8/16/2002
Inefficient Choices in 401(k) Plans: Evidence from
Individual Level Data
Julie Agnew*
The College of William and Mary
*The College of William and Mary, School of Business Administration, P.O. Box 8795, Williamsburg,
Virginia 23187. Tel. (757) 221-2672. E-mail: [email protected].
The author thanks CitiStreet for providing the 401(k) plan data and Stefan Bokor for his
immense help in organizing the data. The author thanks her dissertation committee,
Pierluigi Balduzzi (Chair), Alicia Munnell, Eric Jacquier and Peter Gottschalk, for their
careful comments and guidance. In addition, the author is grateful to Shlomo Benartzi for
his comments and insight. Finally, the author thanks conference participants from the
Retirement Research Consortium Fourth Annual Conference and the Frank Batten Young
Scholars Conference. She gratefully acknowledges financial support from a dissertation
fellowship from the Center for Retirement Research. Any errors are my own. The
research reported herein was performed pursuant to a grant from the U.S. Social Security
Administration (SSA) funded as part of the Retirement Research Consortium. The
opinions and conclusions are solely those of the author and should not be construed as
representing the opinions or policy of SSA or any agency of the Federal Government.
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Inefficient Choices in 401(k) Plans: Evidence from
Individual Level Data
Abstract: This paper investigates how individual characteristics, such as age, salary, job
tenure, and gender, influence an individual’s decision to over-invest in company stock
and follow naïve diversification rules. Using a new and unique data set from one 401(k)
plan with over 73,000 eligible employees, the results suggest that individual
characteristics do influence company stock holdings. Ordered probit regression results
indicate that the probability of over-investing in company stock for the average
participant is greater for males, decreases with salary, increases with past company stock
performance and is related to the participant’s division of employment. In addition, the
paper investigates if individuals tend to follow a simple diversification rule, the 1/n
heuristic. According to this rule, some 401(k) investors will choose to divide their
contributions evenly among the n options available regardless of the type of investment
vehicles offered. While the percentage of individuals who follow the 1/n heuristic in this
study is lower than that found in previous studies, it still represents 5% of the sample.
Probit regression analysis results suggest that the probability of following the 1/n
heuristic decreases with increases in job tenure and salary. Finally, consistent with the
mental accounting literature, participants demonstrate a tendency to treat company stock
as a separate “account”. The evidence from this study indicates that over-investing in
company stock and practicing naïve diversification strategies may be occurring
frequently in 401(k) plans and that certain individuals are more prone to make these
decisions than others. Given the pivotal role 401(k) savings play in individuals’
retirements, this research may help plan sponsors design plans and train participants to
make better-informed decisions.
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Introduction
401(k) holdings are projected to become the largest asset an individual owns, with
the possible exception of his/her home (Sahadi (2001)). As a result, the financial security
of most individuals’ retirements will depend on how well their 401(k) portfolio has
performed. Thus, the importance of an individual’s asset allocation choices cannot be
overstated. As the debate over Social Security moves towards private accounts, these
allocation decisions take on even greater significance. Unfortunately, empirical research
focusing on the quality of asset allocation choices has been difficult to conduct in the past
because of a lack of detailed individual level data. This paper overcomes this obstacle by
taking advantage of a newly available database from one 401(k) plan with over 73,000
eligible participants. The fine level of detail in these data provides a unique opportunity
to analyze two potentially inefficient and commonly made retirement choices in 401(k)
plans: over-investing in company stock and following naïve diversification strategies.
While the influence of plan design on these decisions has already been documented, this
research contributes to the literature by highlighting how individual characteristics, such
as age, salary, job tenure and gender, relate to the efficiency of allocation decisions. It is
the first study to examine these two issues in one paper.
The perils of over-investing in company stock are well known as a result of several
recent high profile cases, including Enron, Lucent and WorldCom, where many
individuals lost most of their 401(k) nest eggs by following this strategy. Given the
benefits of diversification, it has long been a puzzle why so many individuals invest a
substantial amount of their retirement funds in the stock of their own company. Not only
are they concentrating their assets in a single stock, which is more risky than a well-
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diversified portfolio, but they are investing in a security that is highly correlated with
their own human capital. The risks of allocating a large portion of an individual’s
portfolio to company stock or even more simply to just one stock are so great that
legislation limits such investments in defined benefit plans and mutual funds.1 Yet
despite these laws and evidence that individuals are prone to over-invest in company
stock, the majority of 401(k) plans (80 percent) that offer company stock place no
restrictions at all on company stock allocations (Dugas (2000)).
Given the absence of restrictions, understanding what factors might lead an investor
to over-invest in company stock is important. The influence of past company stock
performance and plan design on company stock holding is already well documented in
the literature. Benartzi (2001) finds that company stock holdings are higher for
companies with relatively strong long-run stock performance and for companies with
employer stock only matches. However, until now, no one has tested for an additional
link between individual characteristics and company stock allocations. This paper fills
this gap. It is the first paper to jointly test the significance of past company stock
performance and demographic factors on company stock allocations.
In addition to investigating the determinants of company stock holdings, this paper
also examines the practice of naïve diversification strategies. The psychology literature
predicts that naïve diversification strategies will result when individuals are faced with
complicated decisions. The complexities of these decisions cause them to fall back on
simple rules of thumb. This paper investigates one particular strategy, the “1/n heuristic”,
studied by Bernatzi and Thaler (2001). According to this strategy, some 401(k) investors
overwhelmed by their investment choices will choose to simply divide their contributions
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evenly among the n investment options offered. They do so regardless of the type of
investment options they are given. While it can be argued that this rule of thumb will
often lead to a diversified portfolio, Benartzi and Thaler (2001) show that it can also lead
to large ex ante welfare losses when the portfolio chosen does not correspond to the
individual’s risk preferences.2 This paper investigates the extent to which individuals
follow this rule in this plan and if individual characteristics matter in this decision.
Finally, this paper investigates whether individuals treat company stock as a separate
asset class from other equities. Benartzi and Thaler (2001) find evidence supporting this
practice using aggregate 401(k) plan data. As a result when company stock is an option in
a 401(k) plan, Benartzi and Thaler (2001) predict that participants will choose to divide
their non-company stock contributions evenly among the non-company stock options. In
this paper, I call this the modified 1/n heuristic.
Benartzi and Thaler (2001) test their prediction using a sample of 103 401(k) plans
offering company stock and 67 plans that do not offer company stock. They find that the
mean allocations of the asset balances for the plans not offering company stock are split
approximately 50/50 between equities and fixed income. In contrast, they find that the
mean allocation to equities is over 71 percent when company stock is an option. Looking
closer, they find an average allocation of 42 percent to company stock. The remainder is
divided almost evenly between non-company stock equities (29 percent) and fixed
income (28 percent). This supports the modified 1/n heuristic.
Treating company stock as a separate account does have theoretical foundations.
This investment behavior is consistent with Shefrin and Statman’s (2000) multi-account
behavioral portfolio theory.3 According to their theory, individuals have difficulty
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processing covariances and other properties related to joint probability distributions so
they simplify their decision making by separating their assets into different mental
“accounts”. They ignore any correlation between these accounts when making their
portfolio decisions. In the case of 401(k) plans with company stock, it appears that
individuals are ignoring the correlation between their “company stock account” and their
“other financial investment account”.
The detail of the individual level data in this paper allows for a stronger test of the
modified 1/n heuristic. In addition, the data in this study avoid problems associated with
“allocation drift” of asset balances because the allocations are based on contribution
allocations.
Three main results emerge from the analysis of company stock investments. First, the
company stock investment patterns of individuals tend to be multimodal, with 78 percent
of the sample centered on allocations of 0, 25, 50, 75 and 100 percent. Second, over 75
percent of the individuals invest more in company stock than the maximum limit of 10
percent permitted by law in defined benefit plans. Third, results from ordered probit
regressions that control for past company stock performance suggest that the probability
of over-investing in company stock for the average participant is greater for males,
decreases with salary and is lower for corporate division workers.
The results of the analysis of the 1/n heuristic indicate that some individuals do
appear to follow the 1/n heuristic. However, the percentage is not as large as that found in
Benartzi and Thaler’s (2001) survey results. Kernel densities suggest that individuals are
treating company stock investment as a separate investment from other equities
confirming Benartzi and Thaler’s work. Finally, regression analysis results suggest that
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the probability of following the 1/n heuristic decreases with increases in job tenure and
salary/compensation status. Interestingly, individuals earning relatively higher salaries
tend to make more efficient decision related to both their company stock allocations and
diversification strategies than others.
The remainder of the paper is organized as follows. Section I summarizes the data set.
Section II describes the plan design and asset allocation choices. Section III discusses the
participation level in this plan and provides an overview of the possible reasons why it is
relatively low. Section IV summarizes the demographic and employment characteristics
of the actively contributing participants. Section V and VI present the empirical results
associated with company stock holdings and naïve diversification, respectively. Section
VII concludes.
I.
Data
This paper uses a detailed database supplied by CitiStreet. The cross-sectional data
are from one large 401(k) plan with over 73,000 eligible employees.4 The plan is
sponsored by a global consumer product company. During the first two weeks of August
1998, 28,809 of the eligible participants made contributions. For the purpose of this
study, these participants are considered “active” participants. The data set includes each
active participant’s contribution allocations and, for most participants, the actual date this
allocation was chosen.
CitiStreet took over administration of this 401(k) plan in 1992. As a result, some data
are missing for participants who entered the plan prior to the administration change. In
particular, the actual date the participant made their allocation decision is unavailable for
5,814 participants who were employed prior to 1992 and did not change their
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contribution allocations during State Street’s tenure. An indicator variable identifies these
individuals so that the later analysis can control for the possible effects of administration
style on asset allocation decisions. For these individuals, the date they chose their
contribution allocation is estimated as either the date of employment or the date the plan
began in 1983, whichever is later.
Since these individuals did not change their
allocations between 1992-1998, it seems reasonable to assume that they did not actively
change their allocations prior to 1992. Therefore, their current allocations are most likely
unchanged from the initial allocation decision they made when they first entered the plan.
For each allocation decision date, the past company stock returns over several buy and
hold periods are calculated.
One of the important features of these data is that detailed demographic information
is available for each eligible participant in the plan including each individual’s
participation status, salary, birthdate, date of employment, compensation status, and
gender. For the empirical analysis, age and time employed are calculated based on the
allocation decision date.
This data set has three noteworthy features. First, the asset allocations of the
contributions are broken down at the individual level. Aggregate contribution plan data
can blur the results if high contributing participants invest differently than low
contributing participants. The effect of large contribution levels is analogous to the
influence of large market capitalization stocks on a value-weighted index. Second, the
data are from one plan. While multiple plan data are appropriate for studying across-plan
variation, they can create a potential for omitted variable bias related to plan design or
plan educational efforts. Analyzing one plan eliminates this concern. A final advantage of
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the data is that allocations are based on contributions not asset balances. Asset
performance can move asset allocations based on asset balances away from the
participant’s intended allocation. Contribution allocations do not suffer from this
potential bias.
A disadvantage of these data is that information regarding participants’ assets outside
of the plan is not available. However, the evidence suggests that investors tend to invest
their retirement savings in the same fashion as their non-retirement assets
(Uccello(2000)). Another drawback of the data set is that it is missing some variables
that have been shown to impact asset allocation decisions: such as marital status,
education and financial literacy (eg. Agnew, Balduzzi and Sunden (2001), Sunden and
Surrette (1998), Dwyer, Gilkeson and List (2000)).
II.
Plan Design and Asset Choices
In this plan, each participant may allocate his/her retirement fund contributions
among four different investment vehicles: an equity income fund, an S&P 500 index
fund, a guaranteed income contract fund (GIC), and company stock. Participants have the
option to change their contribution allocations daily. The company offers no financial
incentive for investing in company stock nor do they offer an employer match. The
absence of an employer match is an advantage because it eliminates any confounding
effects caused by the match design.
III.
Plan Participation
Of the 73,721 eligible participants, 39 percent made at least one contribution
during the first two weeks of August 1998. This participation rate is low compared to
other studies.5 The low participation rate observed in this plan might be a result of several
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factors shown to decrease participation in the academic literature. One of the main
reasons might be that the plan does not offer an employer match (Munnell, Sunden, and
Taylor (2000), Papke and Poterba (1995)). Another is that the company offers a defined
benefit plan. Many studies (e.g. Andrews (1992), Bernheim and Garrett (1996)) have
shown that employees tend to participate less in their 401(k) plan if their company offers
a pension plan. Another possible factor is the relatively large size of this plan. This plan
is considered part of the large plan market (over 25,000 participants) and Clark and
Schieber (1998) find that the probability of participation decreases with the size of the
company. On the other hand, the plan sponsor did offer educational services, including
seminars and literature. These forms of corporate communication and education have
been shown to increase levels of participation (Munnell, Sunden and Taylor (2000),
Clark and Schieber (1998), Bernheim and Garrett (1996)). It is unclear how these
educational efforts affected participation in this plan. Finally, the definition of active
participant in this study is fairly restrictive because it limits participants to those who
made a contribution during the first two weeks of August 1998. Other studies use
different definitions. For example, Clark and Schieber (1998) define an active participant
as a person who made at least one contribution in the year 1994.
IV.
Demographic and Employment Characteristics of Active Participants
Panel A of Table I describes the demographic and employment characteristics of
the active participants. Age and time employed are measured as of August 1998, while
salary is the 1997 annual salary. Individuals in this data sample are predominately male
(78 percent) with an average age of 39 years old. It is noteworthy that the participants
have relatively long average job tenures (10 years), which may indicate strong company
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loyalty. Interestingly, the median time employed is approximately eight and half years
and is over double the 1996 national median of nearly four years (CPS (1997)). In the
plan, nine percent of the sample are considered highly compensated individuals. This is a
legal designation based on several factors including salary. This status affects how much
a participant can contribute but does not restrict their allocation decisions.
Participants in the company work in one of four different divisions with the
majority of the participants (99 percent) working in two large consumer product
manufacturing divisions, “Division 1” and “Division 2”.
The “Corporate Division”
employs 1% of the 401(k) participants and under 100 employees work for the “Other
Division”.
Participants earned mean 1997 salaries of approximately $46,000. Panel B of Table I
compares the plan’s median salary by age group to the median salary of the U.S.
population. The table shows that participants in this plan earn more than the general
population. However, the relationship between salary and age is similar between the two
groups with the exception of the 65+ age group. The discrepancy in the 65+ group may
be due to the limited number of participants (29) in this age group in this data set.
Table II describes the demographic characteristics by division. The main difference
between the four divisions appears to be the salary distributions. Employees of the two
smallest divisions make significantly higher salaries than the other divisions. The
Corporate Division’s mean salary is approximately $107,000, while the Other Division’s
mean salary is nearly $140,000. These salaries compare to approximately $48,000 and
$44,000 earned in Division 1 and 2, respectively. Employees in the two small divisions
also earn significantly more in the tenth and ninetieth percentiles of their sample and they
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are more likely to be highly compensated individuals.
Except for the Corporate
Division, the divisions are predominately male. The groups do not differ significantly in
terms of average age or time employed.
V.
Company Stock Allocations
A. General Findings
Consistent with anecdotal evidence, participants in this 401(k) plan show a tendency
to over-invest in company stock. The overall mean allocation to company stock holdings
in this plan is quite high (49 percent) compared to the 10 percent legal maximum defined
benefit plans may hold. The large average allocation might be partially explained by the
above normal price performance of the plan’s company stock. In this study, the company
stock had an annualized stock price return of 20.6 percent over the 10-year period ending
on December 31, 1997, compared to a S&P 500’s annual return of 14.7 percent over the
same time period. Benartzi (2001) shows that firms with relatively high returns over the
previous ten years have higher company stock allocations than poor performing firms.
This finding motivates why past company stock performance is controlled for in the later
regression analysis.
The general patterns of company stock allocations also deserve mention. One
interesting feature of the data is that despite the absence of restrictions on the
participants’ allocations, 78 percent of the allocations are clustered within one percentage
point of zero, 25, 50, 75 and 100 percent. Furthermore, there is a clear tendency for
many of the participants (52 percent) to invest either all or none of their contributions to
company stock.
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B. Nonparametric Analysis
Some interesting trends in company stock allocations emerge when these allocations
are summarized based on the participant’s demographic characteristics. This is not
surprising because demographic characteristics can proxy for several factors that can
affect a participant’s company stock holdings including financial knowledge, nonretirement company stock holdings, risk preferences, company loyalty, and perceived
influence and knowledge of the company. This section will describe in detail why these
demographic characteristics could proxy for these factors. It presents a “nonparametric”
analysis of the data that will complement the regression analysis to follow.
Table III reports the company stock allocations based on demographic characteristics.
The non-normal distribution of the company stock holdings makes standard summary
statistics, such as means and standard deviations, less meaningful descriptors of the data.
Therefore, in addition to these statistics, Table III reports the proportion of each
demographic category that invests in six different investment ranges: zero percent, 1-25
percent, 26-50 percent, 51-75 percent, 76-99 percent, and 100 percent. A simple test of
proportions within each demographic category and investment range is used to test
whether a statistically significant difference exists. If demographic characteristics do not
matter, then a statistically significant difference in proportions should not be found. For
example, under the null hypothesis gender does not matter. Therefore, the proportion of
women investing 100 percent of their contributions to company stock should not be
statistically different than the proportion of men investing 100 percent of their
contribution to company stock. Notice that within each demographic category in Table
III the top row is bolded. This row is considered the base category.
For each
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demographic group this base category is used in each test of proportions. Table III reports
the results of the test of proportions. Two (one) stars beside the proportions denote a
statistically significant difference from the base category at the one (five) percent level.
The first demographic category tested is gender. Empirical evidence suggests that
gender may proxy for financial education or risk tolerance. For example, research shows
that when a measure of financial education is not available, gender may serve as an
effective proxy for it. Dwyer, Gilkeson and List (2000) find that women typically have
less financial knowledge than men and that the educational disparities can substantially
explain the gender differences they find in risky mutual fund allocations.
Indeed, there is broad evidence suggesting that individuals overall lack a general
understanding of the risks associated with company stock investment and that education
may explain much of the variation in financial aptitude.
A recent John Hancock
Financial Services’ survey highlights how individuals misread the risks of the market. In
the survey, respondents on average thought that a diversified stock fund was more risky
than investment in company stock. Benartzi (2001) reports an equally disturbing result
that 84% of respondents to a Morningstar survey believe that the overall stock market is
riskier than company stock. When this sample is limited to individuals with high school
education or less, this number increases to 94%.
Therefore if gender proxies for
differences in education, men might be expected to invest less in company stock than
women. On the other hand, empirical research has found that men are more likely to
invest in riskier assets than women leading to the opposite conclusion (for example,
Sunden and Surette (1998), Hinz, McCarthy and Turner (1997), Agnew, Balduzzi and
Sunden (2001), Barber and Odean (2001)).
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The tests of proportions support the latter. In all but the 51-75% range, there is a
statistically significant (albeit economically small) difference in the proportion of men
investing in each investment range than women. The most pronounced difference
between the proportion of women and men investing in company stock is at the 100
percent investment range. Observe that 29 percent of the men allocate their entire
contribution to company stock compared to 26 percent of the women and that this
difference is significant at the one percent level. Furthermore, the mean allocation to
company stock by men is 50% compared to 47% for women. Interestingly, this gender
difference is smaller than that found by Clark, Goodfellow, Shieber and Warwick (2000).
In their study of several 401(k) plans, men invested an average 41% to company stock
compared to 27% for women. However, these gender differences could be a result of
different plan designs or varied long run company stock performance across plans.
The next two sections of the table demonstrate the influence of compensation level,
either salary or compensation status, on company stock investment. Compensation level
is another potential proxy for financial knowledge. Generally, financial knowledge is
considered positively related to compensation. This leads to the hypothesis that
employees who earn relatively high salaries or are considered highly compensated should
hold less in company stock.
Alternatively, compensation may be proxying for an employee’s opportunities for
stock based compensation. Generally, greater opportunities exist for higher salaried
employees to receive stock based compensation than for their lower wage counterparts.
This is the case in this plan where three stock option plans are offered. One plan is open
to all full-time employees and the number of options available is based on earnings. The
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second and third plans are targeted at middle and senior management. The options in
these plans are based on reaching performance goals. Thus, higher salaried and middle
and upper management employees have more opportunities to earn stock options than
lower salaried employees. Research shows that highly paid executives are concerned
about diversifying their company stock holdings but are often reluctant to sell their stock
based compensation. As a result they are finding sophisticated ways to hedge their
holdings. Results from one recent paper suggest that executives diversify their company
stock holdings through the use of zero cost collars and equity swaps (Ofek and Yermack
(2000)). Additional research shows that executives with high stock ownership negate
much of the impact from their stock compensation by selling previously owned shares
(Bettis, Bizjak and Lemmon (2000)). Given the demonstrated lengths that these
employees go to diversify their holdings, one might expect that these employees will hold
smaller amounts of company stock in their 401(k) accounts.
The results support both theories. Table III shows a decrease from the lowest wage
category to the highest wage category in the proportion of individuals allocating their
entire contribution to company stock that is significant at the one percent level. Twenty
eight percent of the under $25,000 category invest their whole contribution to company
stock compared to 24 percent of the $100,000 plus category. The reverse trend is
observed in the proportion of individuals who invest nothing in company stock. Here, 23
percent of the under $25,000 category invest nothing in company stock compared to 36
percent of the over $100,000 group. This difference in proportions is significant at the
one percent level. This supports results from Goodfellow and Schieber’s (1997) study of
24 different plans where low-wage earners were more likely to hold company stock than
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high-wage earners. Table III also shows fewer of the highly compensated individuals
allocating all of their contributions to company stock and more of these individuals
allocating none of their contributions to company stock.
Similar to gender, age may proxy for risk tolerance. Many life cycle theories
predict that individuals will hold less risk in their financial portfolio as they age.
Jagannathan and Kocherlachota (1996) suggest that young investors have a long stream
of future income. As individuals age, this stream of future income shortens diminishing
the value of their human capital. Therefore, they suggest that individuals should offset
this decline in the value of their human capital by reducing the risk of their financial
portfolio. Bodie, Merton, and Samuelson’s (1992) model leads to a similar prediction. In
their model, individuals can respond to low realized asset returns by increasing their
supply of labor. However, labor flexibility generally declines with age. Therefore, like
the previous model, older individuals are expected to hold more conservative investments
in their financial portfolios.
Table III is consistent with the stated life cycle hypotheses. Note that in Table III,
age is measured at the time the allocation decision is made. The 65 plus age category will
not be discussed because it includes only 6 participants. Notice the downward trend as
individuals age in the proportion of participants investing their entire contribution to
company stock. On the extreme ends, 19 percent of those between 55-64 years old invest
their entire contribution to company stock compared to 31 percent of the participants
under 35 years old. The difference in proportions is significant at the one percent level.
This trend is reversed and significant in the proportions investing nothing in company
stock.
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Time employed may also proxy for risk tolerance. One hypothesis is that a
participant’s human capital is more stable the longer the individual is employed.
Therefore, employees with longer job tenures may choose to invest more in company
stock. An alternative hypothesis is that individuals with long job tenures may feel that
they have more influence on the company’s performance than new employees do so they
invest more. Finally, the length of an employee’s tenure may be a sign of company
loyalty or familiarity with the company. This also leads to the prediction of a positive
relationship.
The final hypothesis is based on Huberman’s (1998) work. Huberman coined the
phrase “familiarity bias” to describe the tendency of investors to invest heavily in what
they know. He suggests that this is a reason for high company stock holdings in 401(k)
plans. However, Benartzi (2001) presents conflicting empirical evidence that shows that
the impact of familiarity on company stock holdings is insignificant when past company
stock performance is included in the regression analysis.
Table III results report a negative relationship between time employed and company
stock holdings which is contrary to the predictions of all three theories. Here the
proportion of participants investing their entire contribution to company stock has a
marked decline with time employed. Thirty four percent of those with less than two
years experience invest their entire contribution to company stock compared to 22
percent of those with greater than 26 years experience. It is not surprising that these
results are similar to the age findings because these variables are most likely highly
correlated.
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The results show that the employee’s company division also explains some variation
in company stock holdings. One possible explanation for this is that there might be a
significant difference in the predominate occupation of the employees in each division.
Among other things, occupation type might proxy for the probability of earning stock
based compensation. For example, a corporate division may be more heavily
concentrated with executives who earn greater stock based compensation than employees
of a division predominately comprised of factory workers. Thus, the expected average
allocation to company stock would be relatively lower in the corporate division compared
to the other division. The occupation type may also provide additional information about
the employee’s education level beyond that obtained from salary information. It seems
reasonable to assume that a corporate division may be more heavily comprised of
executives with college degrees, while a factory division may have a high percentage of
blue-collar workers who are predominately high school graduates. On the other hand, the
division variables may also proxy for many other unobservables so care must be taken
not to over interpret these results.
In this study, the predominate occupation does differ between divisions. A discussion
with CitiStreet indicates that the Corporate Division consists mainly of executives, while
the employees of Division 1 and Division 2 tend to be factory workers. As predicted,
Table III shows the Corporate Division has the lowest proportion of individuals investing
their entire contribution to company stock and the highest proportion of individuals who
invest nothing in company stock. These results support the theory that either the
executives in the Corporate Division are limiting their company stock holdings to
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compensate for stock based compensation or they are doing so because they have a
relatively better understanding of the inherent risks of company stock investment.
Finally, an indicator variable highlights the participants that enrolled in the plan prior
to CitiStreet’s administration and did not make allocations during CitiStreet’s tenure.
This variable controls for the possible influence of plan administration style. Observe that
the difference in the proportions is striking and statistically significant at every
investment range between the two groups. For example, 50 percent of those who made
no allocation changes during CitiStreet’s tenure invested their entire contribution to
company stock compared to 23 percent of those who did make a change or entered the
plan during CitiStreet’s tenure. This finding strongly supports the use of this variable as
a control variable in the following regression analysis.
C. Econometric Analysis of Company Stock Holdings
The nonparametric evidence suggests that there are relationships between the
demographic variables and company stock holdings. This section will econometrically
test for the joint effects of these factors on company stock allocations. In addition, it will
control for the effects of past company stock performance.
Generally, a two-limit censored regression model is used in studies of asset
allocations. For example, Agnew, Balduzzi and Sunden (2001) use this model to study
the relationship between demographic characteristics and equity allocations in one 401(k)
plan. However, given the prevalence of company stock allocations clustered at 0, 25, 50,
75 and 100 percent, an ordered probit regression seems more appropriate for these data.
Therefore for the econometric analysis, the company stock allocations are grouped into
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six categories (0%, 1-25%, 26-50%, 51%-75%, 76%-99%, 100%) and an ordered probit
regression is used to study the effects of the individual characteristics on company stock
allocations. 6
Table IV reports the marginal effects from the ordered probit regression for each asset
allocation range. For the average participant, the marginal effects show the change in
probability of staying in that investment range given a small change in the independent
variable. In the case of indicator variables, the marginal effect is for a discrete change of
the indicator variable from zero to one.
It is clear that most of the economically significant variation is at the extreme
investment ranges (0% and 100%). The intermediate investment ranges marginal effects
while statistically significant are not economically meaningful. Therefore, the discussion
will concentrate on the 100 percent range. The results suggest that men are 3.3 percent
more likely to invest their entire contributions to company stock than women, supporting
the theory that men tend to make more risky asset allocation choices. Salary is also
significantly related to company stock holdings. The results suggest that an average
employee earning $100,000 is 3.7 percent less likely to invest his/her entire contribution
to company stock than an average employee earning $40,000. In this case, salary may be
a proxy for financial education or the amount of stock based compensation. Given the
nonparametric results, it is not surprising that individuals who made their allocation
decision during the previous administrator’s tenure are 20 percent more likely to invest
everything in company stock.
The division of employment also has a significant role in company stock holdings.
Relative to the Corporate Division, participants in Division 1 are 4 percent more likely to
21
invest in company stock. Similarly, participants in Division 2 are 10 percent more likely.
The results support the hypothesis that either the executives in the Corporate Division are
limiting their company stock holdings to compensate for stock based compensation or
they are limiting their company stock holdings because they have a relatively better
understanding of the inherent risks in company stock investment. Interestingly, age and
time employed are not significantly related to company stock holdings.
Finally, the results support Benartzi’s (2001) findings that past raw buy and hold
returns are positively related to company stock holdings.6 The reported regression
includes one year buy and hold company stock returns measured prior to each
individual’s allocation decision date. The sample returns range from a minimum of
negative 26 percent to a maximum of 86 percent. The average return is 26 percent, with a
standard deviation of 21 percent. The regression predicts that a 10 percent increase in the
one year return of the company stock relevant to its sample average increases the
probability of investing the entire contribution to company stock by 1.6 percent.
VI. Naïve Diversification
A. General Findings
The analysis now shifts from a study of the factors related to a participant overinvesting in company stock, to the factors related to the practice of naïve diversification
strategies. One of the main findings is that the frequency of participants following the 1/n
heuristic is less than the percentage found in survey tests conducted by Benartzi and
Thaler (2001). In their study, several different surveys were mailed to University of
California employees. The surveys asked the employees how they would allocate their
investments to a selection of funds. The results vary with the investment choices offered
22
but, in general, over 20 percent of each surveyed group chose the 1/n option. In this
study less than four percent follow the 1/n heuristic and five percent follow the modified
1/n heuristic. In fact, most participants (41 percent) allocate their entire contribution to
only one fund. Looking closer, the majority (70 percent) of those participants that invest
in only one fund invest their entire contribution to company stock. The percent of the
sample decreases with the number of funds held. A little under twelve percent hold all
four funds.
One possible explanation for why these results differ from previous empirical work is
that the participant’s choice may be influenced by the manner in which the allocations are
selected. In Benartzi and Thaler’s (2001) survey, participants selected their allocations by
filling out a form with the possible investment choices listed. In this study’s plan,
individuals chose allocations over the phone using an automated system. Interestingly,
the company stock option was the last option described on the phone. The ordering of
the company stock option might have contributed to its popularity. There is some
psychology literature that suggests that the ordering of choices influences decision
making, with either the options listed first (primacy effects) or listed last (recency effects)
having the largest influence. Understanding how these two approaches to allocation
selection ultimately influence the participant’s final choice is an interesting area for
future research.
23
B. The Modified 1/n Heuristic
Using aggregate data, Benartzi and Thaler (2001) find evidence that individuals treat
company stock as a separate asset class from other 401(k) investments. As a result, the
participants tend to split their non-company stock investment evenly among the noncompany stock options. This paper refers to this practice as the modified 1/n heuristic.
This section investigates whether similar behavior applies to this plan.
This analysis complements previous work because it provides a stronger test of this
practice. It is a stronger test for two reasons. First, the tests in this paper are based on
contribution allocations rather than asset balance allocations. Therefore, the influence of
fund performance on allocations is not a concern. Second, the individual level data allows
for the calculation of the allocation of non-company stock holdings by individual rather
than by plan. This permits the examination of the distribution of company stock holdings
across individuals.
The analysis begins with an examination of the mean and median allocations to each
fund in Table V. The first two columns of Table V list the mean and median allocations
to each fund and the last two columns list the adjusted mean and median allocations to
each fund. The adjusted allocations are simply the percent allocated to the particular noncompany stock investment vehicle divided by the total invested in non-company stock
investment vehicles. The first subsample includes all the participants that invest in all
four funds and comprises roughly eleven percent of the sample. Notice that the adjusted
allocations are very close to 33.3%, which equates to evenly splitting the non-company
stock contributions among the non-company stock assets. The same exercise is repeated
24
for subsamples of investors that hold three funds (including company stock). The results
again support the modified 1/n with the adjusted allocations close to 50 percent.
Kernel densities further support the findings. Panel A of Figure 1 displays a kernel
density representing company stock holdings and adjusted and unadjusted kernel
densities for the holdings of the three non-company stock investment vehicles. These
densities are drawn from the sample of participants who invest in all four funds. As
expected, the company stock density shows a multimodal distribution. The spikes at zero
and one are no longer observed because the sample is restricted to those who invest in all
four funds. Therefore, a zero or 100 percent allocation to company stock, or any
investment vehicle for that matter, is not possible.
Looking at the three other investment vehicle kernel densities, the difference is
striking between the unadjusted (denoted by a line with triangles) and the adjusted
(denoted by a line with squares) kernel densities. The unadjusted kernel densities for the
non-company stock funds have several probable allocations. However, the adjusted
distributions are strongly centered at 33%. This percentage equals the 1/n allocation an
investor would choose if allocating between three funds. This implies that after adjusting
for company stock holdings, these individuals tend to allocate their remaining assets
evenly among the other funds. This finding strongly supports Benartzi and Thaler’s
(2001) assertion that some individuals treat company stock as a separate asset class and
as a result slightly modify how they follow the 1/n rule.
Panels B-D repeat the exercise for subsamples of participants holding company stock
and two other funds. The results for Panel B and D are very similar to the earlier findings.
As expected, the adjusted kernel densities are centered at 50 percent.
25
C. Econometric Analysis
The final empirical question is what type of person is most likely to follow the 1/n
heuristic? To test this a dummy variable that equals one if the individual follows the 1/n
heuristic and zero if not is constructed. An additional dummy variable is created to take
into account the impact of the company stock option on the 1/n rule. This additional
dummy variable is constructed based on the modified 1/n heuristic.
Tables VI displays the results of probit analysis using the two different 1/n dummy
variables. The marginal effects of salary and employment tenure are significant and
negative for both regressions. This suggests that high salary individuals and participants
with longer job tenure are less likely to follow the 1/n rule. In both regressions, the
average employee earning $100,000 is nearly three percent less likely to follow the 1/n
rule than an average employee earning $40,000. One theory is that the higher salaried
individuals are more educated and thus less likely to rely on simple rules for investing. It
is not clear why the employees with longer job tenures are less likely to follow the 1/n
rule.
VII.
Conclusion
This paper focuses on two potentially inefficient and commonly made allocation
choices in 401(k) plans: over-investing in company stock and following naïve
diversification strategies. Given the pivotal role of 401(k) savings on an individual’s
retirement, a better understanding of who may make these uninformed allocation
decisions is important. This research contributes to the literature by highlighting what
types of individuals are most likely to make these inefficient choices. The results can help
26
plan sponsors target high risk individuals and improve plan design, as well as inform the
current Social Security debate.
Three important results emerge from the company stock analysis. First,
employees tend to cluster their allocations at zero, 25, 50, 75 and 100 percent. Empirical
researchers should bear this in mind before applying standard econometric techniques to
allocation data. Second, in this plan the tendency to invest in more company stock than
the recommended limit is high. Third, demographic and employment characteristics
affect company stock allocations. Results of regressions that control for past company
stock performance suggest that the probability of over-investing in company stock for the
average participant is greater for males, decreases with salary and is lower for corporate
division workers.
The investigation of whether employees follow the 1/n heuristic confirms that
investors tend to treat company stock as a separate account. While the percent of the
individuals who follow the 1/n heuristic is lower than that found in previous studies, it
still represents 5% of the participants in this study. Regression results suggest that highly
compensated individuals are less likely to invest follow the 1/n heuristic, as well as
employees with relatively long job tenures.
Interestingly, the results show that individuals earning relatively higher salaries tend
to make more efficient decisions related to both their company stock allocations and
diversification strategies than others. Policy makers and plan sponsors should bear this in
mind. After all, even though the Social Security system provides higher replacement
ratios for individuals with relatively lower incomes, lower income participants will most
27
likely depend the most on their 401(k) savings during retirement. This research shows
that this group tends to make the most inefficient choices.
28
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31
Endnotes
1
For example, the law restricts professional managers from investing more than 10% of a
company’s defined benefit assets in the company’s own stock and the SEC requires that
“diversified” mutual funds invest no more than 5 percent of assets in one company’s
stock. This is with respect to 75 percent of the portfolio’s assets. In addition, Meulbroek
(2002) demonstrates that holding company stock is inefficient for all employees
regardless of an individual’s level of risk tolerance.
2
To illustrate this, suppose that a 401(k) offers ten investment choices that include nine
equity funds and one money market fund. An individual following the 1/n heuristic,
would allocate 10% of their contributions to each fund resulting in a 90% allocation to
equities. It is clear that this allocation would not be optimal for everyone especially a
participant nearing retirement.
3
Thaler (1999) provides an excellent review of the mental accounting literature. He
refers to mental accounting as “the set of cognitive operations used by individuals and
households to organize, evaluate, and keep track of financial activities”. Shefrin and
Statman (2000) apply this concept to their portfolio theory.
4
An eligible employee is an employee that may participate in the 401(k) plan if he/she
chooses.
5
For example, Clark and Schieber’s (1998) found that on average 73.5% of eligible
employees participated in their 401(k) plans in their analysis of plan data from 19 firms
with 700 to 10,000 employees. Similarly, Munnell, Sunden, and Taylor (2000) report a
72% mean participation rate among eligible employees using the 1998 Survey of
Consumer Finances data.
6
Results from the less sensible tobit regression are available upon request. They support
the ordered probit findings.
7
Additional ordered probit regressions that include raw buy and hold returns calculated
over different periods ranging from two to ten years are available. The regression that
includes the one year returns is reported because it produced the highest pseudo rsquared.
32
Table I. Descriptive Plan Statistics
Panel A. General Statistics
This table describes general statistics concerning the plan participants: contribution status (as of August
1998), gender, age in years (as of August 1998), time employed in years (as of August 1998), compensation
status, division of employment and 1997 annual salary.
Obs
%
Contribution Status
Participants Not Contributing
Participants Contributing
Total Eligible Participants
Gender
Male
Female
Age
44,912
28,809
73,721
61%
39%
100%
22,550
6,259
28,809
78%
22%
Years Employed
28,809
Mean
Std
Min
Max
39.41
8.88
18.92
70.88
10.22
7.68
0.10
47.96
Highly Compensated Individual
Yes
2,452
9%
No
26,357
91%
Division
Corporate
325
1%
Division 1
11,964
42%
Division 2
16,449
57%
Other
71
0%
Salary
28,809
$ 46,410
$ 31,167
$15,600
$1,675,025
Panel B. Comparison of Age-Salary Structure for U.S. Population and 401(k) Sample
The table presents a comparison between the median salary by age group for the U.S. population at large
and the 401(k) plan participants. The source for the U.S. population is CPS 1997.
Age Range
Under 35 years old
35-44 years old
45-54 years old
55-64 years old
65+ years old
Median 1997 Salary:
U.S. Population*
$22,846
$30,880
$33,106
$29,434
$21,032
Median 1997 Salary:
401(k) Plan
$37,038
$40,755
$40,555
$39,068
$37,337
*Source: CPS 1997
33
Table II. Descriptive Plan Statistics by Division
This table breaks down each division by demographic information: gender, 1997 annual salary, age (as of
August 1998), time employed (as of August 1998), time enrolled in the plan (as of August 1998) and
compensation status. HCE stands for highly compensated individual.
Division
Number of
Employees
Corporate
Division 1
Division 2
Other
Mean Age
(Years)
48%
81%
77%
89%
43.05
38.34
40.11
41.72
325
11,964
16,449
71
Division
Corporate
Division 1
Division 2
Other
% of Division
Male
Median
Salary
$
$
$
$
70,000
39,750
38,905
160,000
Mean Time
% Division
Employed 100% Invested
(Years)
in Company
Stock
12.29
16%
10.52
23%
9.95
33%
11.49
25%
Mean Salary
Salary-10th Salary- 90th % of Division
Percentile
Percentile
HCE
$
$
$
$
$
$
$
$
107,397
47,866
43,743
139,563
36,000
25,953
26,104
99,800
$
$
$
$
233,000
73,790
63,659
160,000
45%
10%
6%
99%
34
Table III. Summary Statistics of Company Stock Holdings
This table reports summary statistics for company stock holdings based on demographic characteristics. In
addition to the mean and median allocations, the table presents the proportion of each demographic
category invested in each of the six investment ranges. The first row of each demographic category
(bolded) is considered the base category. Within each investment range and demographic category, a test of
proportions is run. ** (*) stars beside the proportions denote a statistically significant difference from the
base category at the one (five) percent level.
Demographic
Category
All
Sort by Gender:
Male
Female
Annual Salary:
Under $25,000
$25,000-$49,000
$50,000-$74,999
$75,000-$99,999
$100,000+
Highly Compensated
Individual:
Yes
No
Age:
Under 35 years old
35-44 years old
45-54 years old
55-64 years old
65+ years old
Time Employed:
0-2 years
3-5 years
6-10 years
11-15 years
16-20 years
20-25 years
26-50 years
Division:
Corporate
Other
Division 1
Division 2
Prior Indicator:
No
Yes
Obs.
Percent of Sample Within Each Investment
Range
0%
28,809 23%
1-25% 26-50% 51-75% 76-99% 100%
13%
26%
7%
2%
29%
Company
Stock
Allocation
Median Mean
50%
49%
22,550 23% 13% 26% 7%
6,259 24% * 15%** 27% * 7%
2%
2% *
29%
26%**
50%
50%
50%
47%
2,218
19,526
4,671
1,148
1,246
1%
2% *
2% *
1%
1%
28%
30% *
26% *
22%**
24%**
50%
50%
50%
35%
30%
48%
51%
47%
42%
41%
23%
22%
22%
30%**
36%**
16%
13%**
15%
14%
11%**
26%
26%
28%
26%
22%**
6%
7%
7% *
7%
6%
2,452 30% 12%
26,357 23%** 14%
24% 7%
26% * 7%
2%
2%
25%
29%**
40%
50%
44%
50%
15,180
9,562
3,377
684
6
21%
25%**
28%**
35%**
67%**
13%
14%
13%
13%
0%
26%
26%
27%
26%
33%
7%
7%
5%**
5% *
0%
2%
2%**
2%
1%
0%
31%
27%**
25%**
19%**
0%
50%
50%
40%
30%
0%
52%
47%
45%
38%
14%
11,133
5,362
5,306
3,227
2,209
988
584
19%
22%**
24%**
28%**
30%**
32%**
35%**
14%
15%
13%
13%
12% *
13%
10% *
25%
27% *
27% *
27%
26%
25%
27%
6%
7% *
8%**
7%**
7% *
5%
4% *
2%
2% *
3%**
2%
2%
1%
2%
34%
27%**
26%**
23%**
22%**
24%**
22%**
50%
50%
50%
40%
40%
34%
32%
54%
48%
48%
44%
43%
42%
40%
325
71
11,964
16,449
34%
34%
26%**
21%**
20%
10% *
15% *
12%**
26%
25%
28%
25%
3%
4%
7% *
7%**
1%
1%
2%
2%
16%
25%
23%**
33%**
25%
34%
40%
50%
34%
42%
44%
53%
2%
1%**
23%
50%**
40%
90%
45%
66%
22,995 25% 15%
5,814 17%** 6%**
28% 7%
20%** 6%**
35
Table IV. Ordered Probit Regression: Company Stock Allocations
The table presents the marginal effects of an ordered probit regression of company stock allocations against
participant characteristics. “Male” is a dummy variable equal to one if the participant is male, zero
otherwise. “Salary” is the annual 1997 salary (unit: ten thousand dollars). “Age” is the age of the
participant at the time the allocation decision is made (unit: years). “Time Employed” equals the time the
participant has been employed at the time the allocation decision is made (unit: years). “Compensation
Status” is a dummy variable that equals one if the individual by law is considered highly compensated,
otherwise it equals zero. “Prior Indicator” equals one for individuals who were employed prior to the
current plan administration and made no changes in their contribution allocations during the current plan
administrator’s tenure. “Division #” is a dummy variable that equals one if the participant is in the division.
The Corporate Division is the omitted dummy. “One Year Co Stock Return” is the one year raw buy and
hold return earned prior to the allocation decision. Robust standard errors, reported in parentheses, are
adjusted for heteroskedacity. The psuedo R-squared is the log-likelihood value on a scale from zero to one,
where zero corresponds to the constant-only model and one corresponds to perfect prediction (a loglikelihood of zero). ** (*) indicates significance at the 1% (5%) level.
Marginal Effects (dF/dx)
Independent
Variables
Male (1)
Age
Age Squared
Time Employed
Salary
Prior Indicator (1)
Compensation Status
Division 1
Division 2
(1)
(1)
(1)
Other Division (1)
One Year Co Stock Return
(1)
Number of Observations= 28,809
Pseudo R 2 = .0204
Dependent Variables:
Y=% Invested in Company Stock
Y=0%
Y=1-25%
Y=26-50%
-0.0307
(0.0048)
-0.0020
(0.0017)
0.0000
(0.0000)
0.0004
(0.0004)
0.0055
(0.0012)
**
-0.0073
(0.0011)
-0.0005
(0.0004)
* 0.0000
(0.0000)
0.0001
(0.0001)
** 0.0014
(0.0003)
-0.1442
(0.0041)
**
0.0015
(0.0103)
-0.0474
(0.0020)
**
*
**
**
0.0004
(0.0026)
0.0004
(0.0003)
0.0000
(0.0000)
0.0000
(0.0000)
0.0000
(0.0000)
0.0001
(0.0000)
-0.0247
(0.0019)
**
0.0000
(0.0001)
-0.0374
(0.0171)
*
-0.0096
(0.0045)
*
-0.0008
(0.0006)
-0.0925
(0.0179)
**
-0.0221
(0.0040)
**
0.0007
(0.0007)
-0.0564
(0.0361)
-0.1416
(0.0093)
-0.0171
(0.0130)
** -0.0357
(0.0025)
**
-0.0061
(0.0080)
-0.0016
(0.0009)
dF/dx is for a discrete change of the dummy variable from 0 to 1
36
Table IV. (Continued) Ordered Probit Regression: Company Stock Allocations
The table presents the marginal effects of an ordered probit regression of company stock allocations against
participant characteristics. “Male” is a dummy variable equal to one if the participant is male, zero
otherwise. “Salary” is the annual 1997 salary (unit: ten thousand dollars). “Age” is the age of the
participant at the time the allocation decision is made (unit: years). “Time Employed” equals the time the
participant has been employed at the time the allocation decision is made (unit: years). “Compensation
Status” is a dummy variable that equals one if the individual by law is considered highly compensated,
otherwise it equals zero. “Prior Indicator” equals one for individuals who were employed prior to the
current plan administration and made no changes in their contribution allocations during the current plan
administrator’s tenure. “Division #” is a dummy variable that equals one if the participant is in the division.
The Corporate Division is the omitted dummy. “One Year Co Stock Return” is the one year raw buy and
hold return earned prior to the allocation decision. Robust standard errors, reported in parentheses, are
adjusted for heteroskedacity. The psuedo R-squared is the log-likelihood value on a scale from zero to one,
where zero corresponds to the constant-only model and one corresponds to perfect prediction (a loglikelihood of zero). ** (*) indicates significance at the 1% (5%) level.
Number of Observations= 28,809
Marginal Effects (dF/dx)
Independent
Variables
Male (1)
Age
Age Squared
Time Employed
Salary
Prior Indicator (1)
Compensation Status
Division 1
Division 2
(1)
(1)
(1)
Other Division (1)
One Year Co Stock Return
(1)
2
Pseudo R = .0204
Dependent Variables:
Y=% Invested in Company Stock
Y=51-75%
Y=76-99%
Y=100%
0.0031
(0.0005)
0.0002
(0.0002)
0.0000
(0.0000)
0.0000
(0.0000)
-0.0005
(0.0001)
**
0.0012
(0.0002)
0.0001
(0.0001)
* 0.0000
(0.0000)
0.0000
(0.0000)
** -0.0002
(0.0000)
0.0103
(0.0004)
**
-0.0002
(0.0010)
0.0046
(0.0002)
**
*
**
**
-0.0001
(0.0004)
0.0037
(0.0017)
0.0093
(0.0018)
*
0.0014
(0.0006)
** 0.0035
(0.0007)
0.0048
(0.0024)
0.0140
(0.0010)
*
0.0020
(0.0011)
** 0.0054
(0.0004)
0.0333
(0.0050)
0.0023
(0.0019)
-0.0001
(0.0000)
-0.0005
(0.0004)
-0.0062
(0.0013)
**
0.2014
(0.0073)
**
*
**
-0.0017
(0.0116)
*
**
**
0.0428
(0.0198)
0.1012
(0.0189)
0.0729
(0.0536)
0.1595
(0.0105)
*
**
**
dF/dx is for a discrete change of the dummy variable from 0 to 1
37
Table V. Asset Allocations and Adjusted Asset Allocations
This table presents the allocations and adjusted asset allocations for investors who hold company stock and
invest in either two or three additional assets. The adjusted allocations reflect the percentage of the noncompany stock holdings the asset class represents.
Invest in All Assets
Investment Vehicle
Company Stock
Equity Income Fund
S&P 500 Index Fund
GIC
Median
Mean Allocation Allocation
33%
25%
23%
25%
24%
25%
20%
20%
Mean Adjusted
Allocation
34%
36%
31%
Invest in Company Stock, Equity Income and S&P 500 Index Fund
Median
Mean Adjusted
Mean Allocation Allocation Allocation
Investment Vehicle
Company Stock
38%
35%
Equity Income Fund
30%
30%
48%
S&P 500 Index Fund
32%
30%
52%
GIC
Invest in Company Stock, Equity Income and GIC Fund
Median
Mean Adjusted
Mean Allocation Allocation Allocation
Investment Vehicle
Company Stock
42%
50%
Equity Income Fund
28%
25%
49%
S&P 500 Index Fund
GIC
30%
25%
51%
Invest in Company Stock, S&P 500 Index and GIC Fund
Investment Vehicle
Company Stock
Equity Income Fund
S&P 500 Index Fund
GIC
Median
Mean Allocation Allocation
44%
50%
29%
28%
25%
25%
Mean Adjusted
Allocation
51%
49%
3,317 obs
Median
Adjusted
Allocation
33%
33%
33%
4,203 obs
Median
Adjusted
Allocation
50%
50%
379 obs
Median
Adjusted
Allocation
50%
50%
626 obs
Median
Adjusted
Allocation
50%
50%
38
Table VI. Probit Regression–1/n Heuristic
The table presents the marginal effects calculated from the results of a probit regression. The dependent
variables equals 1 if the participant follows the 1/n rule or the adjusted 1/n rule. “Male” is a dummy
variable equal to one if the participant is male, zero otherwise. “Salary” is the annual 1997 salary (unit: ten
thousand dollars). “Age” is the age of the participant at the time the allocation decision is made (unit:
years). “Time Employed” equals the time the participant has been employed at the time the allocation
decision is made (unit: years). “Compensation Status” is a dummy variable that equals one if the individual
by law is considered highly compensated, otherwise it equals zero. “Prior Indicator” equals one for
individuals who were employed prior to the current plan administration and made no changes in their
contribution allocations during the current plan administrator’s tenure. “Division #” is a dummy variable
that equals one if the participant is in the division. The Corporate Division is the omitted dummy. Robust
standard errors, reported in parentheses, are adjusted for heteroskedacity. The psuedo R-squared is the loglikelihood value on a scale from zero to one, where zero corresponds to the constant-only model and one
corresponds to perfect prediction (a log-likelihood of zero). ** (*) indicates significance at the 1% (5%)
level.
Marginal Effects (dF/dx)
Independent
Variables
Male (1)
Age
Age Squared
Time Employed
Salary
Unadjusted 1/n
(2)
-0.0016
(0.0026)
0.0012
(0.0009)
0.0000
(0.0000)
-0.0013
(0.0002)
-0.0049
(0.0008)
Adjusted 1/n
(2)
**
**
0.0003
(0.0030)
0.0015
(0.0011)
0.0000
(0.0000)
-0.0017
(0.0002)
-0.0047
(0.0009)
Prior Indicator (1)
-0.0223
(0.0022)
Compensation Status (1)
0.0140
(0.0080)
0.0144
(0.0086)
Division 1 (1)
0.0142
(0.0141)
0.0147
(0.0154)
0.0054
(0.0130)
0.0059
(0.0145)
Division 2
(1)
(1)
**
-0.0282
(0.0026)
**
**
**
-0.0066
(0.0381)
Number of Observations
28,738
28,809
Psuedo R-squared
0.0237
0.0196
(1)
dF/dx is for a discrete change of the dummy variable from 0 to 1
Other
Dropped
39
Figure 1. Conditional Adjusted and Unadjusted Kernel Densities
These graphs represent the adjusted and unadjusted kernel densities of participants that invest in three to
four funds.
Panel A. Sample that Invests in All Four Funds
Invest in All Funds-3,317 observations
Company Stock
Equity Inc
Adj. Equity Inc
15
6
10
4
5
2
0
0
.5
S&P 500
1
0
0
Adj. S&P 500
20
.5
GIC
1
Adj. GIC
8
15
6
10
4
5
2
0
.5
Allocation Percentage
0
1
0
.5
Allocation Percentage
0
1
Panel B. Sample that Invests in Company Stock, Equity Income Fund and GIC fund
Invest in Three Funds- 379 Observations
Company Stock
Equity Inc
Adj. Equity Inc
10
3
2
5
1
0
.5
0
GIC
1
0
0
.5
1
Adj. GIC
10
5
0
0
.5
Allocation Percentage
1
40
Figure 1. (Continued) Conditional Adjusted and Unadjusted Kernel Densities
These graphs represent the adjusted and unadjusted kernel densities of participants that invest in three to
four funds.
Panel C. Sample that Invests in Company Stock, Equity Income Fund and S&P 500 Index
Invest in Three Funds-4,203 observations
Equity Inc
Adj. Equity Inc
Fund
Company Stock
8
3
6
2
4
1
2
0
.5
0
S&P 500
0
1
0
.5
Allocation Percentage
1
Adj. S&P 500
6
4
2
0
0
.5
Allocation Percentage
1
Panel D. Sample that Invests in Company Stock, S&P 500 Index Fund and GIC Fund
Invest in Three Funds-626 Observations
Company Stock
4
3
S&P 500
Adj. S&P 500
15
10
2
5
1
0
0
.5
1
Allocation Percentage
GIC
Adj. GIC
0
0
.5
1
15
10
5
0
0
.5
Allocation Percentage
1
41