results for the common strategies offered by the fund families as specified in Section 2.4.
The results are generated from 1,000 simulations in each scenario, with equity allocation 5%
increments ranging from 0% to 100% (e.g., 20 times).

Table 3 reports four levels of beginning-ending risk aversion: {0–4; 0–6; 2–4; 2–6} in
the first column. We report the expected utility for the best lifestyle strategy and its
corresponding glide path in the second to third columns. For ease of comparison, we use the
expected utility for the best lifestyle strategy as a benchmark, and report the expected utilities
for the seven lifecycle strategies as a percentage difference relative to the benchmark. In
addition, the last three columns in Table 3 compare the best lifecycle strategy with the best
lifestyle strategy by reporting the percentage difference, the glide path, and the t-statistics.
Panel A reports an investor with 40 years of investment horizon followed by Panels B, C, and
D with 30-years, 20-years, 10-years of investment horizons respectively. From Table 3, we

176 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



can see that as risk aversion levels increase, the total expected utilities decrease. Even
though, theoretically, one can always find a lifecycle strategy which has higher expected
utility than lifestyle strategy, but for investors with high levels of risk aversion, the current
common market lifecycle strategies do not consistently generate higher total expected
utilities than lifestyle strategies.

In our base case the representative investor is a young person who has just entered the
work force and is risk neutral (A�0) when she starts saving up for retirement, and becomes
less risk tolerant as she gets older, with risk aversion level increasing in equal increments
every year and reaching the level of 4 at target retirement year. On average this implies risk
aversion of 2. Even though our investor is risk neutral when she starts investing, we find that
100% portfolio does not yield him the highest expected utility among the lifestyle strategies
and she should invest in the 55% equity portfolio instead. Panel A of Table 3 shows that all

Table 3 Total accumulation period expected utility for the investor who becomes more risk averse as she
gets older

Risk
aversion

Best lifestyle
strategy

Lifecycle strategies Best theoretical lifecycle
strategy

E(U) Equity 90 to 50 90 to 40 90 to 30 90 to 20 80 to 40 80 to 30 80 to 20 Glide path t-stat

Panel A: 40 year investment horizon
0 to 4 3.284 55% 2.7% 3.5% 3.8% 3.7% 2.8% 3.0% 2.7% 4.5% 100 to 25 57.45**
0 to 6 3.075 40% �1.0% 1.4% 3.1% 4.0% 1.7% 3.1% 3.7% 4.4% 100 to 10 28.66**
2 to 4 3.051 40% �6.8% �4.9% �3.6% �2.8% �2.9% �1.8% �1.4% 0.3% 50 to 30 5.25**
2 to 6 2.903 35% �13.3% �9.7% �6.9% �5.0% �6.6% �4.2% �2.7% 0.6% 45 to 20 3.89**
Panel B: 30 year investment horizon

80% 80% 75% 70% 70% 70% 65%
0 to 4 2.575 55% 2.2% 2.9% 2.6% 1.7% 2.1% 2.1% 1.1% 4.5% 100 to 25 84.55**
0 to 6 2.411 40% �0.6% 1.6% 2.9% 3.2% 1.6% 2.8% 2.9% 4.3% 100 to 10 29.72**
2 to 4 2.397 40% �4.5% �2.9% �1.1% �0.4% �1.4% �0.6% �0.1% 0.3% 50 to 30 3.54**
2 to 6 2.279 35% �9.9% �6.6% �3.0% �0.9% �4.2% �2.1% �0.3% 0.6% 45 to 20 5.31**
Panel C: 20 year investment horizon

70% 65% 60% 55% 60% 60% 50%
0 to 4 1.796 55% 1.6% 1.7% 1.1% �0.2% 1.2% 1.1% �0.9% 4.6% 100 to 25 31.46**
0 to 6 1.682 40% �0.5% 1.5% 2.3% 2.0% 1.3% 2.3% 1.4% 4.4% 100 to 10 17.48**
2 to 4 1.675 40% �2.8% �0.8% 0.1% 0.0% �0.4% 0.1% 0.0% 0.3% 50 to 30 6.94**
2 to 6 1.591 35% �7.1% �3.1% �0.6% 0.5% �2.3% �0.6% 0.6% 0.6% 50 to 20 8.98**
Panel D: 10 year investment horizon

60% 55% 45% 40% 50% 50% 35%
0 to 4 0.941 55% 0.9% 0.7% 0.2% �2.4% 0.2% 0.0% �3.3% 5.0% 100 to 25 35.41**
0 to 6 0.881 40% �0.5% 1.1% 1.1% 0.2% 0.8% 1.7% �0.6% 4.9% 100 to 10 49.28**
2 to 4 0.879 40% �1.6% �0.1% 0.3% �0.6% 0.0% 0.3% �1.0% 0.3% 50 to 30 5.10**
2 to 6 0.835 30% �5.1% �1.7% 0.4% 0.5% �1.2% 0.2% 0.1% 0.6% 45 to 25 8.42**

Notes. The table reports the best lifestyle strategy as a benchmark for the expected utility (E(U)) of the
lifecycle strategies. The results for the lifecycle strategies are reported as a percentage difference from that
benchmark. The last three columns compare the best lifecycle strategy with the best lifestyle strategy by reporting
the percentage difference, the original 40 year glide path (beginning and ending level of equity), and the
t-statistics.

**Denotes significance at the 1% level. Results for each accumulation period are reported in separate panels.
First row of Panels B through D give the approximate level of equity for each lifecycle strategy at the beginning
of accumulation period (e.g., 30 years before target date).

177R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



the more common lifecycle strategies included in our investigation yield higher expected
utility during accumulation period than the best lifestyle strategy. The highest utility would
be reached with a theoretical lifecycle portfolio that starts out at 100% but then smoothly
decreases the equity allocation to 25% by the target date. Such a strategy would yield to our
representative investor 4.5% higher utility and it is significantly higher than the 55% lifestyle
strategy at the 1% level. Among the more common TDF strategies her best choice would be
to start investing to the TDF with the glide path from 90% to 30% equity, which generates
a 3.8% higher utility than that of the best lifestyle strategy.

If the young investor becomes more risk averse as she gets older, reaching the risk
aversion of 6 at the target date, the best lifestyle strategy is 40% equity portfolio; more
conservative than above. For this investor all except the 90% to 50% lifecycle strategy
outperform the best fixed equity portfolio. Among the lifecycle strategies the highest
expected utility is reached with the theoretical glide path from 100% equity to 10%, with
utility 4.4% higher and is also significantly higher than that of the best lifestyle strategy at
the 1% level.

Our results show that for the investor with higher risk aversion the appeal of more
common lifecycle strategies starts to diminish. In fact none of the more common lifecycle
strategies reported in Table 3 manage to outperform the best lifestyle strategy when the
investor’s beginning risk aversion is as large as 2. However, it is still possible to construct
a lifecycle strategy that generates higher utility. For example, for the investor with risk
aversion from 2 to 4, the theoretical lifecycle strategy with a conservative glide path from
50% equity to 30% equity would outperform the best lifestyle strategy with 40% equity
fixed. The percentage difference in expected utility is though only 0.3%, but is still signif-
icant at the 1% level.9 The higher the investor’s beginning risk aversion the lower should be
the equity allocation in the beginning of the accumulation period. High risk aversion at the
target retirement year shifts the preference towards a more conservative glide path with lower
beginning and ending equity level.

Because we run our analysis for a wide range of strategies we find that even with higher
levels of risk aversion, there exist lifecycle strategies that outperform lifestyle strategies
although none of the currently offered TDFs have sufficiently conservative glide path. To the
investor who has above average risk aversion when she is young, we recommend a more
conservative TDF that has a target year shorter than the investor’s planned retirement. The
TDF with the shorter target date has already decreased the equity allocation to the desired
lower level. By picking the TDF with the target date that does not match her desired target
retirement year, the investor may find a fund with the glide path that matches her risk
aversion and will maximize her expected utility.

One of the main selling points of TDFs is that the target year stated in the fund name is
an easy way for the investor to find the suitable fund. In addition quite often it is the plan
sponsor who picks the fund for the investor as the investor herself has failed to make her
choice. Therefore, the suggestion to deviate from the TDF with the matching target year may
not be very helpful. Therefore, we recommend that fund families should include in their
menu TDFs with more conservative glide paths that may be more suitable for more risk
averse investors.

So far, we have assumed that a young person enters the work force, for example, after

178 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



finishing her undergraduate education at around age 25 and immediately starts making
contributions to the retirement savings plan. Unfortunately, this is quite often not the case as
young people do not take advantage of time as their ally in investing for retirement. We
analyze whether TDFs would also be a good choice for the person who joins the defined
contribution plan later in life, for example 30, 20, or even only 10 years before the desired
target retirement date in the remaining panels in Table 3.

Panel B of Table 3 assumes that our young investor postpones saving for retirement by 10
years. We assume that our investor picks a TDF that has a target year similar to her planned
year of retirement. In such a case the TDF that our investor starts making contributions to has
already decreased the equity allocation for the first 10 years, assuming the smooth glide path.
For example for the investor who picks a TDF with the matching target date and glide path
from 90% equity to 40% equity, the level of equity in the portfolio is at about 80% when she
starts making investments into this fund. In our analysis we assume our investor’s risk
aversion is at its minimum when she starts making contributions into the retirement fund.

If risk aversion of the risk-neutral investor increases from 0 to the level of 4 over her
30-year accumulation period, the lifestyle strategy that yields the highest utility should have
55% equity. From the more common lifecycle strategies listed in Panel B in Table 3, all of
them outperform the best lifestyle strategy in the context of total expected utility. The highest
utility is reached with the strategy with the original glide path from 100% equity to 25%
equity at the target date. This TDF would have decreased the equity allocation to about 81%
when the investor starts to make contributions to her retirement plan, and it yields a utility
4.5% higher than that from the best lifestyle strategy, which is significant at the 1% level.

If the investor is more risk averse and her risk aversion increases from 2 at 30 years before
the target year to 4 at the target year, her best choice would be a portfolio strategy with
original glide path from 50% equity to 30% equity. The increase in expected utility is only
0.3% still significantly higher than the utility from the best lifestyle (40% equity) strategy.
If the investor is very risk averse with risk aversion increasing from 2 to 6, we still find that
a conservative lifecycle strategy with the glide path from 45% equity to 20% over 30 years
yields investor higher utility. However, none of the TDFs in the market have decreased the
equity to such a low level 30 years before the target date. Therefore, the conservative investor
needs a TDF with a far more conservative glide path than any of the fund families currently
offer.

If the investor postpones making contributions into a retirement account even longer and
leaves only 20 years for contributing towards her retirement nest egg, the glide path of
lifecycle strategies has brought the equity level in the portfolio even lower. The summary of
expected utilities under the same assumptions is brought in Panel C of Table 3. If our investor
is still neutral towards risk when she starts saving for retirement and her risk aversion reaches
the level of 4 when she retires, she is still better off with the lifecycle portfolio strategy.
Among the more common lifecycle strategies the highest expected utility is reached with the
original glide path strategy from 90% equity to 40% equity. This strategy would yield our
investor a total accumulation period expected utility that is 1.7% higher than the utility from
the best lifestyle strategy, which has 55% on equity. For the investor who has high risk
tolerance 20 years before the target retirement, the TDFs that have decreased the level of
equity to 55% or less may be too conservative. Starting out with relatively high equity level

179R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



at 20 years before target retirement might help the investor to catch up a little with the lost
years of capital accumulation. However, it is important to keep in mind that in case of periods
of bear markets investors have less time left to recover the losses.

Less risk tolerant investors may now find that for a suitable TDF at 20 years before the
target year the level of equity has to decrease sufficiently. For example, less risk tolerant
investor with risk aversion changing from 2 to 6 over her 20-year accumulation period will
benefit from the conservative lifecycle strategy with the glide path from 50% equity to 20%
equity. It provides significantly higher expected utility than that of the best performing
lifestyle strategy (with 35% equity). This lifecycle strategy starts out at 70% equity 40 years
from the target date and reaches around 50% level 20 years before the target date.

When the investor postpones making contributions to her retirement account even more
and the accumulation period is only 10 years, the glide paths of lifecycle strategies have
brought the equity level down very close to the level at the target date. We find, though, from
Panel D of Table 3 that for our representative investor who is risk-neutral when she starts
investing towards retirement and reaches a risk aversion level of 4 at the retirement date, the
lifecycle strategy with the original glide path from 100% equity to 25% equity yield the
highest expected utility that is 5.0% higher than utility from 55% equity lifestyle strategy that
yields utility of 0.941 and the difference is significant at the 1% level. It is interesting to note
that even the more risk averse investors with risk aversion increasing from 2 to 6 by the target
year may now reach higher utility with some of the common TDFs as they have decreased
the level of equity sufficiently. For example the TDF with the original glide path from 90%
equity to 20% has reached an approximate equity level of 40% 10 years before the target
date. Over the 10 year accumulation period this strategy would yield our investor 0.5%
higher utility than the fixed 30% equity portfolio, which is the best lifestyle strategy.

3.2. Expected utility of the loss averse investor with different accumulation periods

Prior research has concluded that investors have different attitude towards downside risk,
thus, they are more sensitive to the negative changes to their wealth. Table 4 summarizes the
results for the analysis that uses Eq. (5) that incorporates the representative investor’s loss
aversion in our model. Similar to Table 3, in Table 4 we assume an accumulation period of
40, 30, 20, or 10 years and the total expected utility is calculated as the sum of the present
value of monthly utilities over the different accumulation periods. In case the representative
investor’s portfolio strategy yields a loss during the given month, the investor is assumed to
be more risk averse the next month. We use the loss aversion of 2.25 as suggested by Tversky
and Kahneman (1992).

Panel A in Table 4 shows that for the loss averse investor who is risk-neutral when she
starts contributing towards the retirement portfolio and has a 40 year accumulation period,
moderate lifecycle strategies yield higher expected lifetime utility than the lifestyle strate-
gies. Specifically for the risk-neutral investor who reaches a risk aversion of 4 by the target
year, the best portfolio strategy is the lifecycle portfolio with the glide path from 90% equity
to 20% equity. Such a portfolio strategy will yield her a total accumulation period expected
utility that is 1.6% higher than that from the 45% equity lifestyle portfolio, and the difference
is statistically significant at the 1% level. The more common TDF strategies, except the

180 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



aggressive glide path from 90% to 50% all outperform the lifestyle strategies in terms of
expected utility.

For the investor who is more risk-averse when she is young and has a risk aversion of at
least 2 when she starts investing towards retirement and reached risk aversion level of 4 by
retirement the lifecycle strategy with equity decreasing from 50% to 25% over the accumu-
lation period, yields the highest expected utility. The more common lifecycle strategies fail
to outperform the 35% equity lifestyle strategy. The investor needs a more conservative glide
path. As suggested before, this can be accomplished if our investor picks a TDF with the
target date closer to today than her desired retirement year. As the main target investor of
TDFs is the investor who fails to pick the fund herself, it would be more important that fund
families should start to offer TDFs with more conservative glide paths.

We find that even when the loss averse investor postpones making contributions into the
retirement account, conservative lifecycle strategies yield higher expected utility but the

Table 4 Total accumulation period expected utility for the loss averse investor

Risk
aversion

Best lifestyle
strategy

Lifecycle strategies Best theoretical lifecycle
strategy

E(U) Equity 90 to 50 90 to 40 90 to 30 90 to 20 80 to 40 80 to 30 80 to 20 Glide path t-stat

Panel A: 40 year investment horizon
0 to 4 2.679 45% �1.1% 0.2% 1.2% 1.6% 0.5% 1.4% 1.6% 1.6% 90 to 20 7.20**
0 to 6 2.540 35% �6.0% �3.3% �1.1% 0.2% �2.2% �0.2% 0.9% 1.2% 60 to 20 10.77**
2 to 4 2.523 35% �11.6% �9.2% �7.4% �6.1% �6.6% �4.8% �3.9% 0.2% 50 to 25 1.01
2 to 6 2.395 30% �17.9% �13.9% �10.8% �8.5% �10.3% �7.3% �5.4% 0.1% 45 to 25 0.25
Panel B: 30 year investment horizon

80% 80% 75% 70% 70% 70% 65%
0 to 4 1.703 40% �1.0% 0.3% 1.1% 1.3% 0.4% 1.2% 1.1% 1.3% 90 to 20 4.59**
0 to 6 1.611 35% �5.3% �2.4% �0.3% 0.8% �1.7% 0.3% 1.0% 1.0% 70 to 20 3.36**
2 to 4 1.610 35% �8.3% �5.6% �3.6% �2.3% �4.0% �2.1% �1.2% 0.2% 50 to 25 1.10
2 to 6 1.525 30% �13.7% �9.3% �5.8% �3.5% �7.0% �3.7% �1.9% 0.2% 45 to 25 0.37
Panel C: 20 year investment horizon

70% 65% 60% 55% 60% 60% 50%
0 to 4 1.072 40% �0.9% 0.3% 1.0% 0.7% 0.4% 0.9% 0.4% 1.1% 80 to 35 2.31*
0 to 6 1.011 35% �4.4% �1.5% 0.6% 1.1% �1.0% 0.8% 1.0% 1.2% 75 to 35 2.81**
2 to 4 1.014 35% �5.6% �2.9% �0.9% �0.1% �2.2% �0.3% 0.1% 0.2% 50 to 30 2.33*
2 to 6 0.958 30% �10.1% �5.5% �1.9% �0.2% �4.3% �1.1% 0.2% 0.3% 45 to 25 0.37
Panel D: 10 year investment horizon

60% 55% 45% 40% 50% 50% 35%
0 to 4 0.559 40% �0.8% 0.3% 0.4% �0.4% 0.3% 0.4% �0.6% 0.5% 80 to 35 2.68**
0 to 6 0.525 35% �3.8% �0.9% 0.7% 0.4% �0.8% 0.6% 0.2% 0.8% 75 to 30 3.09**
2 to 4 0.531 35% �4.1% �1.2% 0.3% 0.0% �1.0% 0.3% �0.1% 0.4% 50 to 30 3.80**
2 to 6 0.500 30% �8.2% �3.2% �0.2% 0.1% �2.8% 0.0% 0.2% 0.2% 45 to 25 0.45

Notes. The table reports the best lifestyle strategy as a benchmark for the expected utility (E(U)) of the
lifecycle strategies. The results for the lifecycle strategies are reported as a percentage difference from that
benchmark. The last three columns compare the best lifecycle strategy with the best lifestyle strategy by reporting
the percentage difference, the original 40 year glide path (beginning and ending level of equity), and the
t-statistics.

** and *denote significance at the 1% and 5% levels, respectively. Results for each accumulation period are
reported in separate panels. First row of Panels B through D give the approximate level of equity for each
lifecycle strategy at the beginning of accumulation period (e.g., 30 years before target date).

181R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



utility difference between the best lifestyle and best lifecycle strategies is smaller than in case
of the investor who is not loss averse.10 If the investor postpones making contributions into
a retirement account and leaves 30 years for contributing towards her retirement nest egg, the
glide path of lifecycle strategies has brought the equity level in the portfolio lower. The
summary of expected utilities under the same assumptions is brought in Panel B of Table 4.
If our risk-neutral investor is still risk neutral towards risk when she starts saving for
retirement and her risk aversion reaches the level of 4 when she retires, she reaches higher
expected utility with most of lifecycle portfolio strategies. Among the more common five
lifecycle strategies the highest expected utility is reached with the original glide path strategy
from 90% equity to 20% equity. This strategy would yield our investor a total accumulation
period expected utility that is 1.3% higher than the utility from the 40% equity lifestyle
portfolio (E(U)�1.703) and the difference is significant at the 1% level. Less risk tolerant
investor with risk aversion changing from 2 to 6 over her 30-year accumulation period will
benefit from more conservative lifecycle strategy with equity changing from 45% to 25%,
which is only 0.2% higher than that of the best lifestyle strategy (30% equity fixed).

In case our investor’s accumulation period is only 20 years, the glide paths of lifecycle
strategies have brought the equity level closer to the level at the target date. We find, though,
from Panel C of Table 4, that for our representative investor who is risk neutral when she
starts investing towards retirement and reaches a risk aversion level of 4 at the retirement
date, the lifecycle strategy with the original glide path from 80% equity to 35% equity yields
the highest expected utility. For the investor whose risk aversion is 2 when she starts
investing and reaches 6 by the target year, a more conservative strategy with original glide
path from 45% equity to 25% equity provides the highest utility.

For the loss averse investor with the 10 year accumulation period, the glide paths of many
common TDFs have reached low enough levels of equity that a conservative investor may
reach higher utility with lifecycle strategies compared with best lifestyle strategy. However,
the percentage difference in expected utilities is very small.

In summary, our results show that for the loss averse investor the portfolio strategies have
to be more conservative to yield higher utility. Both the best lifestyle and best lifecycle
strategies need to have a lower level of equity. We also find that the difference between the
utility from reported lifestyle and lifecycle strategies has become smaller. For the more risk
tolerant investor the utility from the common lifecycle strategies is less than 1.6% higher
than the utility from the best lifestyle strategy and the most aggressive glide path (90% to
50%) does not outperform the best lifestyle strategy. For the more risk averse and loss averse
investor the utility from the common lifecycle strategies is even less beneficial compared
with the best lifestyle strategy. Such investor needs more conservative TDFs than currently
offered on the market.

3.3. Expected utility from a kinked TDF glide path or a kinked risk aversion

So far we have examined so-called smooth glide path strategies in comparison to constant
equity strategies. Poterba and Samwick (1997) study the age and cohort effects on investor
portfolio allocation and find that households start decreasing equity in their overall portfolio
after age 43. In addition, as shown in Table 2, among the TDFs offered in the market, 57%

182 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



have a kink in their glide paths. Many TDFs keep the equity allocation at maximum in the
beginning of the accumulation period for five to 15 years thus creating a kink into the glide
path. Most TDFs in the market do not keep equity at the maximum level for that long, but
have a kink in the glide path at 35 to 30 years before the target year. To investigate the impact
of a kink, we study the expected utility for glide path strategies with the kink at 30 years
before the target year and report the results in Table 5.11

We examine the lifecycle strategies with the kink at 30 years before the target year in
comparison to the best lifestyle strategy as in Table 3. In Panel A of Table 5 we still assume
that the investor’s risk aversion changes linearly and starts increasing right after she starts
making contributions to her retirement account. This investor, however, has a kinked glide
path 30 years before the target year. When the investor’s beginning risk aversion is neutral
she can easily select a TDF among the most common lifecycle strategies that outperform the
best lifestyle strategy. The higher her ending risk aversion, the more conservative should be
her strategy, keeping both the beginning and ending equity allocation at lower levels. For the
investor whose risk aversion in the beginning of the accumulation period is 2, although the

Table 5 Expected utility with kinked glide path and/or risk aversion

Risk
aversion

Best lifestyle
strategy

Lifecycle strategies Best theoretical
lifecycle strategy

t-stat

E(U) Equity 90 to 50 90 to 40 90 to 30 90 to 20 80 to 40 80 to 30 80 to 20 Glide path

Panel A: Glide path kinked at 30 years before target year, risk aversion linear
0 to 4 3.284 55% 2.4% 3.3% 3.9% 4.1% 3.0% 3.4% 3.4% 4.5% 100 to 15 37.59**
0 to 6 3.075 40% �8.9% �0.2% 1.6% 2.7% 0.7% 2.2% 3.1% 3.4% 80 to 10 26.12**
2 to 4 3.051 40% �9.2% �7.6% �6.5% �5.8% �4.6% �3.7% �3.2% 0.3% 45 to 30 28.20**
2 to 6 2.903 35% �17.2% �14.1% �11.7% �10.0% �9.5% �7.4% �6.1% 0.6% 40 to 20 29.76**
Panel B: Glide path linear, risk aversion kinked at 30 years before target retirement
0 to 4 3.445 75% 4.0% 4.2% 4.1% 3.6% 2.8% 2.6% 1.9% 5.6% 100 to 35 125.9**
0 to 6 3.222 50% 4.3% 5.7% 6.6% 6.8% 4.7% 5.3% 5.4% 8.1% 100 to 20 101.9**
2 to 4 3.092 40% �4.6% �3.0% �2.0% �1.5% �1.5% �0.7% �0.5% 0.5% 55 to 30 17.07**
2 to 6 2.974 35% �8.3% �5.3% �3.2% �1.8% �3.3% �1.5% �0.4% 1.0% 55 to 20 30.34**
Panel C: Both glide path and risk aversion kinked at 30 years before target retirement
0 to 4 3.445 75% 4.7% 5.3% 5.5% 5.5% 3.7% 3.9% 3.7% 7.1% 100 to 25 169.8**
0 to 6 3.222 50% 4.4% 6.1% 7.3% 8.0% 5.1% 6.1% 6.6% 9.4% 100 to 10 78.17**
2 to 4 3.092 40% �6.5% �5.1% �4.1% �3.6% �2.8% �2.0% �1.7% 0.5% 55 to 30 8.68**
2 to 6 2.974 35% �11.0% �8.3% �6.3% �3.4% �5.2% �3.5% �2.4% 0.9% 50 to 20 17.18**

Notes. The table reports the best lifestyle strategy as a benchmark for the expected utility (E(U)) of the
lifecycle strategies. The results for the lifecycle strategies are reported as a percentage difference from that
benchmark. The last three columns compare the best lifecycle strategy with the best lifestyle strategy by reporting
the percentage difference, the original 40 year glide path (beginning and ending level of equity), and the
t-statistics.

**Denotes significance at the 1% level. Panel A of the table reports the results for different lifecycle strategies
that keep the level of equity at the maximum for the first 10 years of the accumulation period. Investor’s risk
aversion is assumed to increase smoothly over the accumulation period. Panel B reports the results for lifecycle
strategies with smooth (linear) glide path, but assumes that the investor’s risk aversion is constant for the first 10
years and starts increasing only 30 years before target date. Panel C reports the results for the lifecycle strategies
with the kink in the glide path at 30 years before the target year and also assumes that the investor’s risk aversion
starts increasing only at 30 years before the target retirement. The full accumulation period is assumed to be 40
years.

183R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



more common lifecycle strategies do not yield higher expected utility in comparison with the
best lifestyle strategy, a very conservative lifecycle strategy is still able to outperform this
constant equity strategy. For example, to the investor with risk aversion increasing from 2 to
6, the best strategy is to invest in the 40% to 20% glide path fund, which has a utility
significantly higher than that of the best lifestyle strategy at the 1% level.

We next examine the expected utility for the investor whose risk aversion starts increasing
many years after she enters the work force and begins making contributions to the chosen
retirement plan; a scenario reported by Poterba and Samwick (1997). In the beginning of the
accumulation period the accumulated capital is still small and worries about potential losses
are low. Certain changes in life can change the investor’s risk tolerance; like for example
starting a family. Agnew, Balduzzi, and Sundén (2003) find that investor’s risk aversion is
low even up to age 45 to 54 and starts increasing after that. Panel B of Table 5 shows the
expected utilities for the investor whose risk aversion starts increasing 30 years before the
target retirement year. The strategies listed in this panel have a smooth glide path or in other
words start decreasing the equity allocation in the portfolio right away.

As our representative investor’s risk aversion starts increasing only later in life, her
average risk aversion over the accumulation period is relatively lower. Therefore, in general
this investor reaches higher utility with more aggressive strategies compared with the
investor whose risk aversion starts increasing right away. More specifically our investor who
is risk neutral when she is young and whose risk aversion starts increasing 30 years before
retirement reaching the level of 4 by the target date, would reach the highest total expected
utility when investing in the TDF that has 100% equity in the beginning and decreases it to
the level of 35% equity by the target date. The more risk averse investor whose risk aversion
changes from 2 to 6, would benefit from choosing a lifecycle strategy with the glide path
from 55% equity to 20% equity. In both cases, the improvements are significant at the 1%
level. Panel B shows that if investor’s risk aversion is constant for a period and starts
increasing later in life, the lifecycle strategies still provide higher expected utility than
lifestyle strategies.

In Panel C of Table 5, we present the results for the case where the glide path has a kink
30 years before target date and investor’s risk aversion starts increasing 30 years before the
target retirement. The more risk tolerant investor (risk aversion increasing from 0 to 4 and
from 0 to 6) will reach higher expected utility from investing in the common lifecycle
strategies than from lifestyle strategies. Given the flexibility in the kinked glide path, the
percentage increase in the expected utilities is higher among the lifecycle strategies. For
example the investor with risk aversion from 0 to 4 (with the kink in 30 years before the
target year) will reach the highest utility with the lifecycle strategy that has a steep glide path
that holds equity at 100% for the first 10 years and decreases it to 25% over the remaining
30 years. Such strategy will yield him 7.1% higher expected utility (significant at the 1%
level) than the best lifestyle strategy with 75% equity fixed over the 40 years of investment.12

In summary, when the investor has a kinked glide path and/or kinked risk aversion before
the target retirement year, our results show that the best lifecycle strategy still outperforms
all lifestyle strategies which have the fixed equity allocation. As in the previous analyses, for
the more risk averse investor the utility from the more common lifecycle strategies is

184 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



typically less than the best lifestyle strategy, thus needs more conservative TDFs than
currently offered on the market.

4. Conclusions

Prior literature has examined several reasons why investors should follow the conven-
tional wisdom of switching their investment portfolio gradually into safer assets when they
get older. This article adds investors’ increasing risk aversion to this list and shows that for
the investors who become less risk tolerant over their lifetime, the lifecycle strategy used by
TDFs is a choice that would yield higher expected utility than a constant allocation strategy.

For investors who start saving for retirement early and have 40 years to accumulate wealth
to support their golden years, the best choice for the retirement plan depends on their risk
aversion. To the investors who are less risk averse when young and become moderately risk
averse by the time they plan to finish working, the best fit would be a plan that is relatively
aggressive and starts the portfolio glide path at a high level of equity (close to 100%),
decreasing it over the accumulation period to a low level (about 25%) at the target date.
Investors, who are more risk averse and become even less risk tolerant throughout their life,
may not find a beneficial lifecycle strategy among the TDFs offered currently by the fund
families and would need a lifecycle strategy with a more conservative beginning and ending
level of equity.

Procrastinators who leave saving for retirement until later in life are also better off with
investment strategies that have a glide path with decreasing stock allocation over time. In
most cases they would still be better off picking the TDF that matches their planned
retirement year. If the investor’s risk tolerance starts decreasing later in life, for example 30
years before their planned retirement, lifecycle strategies will still provide a higher expected
utility over the accumulation period than the constant allocation strategy. Compared to the
lifestyle strategies, the investor also enjoys higher utility from a kinked TDF strategy that
keeps the equity allocation at the maximum in the beginning years.

After incorporating the investor’s loss aversion into the conventional expected utility
framework, our results show that conservative lifecycle investment strategies provide higher
expected utility than strategies with constant equity allocation, though the TDFs currently
offered by fund families are not conservative enough for the loss averse and extremely risk
averse investor.

We find it important to remember that TDFs are not a one-size-fits-all solution. Investors
should look at the TDFs strategy a bit closer than just the target date. Financial advisors
should determine individual investors’ risk aversion characteristics before suggesting the
appropriate TDF. Though it is hard to predict an investor’s future risk tolerance, her
beginning risk aversion can give at least some indication for the starting point of the glide
path of the portfolio strategy.

As one of the QDIA options, lifecycle funds are targeted at individuals who have failed
to pick the fund for their retirement contributions. Our analyses suggest that the plan
sponsors who make the choice for them should become more familiar with the plan

185R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



participants’ risk aversion. In particular, fund families should consider offering some TDFs
with more conservative glide paths for those investors who are more risk averse.

Notes

1 With the enactment of the Pension Protection Act (PPA) of 2006, the U.S. Department
of Labor defines qualified default investment alternatives (QDIAs) for retirement plan
participants who fail to choose an allocation for their retirement contributions. One of
the four mechanisms described in the PPA says that the qualified default instrument
should have a portfolio mix that considers an investor’s age or retirement date
(Employee Benefits Security Administration, 2009). TDFs, also known as lifecycle
funds, change asset allocation on a pre-stated schedule, depending upon an investor’s
age relative to retirement, can therefore be used by plan sponsors as a default option
for those participants who fail to choose an investment allocation for themselves.

2 In this article we use terms “lifecycle fund” and “target-date fund (TDF)” interchange-
ably.

3 When wealth is taken into account, some studies have shown that as investors get older
and their wealth increases, their (absolute) risk aversion may not increase. However,
Siegel and Hoban (1982) show that there is an increasing relative risk aversion with
wealth if a broader based sample and a more comprehensive measurement of wealth
are used.

4 In this article we focus on a representative investor who has failed to choose a fund
for his contributions towards retirement, or who wants to make his contributions with
minimal or no interference during the full investment period. This is an investor who
is kept in mind in the PPA 2006 that defined QDIAs. This is also the investor who
without this default choice would have made no or very small contributions toward his
retirement welfare. Therefore, it is important to remember that an investor who
actively manages his retirement portfolio may find other strategies more suitable.

5 Hereafter, all risk aversions included in this article mean relative risk aversion.
6 We assume that the relative risk aversion changes annually. Within each month during

a year the investor’s risk aversion is assumed to stay the same.
7 For robustness, we also test with � of 0.95 and 0.90. The results are available upon

request.
8 As in Liu, Chang, De Jong, and Robinson (2011), we rebalance the portfolio annually

in the beginning of each year. Therefore, within the year the level of equity in the
portfolio is kept constant.

9 In Eq. (2), the lifetime expected utility is based on the mean and variance of the
portfolio, which are the same in the 1,000 simulations. This leads to a small standard
deviation of the utility difference series and very large t-statistic correspondingly.

10 Unlike Table 3, the utility difference between the best lifecycle and lifestyle strategies
is not statistically significant at any conventional level for many highly risk averse
investors. This is because of the much higher standard deviation of the utility differ-

186 R.P. Chang et al. / Financial Services Review 23 (2014) 169–188



ence series in the 1,000 simulations, generated from a path-dependent utility model
specified in Eq. (3).

11 We also calculate the expected utility for glide path strategies with the kink at 20 and
10 years before the target year and our results are qualitatively similar as in the 30 year
case. These results are unreported to save place, and are available upon request.

12 The results are similar when we assume the investor’s risk aversion starts to increase
20 years before the target retirement. They are available upon request.

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