household investment—the horizon effect

Household Investment—The Horizon Effect

PING HE1 and XIAOQING HU2*1School of Economics andManagement,TsinghuaUniversity, Beijing 100084, China2University of Illinois at Chicago, 601S. Morgan, UH 2422, Chicago, Illinois 60607, USA

ABSTRACT

Individuals tend to simplify a complex portfolio decision problem into several manageabledimensions, each of which can frame their perception of risk. We check this view by studyingthe effect of investment horizons on households’ portfolio decisions. Using the Survey ofConsumer Finances (SCF) data, we find that households allocate more of their wealth in stocksif they report longer planning horizons. The existence of foreseeable expenditure significantlychanges the dependence of risky stock investment on the planning horizon. We decompose thereported planning horizon into an objective part and a subjective mental accounting part, andfind that the mental accounting part has a greater effect on household portfolio choice. This isconsistent with the argument that individuals make investment decisions based on the horizonat which the risk is perceived rather than the horizon at which the investment reward or cash isneeded. Copyright # 2010 John Wiley & Sons, Ltd.

key words portfolio choice; time diversification

INTRODUCTION

Individuals have bounded rationality in processing information and making decisions. A

complex decision problem is often simplified. For example, in a standard investment decision

problem, investors focus on the mean and variance of risky asset returns. The way an investor

structures his decision problem can frame his perception of risk. In a dynamic setting, the time

varying risk characteristics are important inputs of an investment decision problem. Thus how

these risk characteristics affect individuals’ investment decisions is one of the central issues in

finance research. One input of an individual’s portfolio decision problem is the horizon over

which the investment is made. Some people tend to believe that there is a positive correlation

between the proportion of wealth invested in risky assets and the investment horizon. One

justification is that above-average returns tend to offset below-average returns over long

horizons. This is often referred to as ‘‘time diversification’’ in many studies. In this paper, we

Review of Behavioral Finance, 2: 81–105 (2010)

Published online 7 June 2010 in Wiley Online Library

(wileyonlinelibrary.com) DOI: 10.1002/rbf.10

�Correspondence to: X. Hu, University of Illinois at Chicago, 601 S. Morgan, UH 2422, Chicago, IL60607, USA.E-mail: [email protected]

Copyright # 2010 John Wiley & Sons, Ltd.

empirically study the impact of households’ reported planning horizons on their stock

investments, and we then further explore the source of this impact.

The Federal Reserve Board’s Survey of Consumer Finances (SCF) data contain important

information on the attitudes of US households toward financial risks. Among other things, the

SCF asks survey respondents about their most important saving and planning horizons. We

construct a ‘‘planning horizon’’ variable for each household based on its answer to this

question. First, we study the factors that determine a household’s planning horizon. Our

summary statistics show that a household’s planning horizon does not decrease uniformly

with age. Thus, we conjecture that households make ‘‘plans’’ based on their expected future

expenses. Consistent with this conjecture, we find that a household’s planning horizon is

related to the household’s foreseeable expenditures. In particular, we find that the existence of

foreseeable expenditures generally shortens a household’s planning horizon. Moreover, we

find that many other household characteristics also affect a household’s planning horizon, for

example risk aversion and education. Then, we decompose the planning horizon into two

parts, the first part depends on age and foreseeable expenditures, and the second part depends

on other household characteristics including income, wealth, education, risk aversion, marital

status, number of members in the household, health condition, and borrowing constraints. We

use this decomposition to differentiate two different concepts of horizon: the objective

investment horizon, over which the investment is made, and the subjective mental accounting

horizon, which determines at what frequency risks are perceived. This decomposition is based

on the assumption that households’ reported planning horizons reflect both their investment

horizon and their preference on risk-perceiving frequency.

We study the effect of our constructed horizon variables on household portfolio choice. We

find that households with a longer planning horizon invest more in risky assets, this result is

robust to various estimating methods. In particular, the proxy for the subjective mental

accounting horizon has a larger effect on household portfolio choice. These results are

consistent with the experimental results in Thaler et al. (1997).

Moreover, we also find that the structure of stockholdings is linked to the planning horizon.

Specifically, our results show that households invest more in indirect stockholding (in the

form of mutual fund holdings) when they report longer planning horizon. It is possible that

households invest more in risky assets because they diversify more when they have longer

horizon. However, including the structure of stockholdings as an independent variable in our

regression does not eliminate the significance of the planning horizon effect. Therefore, the

hypothesis that time diversification is driven by cross-asset diversification is rejected.

The paper proceeds as follows. In ‘Literature Review’ section we review previous studies

and related literature. In ‘Data and Summary Statistics’ section, we present a description of

the data and summary statistics. In ‘Determination of Planning Horizon’ section, we explore

the relationship between planning horizon and other household characteristics. In ‘Household

Portfolio Choice’ section, we study household portfolio choice and test the horizon effect.

‘Robustness Tests’ section provides robustness checks. We conclude in the last section.

LITERATURE REVIEW

In many studies, economists formalize the portfolio decision problem with time-separable

Von Neumann-Morgenstern utility functions as a representation of intertemporal preference.

Under this setting, Samuelson (1969) gives an example of a multi-period portfolio choice

Copyright # 2010 John Wiley & Sons, Ltd. Review of Behavioral Finance, 2, 81–105 (2010)

DOI: 10.1002/rbf.10

82 P. He and X. Hu

problem in which the proportion of wealth invested in stocks is independent of the horizon for

an individual with constant relative risk aversion (CRRA) preferences. Samuelson (1963)

points out that the rationale behind time diversification is a fallacious interpretation of the law

of large numbers.1

While Samuelson’s refutation of time diversification remains a ‘‘mathematical truth,’’

many research studies challenge the assumptions of his arguments. In terms of the investor’s

preferences, Thorley (1995) shows mathematically that if an investor has decreasing relative

risk aversion toward serially uncorrelated returns, the allocation toward risky stocks should

increasewith the investment horizon.2 In terms of the dynamic characteristics of asset returns,

Campbell and Viceira (1999) and others3 show that time-varying investment opportunities

result in an intertemporal hedging demand of stocks, and the magnitude of hedging demand

depends on an investor’s investment horizon. In addition, background income risk

characteristics also influence an individual’s life-cycle portfolio choice problem. For

instance, Viceira (2001) suggests that the optimal allocation to stocks is unambiguously

larger for employed investors (who are younger and have longer investment horizons) than for

retired investors (who are older and have shorter investment horizons) when the labor income

risk is idiosyncratic and non-tradable. He also finds that when labor income is correlated with

stock returns, time diversification appears to be optimal as long as the correlation between

labor income and stock returns is low.4

The time diversification phenomenon, or the horizon effect, is also discussed in the

behavior economics literature, in which the term ‘‘horizon’’ sometimes refers to the risk

perceiving horizon. Thaler et al. (1997) show experimentally that investors who demonstrate

myopic loss aversion are more willing to accept risks if they evaluate their investments less

often.5 Thaler et al. argue that investors who look at short-term stock returns make incorrect

decisions because they are fooled by myopic loss aversion and believe that the probability of

losses over the long run is higher than it actually is. On the other hand, Samuelson (1994)

suggests that investors who look at 30-year stock returns make incorrect decisions because

they are fooled by the illusionary happy ending and believe that the probability of losses over

the long run is zero. Nevertheless, both arguments lead to the conclusion that an investor will

allocate more of his wealth to stocks if he values them at a lower frequency, that is, his risk-

perceiving horizon is longer. In this paper, we empirically test these arguments using

household wealth and expectation data.

1Statistically, for a sequence of independent random stock returns, while the expectation of the sum increases linearlywith the number of periods, the standard deviation only increases with the square root of the number of periods.However, the size of an investor’s potential loss increases in proportion to the expected returns, thus reducing theattractiveness of the higher return-risk ratio. It is the increasing size of the potential loss that makes timediversification differ from cross-asset diversification.2Gollier (2002) provides an argument for decreasing risk aversion on wealth; he also finds that the introduction ofliquidity constraints increases an agent’s risk aversion.3See, for example, Kim and Omberg (1996), Brennan, Schwartz, and Lagnado (1997), Brandt (1999), and Barberis(2000).4Related works include Bodie, Merton, and Samuelson (1992), Jagannathan and Kocherlakota (1996), and Heatonand Lucas (1997).5The notion of myopic loss aversion is a combination of two behavioral principles, namely, loss aversion and mentalaccounting. Consistent with the prospect theory (Tversky and Kahneman, 1992), which suggests that the valuefunction has a kink at the reference point, loss aversion refers to the fact that people tend to be more sensitive todecreases in their wealth than to increases. Mental accounting, on the other hand, concerns aggregation, that is, howtransactions are grouped both cross-sectionally (whether securities are evaluated one at a time or in portfolios) andintertemporally (how often portfolios are evaluated).


DOI: 10.1002/rbf.10

Household Investment—The Horizon Effect 83

DATA AND SUMMARY STATISTICS

Data discussionSome of the recent research on investment behavior is based on experimental data, where

participants make investment decisions in hypothetical situations with small financial

consequences (see, for example, Thaler et al. (1997)). Other studies such as Papke (1998)

explore individuals’ actual investments in 401(k) plans. An important drawback in

exclusively using 401(k) data is the lack of reliable demographic information with respect to

the individuals who invest in 401(k)s. Our analyses focus on how households’ financial

investments vary with their mental accounting and planning horizons. A panel data of

households’ wealth and future plans would be ideal for the study. However, the only

comprehensive household panel data available is the Panel Studies of Income Dynamics

(PSID). Though the PSID data contain some information on household wealth and asset

portfolios, it does not have data on ex ante expectations on future financial needs or goals.

Those variables are crucial to our study. Therefore, we use the best available alternative—the

SCF, conducted by the Federal Reserve Board. The SCF provides a detailed survey of the

asset holdings, consumer debt, pensions, income, and other demographic characteristics

of U.S. families. It also contains reasons for various financial choices and attitudes toward

financial risks. The SCF is widely considered to be the most comprehensive source of wealth

data in the United States.6 The advantages of using SCF data for our study can be summarized

as follows. First, the SCF data give a representative sample of the entire U.S. population.

Second, the SCF data contains rich information on the demographic characteristics as well as

the economic situation of individual households. Finally, and most importantly, the SCF data

disclose the information on households’ planning horizons as well as other investment-related

characteristics.

As any survey dataset, the SCF has its drawbacks. Morgan and Sonquist (1963) discussed

general problems with all survey data, such as classification issues and measurement errors.

Almost all survey samples are clustered and stratified, thus require proper application of

statistical techniques. The explanatory variables to be used in the analysis could be highly

correlated, which may reduce the power of the tests. In addition, household wealth estimates

based on the SCF were lower than independent, institution-based, estimates mainly due to an

under-sampling of wealthy households, which are believed to hold highly disproportionate

shares of many types of assets. This could affect our estimates of household portfolio choices,

though the impact is not necessarily significant. Despite of all these potential problems, the

SCF data are still the best available data for our study.

We mainly use the 2004 SCF data since it is the latest wave of SCF data for which the data

are not preliminary. By restricting our study to one specific wave of data, we can guarantee

that all investment decisions are made during approximately the same brief time period, and

thereby reduce the noise associated with changes in the economic environment. There is a

concern that using data from a survey taken just after a major equity bear market (2001–2003)

may bias the result. To make sure that our study is robust and to explore the potential impact

6SCF data exist in two versions, the raw data prepared by the University of Michigan’s Survey Research Center, andthe recoded data prepared by the Federal Reserve Board. The latter file uses a series of consistency checks andimputation procedures for missing data. Additional weights are constructed and included in the recoded data file, andnew variables are constructed not only from original variables but also by matching information from other sourcessuch as the U.S. Census. We use the latter version for our study.


DOI: 10.1002/rbf.10

84 P. He and X. Hu

of this bear market on our results, we pool 2001 and 2004 SCF data together to analyze the

effect of changes in economic environment in some of our major empirical tests. Before any

analysis, we define the variables that we use, and present summary statistics.

Variable definitionsThe primary variable of interest in this study is the planning horizon, denoted as PLN_HRZ.

The SCF asks survey respondents about their most important saving and planning horizons.

The choices are: (1) The next few months; (2) the next year; (3) the next few years; (4) the

next five to 10 years; (5) more than 10 years. Based upon these choices, we construct

PLN_HRZ as follows:7

Reported horizon Planning horizon (Years)

Next few months 0.51 year 11–5 years 2.55–10 years 7.510þ years 10

Next, because households’ portfolio choices are related to their reported risk preferences,

we construct a household risk aversion variable, denoted as RSK_AVS, based on a household’s

self-reported attitude toward financial risks. The willingness to accept risks is categorized by

the integer numbers from one to four, where a higher number indicates more risk aversion.We

use these numbers as proxies for risk aversion. Note that these numbers only reflect the

subjective view of a household about its own risk attitude; they have nothing to do with the

risk aversion coefficients in any standard CRRA or constant absolute risk aversion (CARA)

utility function.

We expect that households with borrowing constraints have less of an incentive to take

risks, and thus invest less in stocks (see, for example, Guiso et al. (1996)). To incorporate this

concern into our study, we construct a dummy variable of borrowing constraints, or

BRW_CTR, as follows: The SCF asks whether a household had applied for credit in the past 5

years. If the household was denied credit, or approved for a smaller amount than desired, or if

the household did not apply for credit in the past 5 years because it was afraid of denial, the

dummy variable is set to one; otherwise, the dummy is set to zero.

The next two variables are measures of household wealth. Household income (INC) is the

sum of wages, salaries, income from pensions or social security, and income from private

business. This measure includes both the respondent’s and the spouse’s income. Net worth

(NTW) is defined as total assets minus total debt, where total assets are the value of all assets,

including liquid assets (such as cash, stocks, and bonds), real estate assets, the value of

pensions, and the value of all private businesses; and total debt includes liquid debt (such as

credit card balances) and mortgage debt associated with real estate assets.

To address the issue of horizon effect, or time diversification, the dependant variable of

interest is the fraction of wealth a household allocates to risky assets, which, in our study, are

stocks. We capture this quantity using the amount of wealth invested in stocks divided by

7All the major regression results in this paper are robust to different specifications of the planning horizon variable.


DOI: 10.1002/rbf.10


liquid assets, or ST/LIQ. Liquid assets are defined as the sum of cash, stocks, and bonds.

Another competing candidate would be the amount of wealth invested in stocks divided by net

worth, or ST/NW. In this study, we mainly discuss the results using ST/LIQ as the dependant

variable; however, we also study the case using ST/NW as a robustness check.

We prefer ST/LIQ to ST/NW for three reasons. First, the investments in stocks are deemed

to be a component of liquid assets, whereas a household’s net worth contains many other

illiquid assets. Thus, the ratio of stocks over liquid assets is more consistent with the idea of

‘‘portfolio choice’’ within the category of liquid assets, especially for individuals with mental

accounting, which is a particularly relevant concern in our study. Second, because net worth is

one of the independent variables in our regressions, the negative correlation between net

worth and ST/NW could generate unnecessary noise in the results. Third, we control for

background risks due to illiquid assets included in net worth. We discuss background risk in

more detail below.

In the literature, stockholdings divided by net worth plus capitalized human capital are

also used as a proxy for the level of risky asset holdings. However, we do not use this measure

for several reasons. First, the best way to capitalize human capital remains a subject of

controversy. Second, we do not have sufficient information on each household’s income

dynamics to accurately carry out capitalization as in Carroll and Samwick (1997). Third,

because there could be more than one working individual in a household, any capitalization

method that is appropriate to only one individual could lead to a very inaccurate estimate of

the household wealth. Fourth, in reality, the market to borrow against future income is

imperfect, and this capitalized human capital cannot be used to invest in stocks.

We also construct ratios of various other asset values to a household’s net worth, including:

real estate assets to net worth (RE/NW), business value to net worth (BUS/NW), pension value

to net worth (PEN/NW), cash to net worth, and bonds to net worth. The value of real estate

assets includes both the owner-occupied house’s value and the value of other real estate.

The value of owner-occupied housing is the self-reported market value of a homeowner’s

principle house. The value of other real estate is the sum of vacation homes and commercial

real estate. Business value is the total value of a household’s private businesses. Pension

value is total value of retirement accounts other than what is reported in other categories. Cash

is the sum of a household’s cash, checking account and savings account balances. Stocks

and bonds consist of direct and indirect holdings of equity and bonds, respectively.

Indirect holdings are assets such as mutual funds and defined contribution pensions.

Households are asked to classify their mutual funds into equity mutual funds or bond mutual

funds. If they hold balanced funds, half of the fund value is identified as stocks, and half as

bonds.

We use RE/NW, BUS/NW, and PEN/NW in our regressions to control for background risks.

Many studies show that individuals bearing more undiversifiable income risk reduce the

proportion of wealth held in risky stocks (see, for example Pratt and Zeckhauser (1987),

Kimball (1990), and Viceira (2001)). Similarly, Heaton and Lucas (2000) report a negative

effect of entrepreneurial income risk on portfolio choice, and Fratantoni (1998) shows that

committed expenditure risks associated with owner-occupied housing also have a negative

impact on relative stockholding. Labor income risk, entrepreneurial risk, and homeownership

risk are examples of background risks.

Finally, in our analysis,MRT_STS represents the marital status of a household, NOM is the

total number of people in a household, and HLTH is a dummy that equals one if the

respondent’s self-assess health (of self or spouse) is poor, and zero otherwise. Other related


DOI: 10.1002/rbf.10

86 P. He and X. Hu

household demographic information such as age (AGE) and years of education (EDU) is also

used in our analysis.

Summary statisticsThe 2004 SCF data contain about 22,000 household observations. Since we are interested in

the variation of the composition of wealth across different planning horizons, we group

households by their planning horizons. We then report the mean and the median8 of the

relevant variables for each cohort as well as the whole sample. Table 1 presents the means and

medians for some of the variables defined in subsection ‘Variable Definitions’ above across

planning horizon cohorts as well as at the aggregate level.

Table 1 demonstrates that households with longer planning horizons are wealthier on

average than those with shorter horizons; they have higher income as well as higher net worth.

At the same time, households with longer planning horizons are less financially constrained

and less risk averse, which can be due to the fact that they are wealthier. The statistics also

suggest that on average households with longer planning horizons have more years of

education, which might be one of the reasons why they are wealthier. From the table we also

observe that relative business value (relative to net worth) is increasing in the planning

horizon, relative real estate value is decreasing in the planning horizon, and relative pension

value do not depend on the planning horizon, and cash holdings are decreasing with planning

horizons, while stock and bond holdings are increasing with planning horizons. The statistics

also suggest that more than half of the households in our sample do not hold any stocks or

bonds. Therefore, the portfolio choice puzzle as reported in Heaton and Lucas (1997), for

example, still exists in the 2004 SCF data.

DETERMINATION OF PLANNING HORIZON

One interesting finding in Table 1 is that we do not observe a smaller mean or median of age

when the planning horizon is longer. Instead, we observe a hump shape in the average age as

the planning horizon increases. In particular, there is a substantial drop in age when a

household reports a planning horizon longer than 10 years. The age can affect planning

horizon in at least two ways. On one hand, older people tend to be more patient, thus tend to

have longer planning horizons. On the other hand, as assumed in the life-cycle portfolio

choice literature, older individuals have shorter investment horizon because of shorter life

expectancy. Consistent with these two explanations, for the households with short horizons

(few months and 1 year), the mean age (46) is 3 years less than the median age (49) of the

same group. For households with medium or long horizons, the statistical median and mean

ages are similar, and longer than those within the households with short horizons. This can be

explained by a right skewed distribution in age in the short horizon group, that is, there are

many young households but also some very old ones with short horizons. Table 2 below

presents the population distributions across age and planning horizon.

8When respondents take the survey, they tend to be in the wealthy end of the distribution. The Federal Reserve Boardtherefore designs a "frequency variable" that assigns a weight to each respondent so that the resulting summarystatistics are representative of the entire U.S. population. We apply this frequency variable to calculate the mean andthe median.


DOI: 10.1002/rbf.10


Table

1.Summarystatistics

Planninghorizon

Few

months

Within

1year

1–5years

5–10years

10þ

years

All

Mean

Median

Mean

Median

Mean

Median

Mean

Median

Mean

Median

Mean

Median

Ageofthe

respondent

49.09

46.00

49.07

46.00

51.43

50.00

50.27

50.00

46.79

45.00

49.73

48.00

Years

ofeducation

12.38

12.00

12.77

12.00

13.42

14.00

13.91

14.00

14.32

15.00

13.38

13.00

Riskattitude

3.40

4.00

3.29

3.00

3.22

3.00

3.06

3.00

2.92

3.00

3.18

3.00

Marital

status

0.40

0.00

0.44

0.00

0.51

1.00

0.60

1.00

0.61

1.00

0.52

1.00

No.ofmem

bers

inhousehold

2.61

2.00

2.49

2.00

2.45

2.00

2.60

2.00

2.60

2.00

2.54

2.00

Borrowingconstraint

0.35

0.00

0.33

0.00

0.22

0.00

0.20

0.00

0.17

0.00

0.25

0.00

Jobincome

$27,255

$12,000

$31,725

$18,000

$38,343

$25,000

$55,572

$37,440

$70,005

$44,000

$44,141

$26,000

Net

worth

$190,076

$42,680

$252,966

$43,900

$332,272

$91,550

$625,072

$169,670

$785,999

$210,300

$432,566

$93,400

Realestate

$137,098

$50,000

$188,334

$70,000

$199,349

$103,000

$327,406

$157,000

$371,300

$177,000

$242,926

$120,000

Liquid

/totalasset

0.141

0.024

0.160

0.033

0.203

0.064

0.191

0.081

0.194

0.088

0.181

0.055

Stocks/liquid

asset

0.170

0.000

0.154

0.000

0.234

0.000

0.306

0.067

0.345

0.247

0.247

0.000

Bonds/liquid

asset

0.114

0.000

0.118

0.000

0.160

0.000

0.173

0.000

0.182

0.021

0.153

0.000

Cash/liquid

asset

0.716

1.000

0.728

1.000

0.606

0.877

0.521

0.453

0.473

0.333

0.600

0.800

Stocks/net

worth

0.070

0.000

0.053

0.000

0.098

0.000

0.107

0.005

0.136

0.028

0.095

0.000

Realestate

/net

worth

2.077

0.806

1.961

0.742

2.247

0.711

1.191

0.719

1.227

0.731

1.751

0.731

Businessvalue/

net

worth

0.055

0.000

0.032

0.000

0.044

0.000

0.057

0.000

0.071

0.000

0.052

0.000

Pension/net

worth

0.143

0.000

0.111

0.000

0.247

0.000

0.129

0.000

0.133

0.000

0.162

0.000

Note:Thistablecontainsthesummarystatistics

foroursample.Themeanandmedian(inparentheses)ofrelevantvariablesforeach

planninghorizoncohortas

wellas

thewhole

sample

arereported.Alltheratiovariablesaresignificantat

the1%

level.


DOI: 10.1002/rbf.10

88 P. He and X. Hu

As we can see from Table 2, on average retired households have shorter horizons. For

households older than 65, the population with the planning horizon of 10þ years drops more

than those younger than 65. This is consistent with the results in Table 1. The distribution

across other planning horizons is similar across two age groups. In summary, age is not a

sufficient statistics for horizon as we do not observe a monotone relationship between age and

planning horizon.

The planning horizon might also be linked to different types of foreseeable expenditures.

Survey respondents are asked to report whether they anticipate major expenditures in the next

5–10 years. Theymay list up to six of such expenditures. In total, the SCF includes 21 types of

major expenditures, which are listed in the Appendix. The most-reported major expenditures

include a home purchase, education, health care, general support for family members or a

baby, the purchase of a car or other durable goods, business, investments, etc. Intuitively, not

only do age and foreseeable expenditures individually affect a household’s planning horizon,

but the interaction of age and foreseeable expenditures also affects planning horizon as well.

For instance, the education of children is a long-horizon plan for young households, but it

could be a short-horizon event for middle-aged households. In our 2004 SCF data, about 53%

of households report foreseeable major expenditures. Among those who report foreseeable

expenditures, about 60% report that they are currently saving for these foreseeable

expenditures. Some of the empirical exercises below are based on this particular group of

households, that is, those saving for self-reported foreseeable major expenditures in the next

5–10 years. For convenience, we define the households in this sub-sample as ‘‘savers,’’ and

we define those who report foreseeable expenditures but that are not saving for them as ‘‘non-

savers.’’ We define the remaining households as ‘‘others.’’

Before we study the effect of foreseeable expenditures on a household’s planning horizon,

we first report in Table 3 the population distribution of major foreseeable expenditures across

two age groups for those who report foreseeable expenditures, including both ‘‘savers’’ and

‘‘non-savers.’’ We group the 21 types of expenditures into seven categories. For example, the

education category includes ‘‘education for self and spouse’’ and ‘‘education for children and

grandchildren,’’ the Family/Children category includes ‘‘general support for self and

spouse,’’ ‘‘general support for children and grandchildren,’’ ‘‘general support for parents,’’

and ‘‘baby;’’ etc.

As we can see from Table 3, the distributions of major foreseeable expenditures are

different across age. More than 76% of households older than 65 claim that they anticipate

Table 2. Sample distribution by planning horizon and age

Population distribution

Age<¼ 65 Age> 65 All

Few months 18.2% 20.0% 18.54%1 Year 13.7% 15.5% 14.05%1–5 years 26.1% 34.5% 27.82%5–10 Years 27.1% 21.7% 26.00%10þ Years 15.0% 8.3% 13.59%Horizon in Yrs (Mean/Median) 4.41/2.5 3.58/2.5 4.24/2.5

Note: This table reports the population distributions across planning horizons. For each age cohort, we report the

proportion of population with certain planning horizon. All percentage values are significantly different from zero.


DOI: 10.1002/rbf.10


health-related expenditures, whereas only about 21% of the younger households are

concerned about health expenditures. About half of the households younger than 65 report a

home purchase and education as major foreseeable expenditures, while these expenditures are

of much less importance to older households.

We now demonstrate which household characteristics affect the planning horizon.

Specifically, we run the following regression for the full sample and for ‘‘savers:’’

PLN HRZi ¼ b0 þ bXi þX21

k¼1

gkEXPik þX21

k¼1

dkAGEi � EXPik þ "i (1)

where Xi includes log(INC), log(NTW), EDU, RSK_AVS, MRT_STS, NOM, HLTH,

BRW_CTR and AGE, and EXPik is a dummy variable indicating whether (¼1) or not

(¼0) household i has a foreseeable expenditure k. The product term AGEi�EXPik captures

the impact of the interaction between age and foreseeable expenditures on a household’s

planning horizon. We report the results in Table 4 for the full sample and for ‘‘savers.’’ Again,

we separate ‘‘savers’’ out because we expect that households who are saving for foreseeable

expenditures should be more affected by these expenditures.

In Table 4, the regression coefficients are qualitatively similar in the full sample and in the

sub-sample of savers. In the full sample regression, we find that a 1% increase in income leads

to a weak 0.05 years increase in planning horizon, and a 1% increase in net worth leads to a

0.27 years increase in planning horizon. The planning horizon of a household with one more

year of education is 0.14 years longer. More risk averse households have shorter planning

horizon. Married households have a longer planning horizon than unmarried ones, on average

by 0.72 years. One addition family member in a household reduces its planning horizon by 0.1

years. Households in poor health condition and those with borrowing constraints have shorter

planning horizons.

Many foreseeable expenditure dummies are significant in our regression despite the fact

that these expenditures are expected in 5–10 years while most households report planning

horizons much shorter than that. The existence of foreseeable expenditures has negative

impact on planning horizons. In our full sample results, the coefficient for EXP1 (for

education of children, see Appendix) is �0.88, and for AGE�EXP1 is 0.01; for a household

with median age (48 years), the joint effect is�0.40, that is, the planning horizon is shortened

Table 3. Sample distribution by type of expenditures and age

Foreseeable expenditures Age <¼ 65 (%) Age> 65 (%) All (%)

Home 46.36 11.36 42.09Education 49.64 6.29 44.36Health 21.05 76.78 27.84Family/Children 3.84 3.46 3.80Durable Good Purchases 9.01 6.08 8.65Investment 1.19 0.48 1.10Others 3.29 10.29 4.14

Note: This table reports the population distributions across major foreseeable expenditures. For each age cohort, we

report the proportion of population that reports certain foreseeable expenditures. Note that households can report up

to six types of expenditures at the same time. All percentage values are significantly different from zero.


DOI: 10.1002/rbf.10

90 P. He and X. Hu

Table

4.Household

characteristicsandplanninghorizons

Fullsample

Subsample-savers

Variables

Coeff.

t-stat

Variable

Coeff.

t-stat

Variable

Coeff.

t-stat

Variable

Coeff.

t-stat

Variable

Coeff.

t-stat

Variable

Coeff.

t-stat

CST

1.78

6.45

EXP1

�0.88

�3.13

AGE�EXP1

0.01

2.30

CST

0.45

0.79

EXP1

0.37

0.88

AGE�EXP1

�0.02

�1.95

Log(INC)

0.05

2.54

EXP2

�0.80

�2.17

AGE�EXP2

0.00

0.20

Log(INC)

0.12

3.74

EXP2

1.16

2.19

AGE�EXP2

�0.04

�3.28

Log(NTW)

0.27

18.25

EXP3

�0.87

�2.86

AGE�EXP3

0.01

2.91

Log(NTW)

0.31

11.28

EXP3

0.23

0.49

AGE�EXP3

�0.01

�0.64

EDU

0.14

13.38

EXP4

0.37

0.79

AGE�EXP4

�0.01

�0.88

EDU

0.11

5.27

EXP4

2.30

3.48

AGE�EXP4

�0.04

�3.49

RSK_AVS

�0.28

�8.74

EXP5

8.88

3.42

AGE�EXP5

�0.18

�3.79

RSK_AVS

�0.14

�2.66

EXP5

8.13

3.20

AGE�EXP5

�0.17

�3.84

MRT_STS

0.72

11.60

EXP6

�14.56

�1.14

AGE�EXP6

0.24

1.06

MRT_STS

0.46

4.18

EXP6

�7.76

�0.55

AGE�EXP6

0.11

0.43

NOM

�0.10

�4.44

EXP7

�2.39

�1.73

AGE�EXP7

0.05

1.97

NOM

�0.03

�0.67

EXP7

�4.38

�2.41

AGE�EXP7

0.07

2.51

HLTH

�0.65

�6.16

EXP8

2.61

1.51

AGE�EXP8

�0.04

�1.24

HLTH

�0.48

�2.37

EXP8

�1.77

�0.44

AGE�EXP8

0.04

0.42

BRW_CTR

�0.54

�7.86

EXP9

�1.70

�2.16

AGE�EXP9

0.04

2.50

BRW_CTR

�0.65

�5.51

EXP9

�3.51

�2.63

AGE�EXP9

0.05

2.21

AGE

�0.03

�13.74

EXP10

13.82

2.93

AGE�EXP10

�0.49

�3.47

AGE

�0.02

�2.59

EXP10

26.02

4.14

AGE�EXP10

�0.84

�4.47

EXP11

�1.04

�4.62

AGE�EXP11

0.01

1.67

EXP11

�1.52

�3.88

AGE�EXP11

0.02

1.87

EXP12

0.60

1.24

AGE�EXP12

�0.01

�1.36

EXP12

�0.60

�0.89

AGE�EXP12

0.01

0.44

EXP13

�9.68

�2.53

AGE�EXP13

0.11

2.19

EXP13

�3.70

�0.66

AGE�EXP13

0.02

0.24

EXP14

�9.85

�4.80

AGE�EXP14

0.16

4.92

EXP14

�8.01

�3.53

AGE�EXP14

0.11

2.64

EXP15

0.37

0.56

AGE�EXP15

�0.01

�0.92

EXP15

1.56

1.77

AGE�EXP15

�0.04

�2.32

EXP16

0.54

0.57

AGE�EXP16

�0.02

�1.13

EXP16

2.27

1.95

AGE�EXP16

�0.05

�2.28

EXP17

0.30

0.17

AGE�EXP17

�0.03

�0.76

EXP17

6.90

2.24

AGE�EXP17

�0.23

�3.11

EXP18

�0.44

�0.12

AGE�EXP18

�0.03

�0.45

EXP18

�2.96

�2.09

AGE�EXP18

0.17

0.90

EXP19

�1.35

�0.57

AGEs�EXP19

0.07

1.46

EXP19

�0.71

�0.29

AGE�EXP19

0.05

0.93

EXP20

0.09

0.03

AGE�EXP20

�0.01

�0.19

EXP20

2.22

0.67

AGE�EXP20

�0.05

�0.94

Adjusted

R2

0.18

EXP21

3.64

2.17

AGE�EXP21

�0.09

�2.62

EXP21

�5.00

�1.90

AGE�EXP21

0.05

0.99

Note:This

table

documents

how

household

characteristicsaffect

theplanninghorizonin

thefullsample

andthesub-sam

ple

ofsavers.Weregress

theplanninghorizonon

household

income,

net

worth,education,risk

aversion,marital

status,

thenumber

ofhousehold

mem

bers,

healthconditions,

borrowingconstraints,age,

majorforeseeable

expenditures,andtheproductsofageandmajorforeseeable

expenditures.Wereportthecoefficientsandtheirt-statistics

usingtheOLSregression.


DOI: 10.1002/rbf.10


by 0.40 years. For all 21 foreseeable expenditures, the average age and expenditure effect is

�1.14 years in the full sample, and �1.34 years in the savers sample. Hence the age and

expenditure effect are quantitatively stronger in the savers sample.

To summarize, a household’s planning horizon is affected by various household

characteristics. We can divide these factors into two groups: those related to the timing of

divesting, that is, when the investment will be discontinued, and those related to subjective

mental accounting, or perception of risks. The first group of factors includes age and

foreseeable expenditures. We categorize other factors into the second group. It is easy to

understand that one’s risk aversion and self-assessed health condition are subjective

household characteristics. With respect to income, wealth, education, marital status, number

of people in the household, and borrowing constraints, we believe that these factors indirectly

affect a household’s emotional stability, patience, confidence, and other mental

characteristics.9

HOUSEHOLD PORTFOLIO CHOICE

The effect of planning horizon on portfolio choiceThe summary statistics in Table 2 suggest that the composition of wealth, as well as many

other household demographic characteristics, vary with the planning horizon. In particular,

households with longer planning horizons tend to hold more stocks and bonds and less cash;

they tend to be older, and have more years of education; they are wealthier; they own more

private businesses; and they are less financially constrained and less risk averse. Even though

the summary statistics document that households with longer planning horizons tend to hold

more stocks, it is not clear whether this result is driven by variations in other demographic

characteristics such as age, years of education, net worth, etc. To more systematically study

the correlation between stockholding and planning horizons, we run a regression that relates

the proportion of stockholdings relative to liquid assets to a number of independent

variables10. In particular, we estimate

ST

LIQ¼ b0 þ bXi þ gPLN HRNi þ "i (2)

where Xi includes log(INC), log(NTW), AGE, EDU, RSK_AVS, BRW_CTR, BUS/NW, RE/NW

and PEN/NW.

Table 5 reports regression results using the 2004 SCF data in Panel A, as well as the results

using both 2001 and 2004 SCF data in Panel B. For the results using both 2001 and 2004 SCF

data, we add a dummy variable (2001 SCF data¼ 1) to control for the business cycle effect.

We conjecture that during or right after an equity bull market, households hold relatively

more equity in their assets due to performance chasing, hence the coefficient on the 2001

dummy variable is expected to be significantly positive. In both Panel A and Panel B, the first

column of estimates presents ordinary least squares (OLS) regression results. The second

9By similar reasoning, age can also be categorized as a subjective factor, but we include it in the first group as assumedin many portfolio decision studies.10Endogeneity issue could be a problem with the OLS regression. A household’s stock investment may contribute toits total net worth; and a household who hold significant stocks may say that it has a long planning horizon. Weexplore the endogeneity issue in ‘Robustness Tests’ section, and find that the results are robust.


DOI: 10.1002/rbf.10

92 P. He and X. Hu

column of estimates contains results of a Tobit regression based on the following latent

variable model:

Y� ¼ Xbþ "; "~Nð0; s2ÞY ¼ max f0; Y�g (3)

In our sample, more than 50% of the households have no stocks, so the data is left-

censored. One justification for using the Tobit model is the existence of some fixed costs for

entering into equity market, including mental cost.

In Panel A, both the OLS regression and the Tobit regression indicate that households with

longer planning horizons hold proportionally more stocks. For a household with 1 year longer

planning horizon, its ST/LIQ ratio is 0.34 percentage point higher (in OLS). This implies a

1.4% more investment in stocks given the mean of ST/LIQ ratio is 24.70% in the full sample.

As expected, the Tobit regression result is stronger. A household with 1 year longer planning

horizon would increase its ST/LIQ by 2.6%.

With similar calculation, we find that, with Tobit results, households with 1% more in

wealth leads to a 0.31% more in stock investment. We also observe that when households are

1 year older, they hold 0.25%more in stocks, while 1 more year of education brings additional

20.9% in stock investment! Households with one level higher risk aversion will invest 57.2%

less in stocks, and those with borrowing constraints will invest 41.8% less in stocks. Among

background risks, 1% increase in relative business value (which is an approximate 0.052%

increase in BUS/NW, as the mean of BUS/NW is 0.052 in full sample) leads to a 2.1% decrease

Table 5. Household portfolio choices and planning horizons

Panel A: 2004 SCF data Panel B: 2001 & 2004 SCF data

VariablesOLS Tobit OLS Tobit

Coeff. t-stat Coeff. p-value Coeff. t-stat Coeff. p-value

CST �0.2821 �11.57 �0.9931 0.00 �0.2532 �14.71 �0.9300 0.00Log(INC) 0.0002 0.12 �0.0148 0.00 0.0006 0.48 �0.0134 0.00Log(NTW) 0.0349 24.04 0.0762 0.00 0.0416 42.10 0.0883 0.00AGE 0.0008 4.57 0.0006 0.04 0.0002 1.77 �0.0008 0.00EDU 0.0269 26.23 0.0517 0.00 0.0220 31.61 0.0425 0.00RSK_AVS �0.0867 �28.07 �0.1414 0.00 �0.0927 �43.37 �0.1517 0.00BRW_CTR �0.0429 �6.40 �0.1032 0.00 �0.0406 �8.69 �0.0859 0.00BUS/NW �0.0599 �7.59 �0.0977 0.00 �0.0721 �12.69 �0.1302 0.00RE/NW 0.0007 2.35 0.0019 0.00 0.0000 0.88 0.0000 0.97PEN/NW �0.0006 �0.38 �0.0003 0.90 �0.0001 �0.08 0.0020 0.46PLN_HRZ 0.0034 4.90 0.0065 0.00 0.0039 8.07 0.0072 0.00DUMMY_2001 0.0122 3.80 0.0149 0.00Adjusted R2 0.28 0.31

Note: This table documents how household characteristics, including the planning horizon, affect household portfolio

choices in the full sample. We regress the proportion of stockholdings relative to liquid assets (ST/LIQ) on household

income, net worth, age, education, risk aversion, borrowing constraints, relative values of business, real estate assets,

and pension, and the planning horizon. We report the coefficients and their t-statistics or p-values for the OLS and

Tobit regressions; the adjusted R2 for the OLS regression is also reported.


DOI: 10.1002/rbf.10


in stock investment; 1% increase in relative real estate value leads to an increase of 1.6%

stocks; the impact of pension value is negligible.

The results in Panel B are similar, and we observe a significantly positive coefficient for the

2001 dummy, consistent with our conjecture. For a household in 1998–2000, its ST/LIQ ratio

is 1.22 percentage points higher (in OLS). This implies a 4.9% more investment in stocks

given the mean ST/LIQ ratio is 24.70% in the full sample of 2004.

It has been documented that households with low or moderate wealth do not hold any

stocks. It is not surprising, therefore, to observe that relative stockholdings increase in net

worth. The positive age effect is inconsistent with the predictions of rational portfolio choice

models such as that in Viceira (2001), who finds the opposite. However, this result does not

contradict with the results in Heaton and Lucas (2000), who document that ‘‘. . . [the] share ofstocks rises slightly with age for cohorts under age 65, and then declines significantly for

those age 65 and over. . ..’’ In our regression, pooling in age cannot reveal their finding. We

explore the age effect further in the robustness check in Section ‘Robustness Tests’, and their

results are confirmed. The effect of education suggests that more educated households are

more likely to take advantage of the equity premium. Households’ relative private business

has a strong negative effect on households’ stockholdings. This is consistent with Heaton and

Lucas (2000b), who show that entrepreneurial risks reduce the risky financial asset holdings.

The relative pension fund value is also negative but not significant. The relative real estate

value has a positive effect, probably because the real estate value here include both owner-

occupied housing and all other real estate values, hence it is a noisy measure for background

risk associated with owner-occupied housing.

In summary, our results show that controlling for other factors, a household’s planning

horizon affects its portfolio choices. The effect is both statistically and economically

significant. We also compare the effect of planning horizon on household portfolio with that

of age and education. In the full sample, the standard deviations for planning horizon, age,

and education are 3.49, 7.29, and 2.84, respectively. With the OLS coefficients, one standard

deviation change of planning horizon leads to a 4.8% change in stock investment, the same

measure is 2.4% for age, and 30.9% for education. Therefore, the planning horizon

contributes more to the variation in risky asset investment than age, but less than education.

Cross group differenceIn this subsection, we explore further the effect of planning horizon on household portfolio

choice by studying cross-group differences. Specifically, we conduct two comparisons, one

on households with foreseeable expenditures versus thosewithout, and another on households

saving for foreseeable expenditures (‘‘savers’’) versus those not saving for foreseeable

expenditures (‘‘non-savers’’). We seek to determine how the existence of foreseeable

expenditures affects the role of planning horizon on household portfolio choice. We modify

the regression in Equation (2) by allowing for different planning horizon coefficients across

the two groups, and we also test the fixed effects by allowing for different constant terms

across the two groups. The results are in Table 6.

Table 6 shows that households with foreseeable expenditure care more about planning

horizons than those without expected expenditures when they make investment decision.

Furthermore, those who are saving for the foreseeable expenditures care more about planning

horizon than who are not saving. One possible explanation is that the existence of foreseeable

expenditures enhances the awareness of planning horizon. The awareness is particularly

strong for those who are saving for the foreseeable expenditures.


DOI: 10.1002/rbf.10

94 P. He and X. Hu

Spending horizon and risk-perceiving horizonThe classic portfolio choice models define horizon as a function of age from the perspective

of the spending horizon (or investment horizon). We do find that the reported planning

horizon has a significant impact on household portfolio choice. We have discussed that age

variation does not fully capture the difference in household planning horizon. Instead,

the planning horizon is related to various household characteristics. Another finding is that the

existence of foreseeable expenditures not only affects the planning horizon, but also affects

the dependence of portfolio choice on planning horizon. This creates a puzzle: If the existence

of foreseeable expenditures only shifts the planning horizon due to its effect on the spending

horizon, which is defined as the horizon over which consumption occurs or wealth is

maximized, then it should not affect the dependence of portfolio choice on the planning

horizon. Our findings suggest that the effect of foreseeable expenditures is more than the

effect through its impact on the objective spending horizon. We conjecture that the existence

of foreseeable expenditures also affects household mental accounting. To further explore this

subjective effect as well as the pure spending horizon effect, we decompose the planning

horizon into the following two parts using the estimated regression coefficients from

Equation (1)

SPD HRNi ¼ baAGEi þP21

k¼1

g iEXPik þP21

k¼1

diAGEi � EXPik

PEC HRNi ¼ b0 þ b�aX�ai

(4)

Table 6. Household portfolio choices and planning horizons across groups

Variablesw/ EXP (1) vs. w/o EXP (2) Savers (1) vs. non-savers (2)

Coeff. t-stat Coeff. t-stat

CST (1) �0.2851 �11.65 �0.2632 �10.50CST (2) �0.2734 �10.89 �0.2814 �11.47Log(INC) 0.0000 �0.02 �0.0005 �0.26Log(NTW) 0.0349 24.05 0.0347 23.92AGE 0.0009 4.70 0.0010 5.40EDU 0.0267 26.02 0.0264 25.80RSK_AVS �0.0869 �28.07 �0.0868 �28.11BRW_CTR �0.0423 �6.30 �0.0421 �6.29BUS/NW �0.0599 �7.59 �0.0580 �7.34RE/NW 0.0008 2.41 0.0008 2.56PEN/NW �0.0006 �0.40 �0.0009 �0.56PLN_HRZ (1) 0.0055 5.92 0.0050 4.39PLN_HRZ (2) 0.0013 1.32 0.0026 3.19Adjusted R2 0.63 0.64F-test for CST (p-value) 1.96 (0.16) 4.31 (0.04)F-test for PLN_HRZ (p-value) 10.52 (0.00) 3.13 (0.08)

Note: This table documents how the effect of planning horizon on household portfolio choice differs across groups.

We make two comparisons: Households with major foreseeable expenditures versus those without; and households

who are saving for major foreseeable expenditures versus those who are not. In our regressions, we allow for different

constant terms and different coefficients for the planning horizon across groups. We report the coefficients and their

t-statistics for the OLS regressions; the adjusted R2 and F-test results for the coefficient difference are also reported.


DOI: 10.1002/rbf.10


where X-a represents all the independent variables in Xi of Equation (1) other than AGE,

namely log(INC), log(NTW), EDU, RSK_AVS, MRT_STS, NOM, HLTH, and BRW_CTR.

SPD_HRZ captures the planning horizon variation due to age and foreseeable expenditures,

and PEC_HRZ captures the planning horizon variation due to other factors, which, as we

argue earlier, are categorized as subjective mental accounting factors. We use SPD_HRZ as a

proxy for the spending horizon and we use PEC_HRZ as a proxy for the risk-perceiving

horizon. The means and standard deviations of SPD_HRZ and PEC_HRZ for the full sample

and sub-samples are reported below:

Full sample Savers

Mean STD Correlation Mean STD Correlation

SPD_HRZ �1.91 0.62 0.006 �2.04 0.59 0.02PEC_HRZ 6.38 1.18 6.63 1.12

Consistent with Table 4, SPD_HRZ has a negative mean since both age and the existence

of foreseeable expenditures shorten the horizon. The standard deviation of PEC_HRZ is twice

as large as that of SPD_HRZ. At the same time, the correlation between these two horizon

variables is very low.

With the planning horizon decomposition, we rerun the regression with the full sample and

the sub-sample of savers of 2004 SCF data. The results are reported in the Panel A of Table 7.

We also include the results using both 2001 and 2004 SCF data in Panel B with a 2001 data

dummy.

Results in Table 7 show that the proxy for the risk-perceiving horizon has a more

significant effect on household portfolio choice than the proxy for the spending horizon. The

coefficient for PEC_HRZ is much larger (about 10 times in the full sample results of Panel A)

than that for SPD_HRZ; given that PEC_HRZ has a larger standard deviations, the variation of

PEC_HRZ explains a lot more of the variation in household stockholdings than does the

variation of SPD_HRZ.

The horizon effects in Panel B are similar. We only observe a significantly positive

coefficient for the 2001 dummy in the full sample, but not in the sub-sample of savers. One of

the possible reasons is that savers rationally adjust their portfolios with less performance

chasing, so their asset structure is relatively stable.

The results in Table 7 confirm that the subjective mental accounting part of the planning

horizon has more explanatory power than does the objective part. This is consistent with the

behavioral story (as in Thaler et al., 1997) that what matters is the frequency at which risks are

perceived. 11

ROBUSTNESS TESTS

In this section, we present robustness tests on the horizon effect using the ‘‘savers’’ sub-

sample. The results using the full sample are similar.

11We also conduct a cross-group comparison between those with foreseeable expenditures and those without, as wellas between savers and non-savers. The results are consistent with our general conclusion, thus omitted. Tables areavailable upon request.


DOI: 10.1002/rbf.10

96 P. He and X. Hu

Table

7.Household

portfoliochoices,spendinghorizonsandrisk

perceivinghorizons

Panel

A:2004SCFdata

Panel

B:2001&

2004SCFdata

Fullsample

Subsample-savers

Fullsample

Subsample-savers

OLS

Tobit

OLS

Tobit

OLS

Tobit

OLS

Tobit

Variables

Coeff.

t-stat

Coeff.

p-value

Coeff.

t-stat

Coeff.

p-value

Variable

Coeff.

t-stat

Coeff.

p-value

Coeff.

t-stat

Coeff.

p-value

CST

�0.2539

�10.07

�0.9343

0.00

�0.2515

�5.78

�0.8084

0.00

CST

�0.3465

�16.47

�1.1926

0.00

�0.3645

�9.79

�0.9925

0.00

Log(INC)

�0.0039

�2.06

�0.0236

0.00

�0.0126

�4.06

�0.0247

0.00

Log(INC)

�0.0033

�2.46

�0.0239

0.00

�0.0081

�3.63

�0.0204

0.00

Log(NTW)

0.0170

6.30

0.0380

0.00

0.0205

4.31

0.0365

0.00

Log(NTW)

0.0273

14.20

0.0509

0.00

0.0298

8.77

0.0423

0.00

AGE

0.0006

2.60

0.0000

0.90

0.0005

1.42

0.0005

0.33

AGE

0.0002

1.47

�0.0010

0.00

0.0009

3.43

0.0010

0.01

EDU

0.0181

12.12

0.0323

0.00

0.0234

8.32

0.0383

0.00

EDU

0.0167

18.14

0.0281

0.00

0.0188

11.08

0.0288

0.00

RSK_AVS

�0.0691

�18.33

�0.1032

0.00

�0.0713

�10.93

�0.1000

0.00

RSK_AVS

�0.0794

�30.03

�0.1159

0.00

�0.0856

�18.72

�0.1225

0.00

BRW_CTR

�0.0086

�1.07

�0.0266

0.05

�0.0254

�1.79

�0.0607

0.00

BRW_CTR

�0.0077

�1.28

0.0016

0.87

�0.0032

�0.31

0.0031

0.84

BUS/NW

�0.0589

�7.46

�0.0966

0.00

�0.1414

�9.44

�0.2217

0.00

BUS/NW

�0.0717

�12.61

�0.1292

0.00

�0.1167

�10.99

�0.1713

0.00

RE/NW

0.0006

1.97

0.0016

0.00

0.0003

0.13

�0.0076

0.15

RE/NW

0.0000

1.04

0.0000

0.91

0.0003

0.29

�0.0132

0.00

PEN/NW

�0.0005

�0.32

�0.0003

0.93

�0.0017

�0.25

�0.0423

0.02

PEN/NW

�0.0003

�0.21

0.0013

0.64

�0.0022

�0.68

�0.0593

0.00

SPD_HRZ

�0.0081

�1.58

�0.0168

0.04

�0.0076

�1.03

�0.0051

0.62

SPD_HRZ

0.0053

1.28

0.0037

0.59

0.0094

1.52

0.0206

0.02

PEC_HRZ

0.0626

8.39

0.1360

0.00

0.0666

4.93

0.1167

0.00

PEC_HRZ

0.0514

9.35

0.1348

0.00

0.0553

5.54

0.1210

0.00

DUMMY_2001

0.0124

3.88

0.0148

0.00

0.0040

0.74

�0.0022

0.78

Adjusted

R2

0.28

0.28

Adjusted

R2

0.31

0.30

Note:Thistabledocumentstheeffectofthetwocomponentsoftheplanninghorizon,SPD_HRZandPEC_HRZ,onhouseholdportfoliochoice.Westudythiseffectinboththefull

sampleandthesub-sam

pleof‘‘savers.’’Wereportthecoefficientsandtheirt-statistics

orp-values

forboththeOLSandTobitregressions;theadjusted

R2fortheOLSregressions

arealso

reported.


DOI: 10.1002/rbf.10


EndogeneityIn our first robustness check, we look at the endogeneity issue in our regression defined in

Equation (2). There are two major sources for the endogeneity problem: net wealth (lg(NTW)

and the planning horizon (PLN_HRZ). When households invest more in stocks, they may

cumulate more wealth. Hence stockholdings could contribute to households’ net wealth. The

self-reported ‘‘planning horizon’’ could also depend on stockholdings, as households who

hold significant stocks may say that they have long planning horizons.12 To resolve the

endogeneity issue we identify some instrumental variables for each endogenous variable, and

use two-stage least squares (2SLS) regression method.

Specifically, we use the variable ‘‘income’’ (lg(INC)) as the instrumental variable for net

wealth (lg(NTW)). This is a natural choice since most households build up their wealth from

labor income. In addition, lg(INC) is not significant in our regression (2) as shown in Table 5, so

it is a qualified instrument variable. Using the same criteria, we find that household foreseeable

education expenditures and (EXP1,EXP2) are good candidates of instrumental variables for the

planning horizon (PLN_HRZ). These instrumental variables are both economically and

statistically important in determining households planning horizon as shown in Table 4. From

the untabulated regressions, households’ stockholdings do not depend on these variables.13

The main results remain robust in Table 8: The coefficient on the planning horizon is

positive and significant, while the proxy for the risk-perceiving horizon has more explanatory

power than the proxy for the spending horizon.14 More importantly, although the statistical

significance of horizon variables is reduced after considering the endogeneity problem, the

economic significance is substantially improved as the coefficients are much larger in

absolute value for the planning horizon and the risk perceiving horizon when the horizon is

decomposed. Hence if we endogenize household planning horizon and/or net wealth, the

results are economically stronger.

Direct/indirect holdings and cross-asset diversificationWe have shown statistically that the value of stockholdings relative to liquid assets is

increasing with the planning horizon. Next, we use our sample to analyze the effect of

planning horizon on the structure of stockholdings. The stockholdings of a household can be

divided into direct holdings and indirect holdings. Indirect holdings mainly consist of mutual

funds, and are more diversified. The structure of stockholdings reflects the degree to which a

household is diversified in its stock investments. Of particular interest is the interaction

between cross-asset diversification and time diversification. We run a new set of regressions

by replacing the dependent variable in specification (2) with direct stockholdings divided by

liquid assets (DIR/LIQ) and indirect stockholdings divided by liquid assets (IND/LIQ).15

Direct stockholdings are values of all shares of stocks in households’ portfolio. Indirect

12This is confirmed by including the ST/LIQ variable in our regression (1), which yields a positive and significantcoefficient for ST/LIQ.13We have tried different combinations of expenditure variables and the product of expenditure variable with age asinstrumental variables, the result is still robust.14There is no endogeneity problem for spending horizon and risk-perceiving horizon as they are already linearcombinations of exogenous variables by construction.15Asset risk characteristics can affect a household’s cross-asset diversification behavior. For example, Moskowitz andVissing-Jørgensen (2002) and others suggest that a low level of cross-asset diversification might be due to the positiveskewness of the underlying asset returns held by an investor. Unfortunately, we are not able to control asset riskcharacteristics in our regression due to the limitation of the data.


DOI: 10.1002/rbf.10

98 P. He and X. Hu

stockholdings are equity holdings through mutual funds, trusts, or annuities. We report results

in Table 9.

In Table 9, wealthier households invest more in both direct and indirect stockholdings, but

the effect of wealth on direct stockholdings is larger.We argue that the rich people tend to take

more risks. At the same time, younger households tend to own more direct holdings but less

indirect holdings, or younger households tend to take more risks. Education increases

stocking holdings, but more so on indirect stockholdings. It is consistent with the idea that

cross asset diversification is better accepted by more educated households. Risk aversion has

a bigger impact on indirect holdings. This might sound a bit counter intuitive, but our

interpretation is that those who own indirect stockholding are more risk averse and more

affected by risk aversion level. Consistent with this explanation, we find that the correlation

between risk aversion and the ratio of indirect stockholdings to the sum of (directþ indirect

stockholdings) is negative.

The effects of background risks are also different for direct stockholdings and indirect

stockholdings. The existence of real estate assets shift stockholdings from direct holdings to

indirect holdings, which can be justified by risk reduction efforts from households. The

existence of pension depresses the indirect holdings because of the substitution effect

between pension and indirect stockholdings.

Our major results on horizon variables are interesting. The horizon variables are

insignificant for direct stockholdings, but are significant for indirect stockholdings. This

indicates a positive correlation between cross-asset diversification and time diversification,

that is, a household with a longer horizon tends to hold a more diversified portfolio. We

provide two interpretations for this result. First, households with shorter planning horizons

Table 8. Robustness check with endogenous independent variables

Variables

EndogenizeLog(NTW)

EndogenizePLN_HRZ

Endogenize bothLog(NTW) andPLN_HRZ

Horizondecomposition

Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat

CST �0.3179 �8.46 �0.2101 �2.99 �0.2254 �3.85 �0.4344 �9.53Log(INC) �0.0169 �1.23Log(NTW) 0.0340 15.50 0.0112 2.51 0.0037 2.16 �0.0110 �2.32AGE 0.0010 3.19 0.0025 1.72 0.0029 2.00 0.0017 4.20EDU 0.0322 16.77 0.0236 3.00 0.0311 6.39 0.0195 8.16RSK_AVS �0.0901 �17.34 �0.0800 �7.55 �0.0916 �13.10 �0.0648 �11.14BRW_CTR �0.0633 �5.57 0.0001 0.00 �0.0445 �1.33 �0.0123 �0.97BUS/NW �0.1577 �11.02 �0.1181 �4.10 �0.1098 �3.83 �0.1262 �7.40RE/NW 0.0004 0.18 �0.0053 �1.03 �0.0025 �0.64 0.0009 0.37PEN/NW �0.0023 �0.35 0.0143 0.96 0.0049 0.46 �0.0044 �0.65PLN_HRZ 0.0050 4.13 0.0597 1.93 0.0463 1.97 �0.0052 �0.70SPD_HRZ 0.1092 14.63PEC_HRZ �0.4344 �9.53Adjusted R2 0.28 0.19 0.22 0.27

Note: This table documents the two-stage least squares regression result.We use log(INC) as the instrumental variable

for log(NTW), and/or EXP1, EXP2 for PLN_HRZ. We study the effect of horizon variables in household stock

investment decision in the savers’ sample with or without horizon decomposition. We report the coefficients and their

t-statistics for the 2SLS; the adjusted R2 for the second stage regressions are also reported.


DOI: 10.1002/rbf.10


are more speculative, thus taking more risk by investing in individual stocks instead of mutual

funds. Second, investing in mutual funds is associated with more initial costs such as a front-

end load and/or a minimum investment amount. The possible redemption fees may also

discourage short-term mutual fund holdings. All these costs make it worthwhile to invest in

mutual funds instead of individual stocks only when the planning horizon is not too short.

Our findings on direct and indirect stockholdings lead to the following question: Does

cross-asset diversification cause time diversification? Put differently, when households have a

longer planning horizon, do they diversify across assets? Since cross asset diversification

reduces risk and in turn leads households to invest more in stocks. We explore this question by

adding a proxy for cross-asset diversification into the regression in Equation (2). The proxy

that we use is the number of mutual funds that a household invests in. We report the results in

Table 10.

As we can see from Table 10, the number of mutual funds in which a household invests

does have a positive effect on household stockholdings, however, the horizon effect is not

affected. Therefore, the hypothesis that cross-asset diversification causes time diversification

is rejected.

Residual horizonThe decomposition of the household planning horizon into spending horizon and risk-

perceiving horizon is in no way aiming to fully and accurately separate out the subjective

factors that are affected by mental accounting. On one hand, the choice of subjective factors

that we choose is not supported by any theories. These factors can also be argued as factors

that affect household spending horizon instead. On the other hand, there are many other

factors that can affect households in reporting their planning horizon. The adjusted R2 is only

Table 9. Household direct and indirect stockholdings and planning horizons

VariablesDirect holdings Indirect holdings

Coeff. t-stat Coeff. t-stat Coeff. t-stat Coeff. t-stat

CST �0.2389 �7.25 �0.2423 �6.97 �0.0290 �0.76 �0.0093 �0.23Log(INC) 0.0002 0.09 �0.0001 �0.05 �0.0090 �3.25 �0.0125 �4.33Log(NTW) 0.0284 13.59 0.0269 7.08 0.0098 4.03 �0.0064 �1.45AGE �0.0003 �1.15 �0.0004 �1.40 0.0011 3.51 0.0009 2.75EDU 0.0081 5.27 0.0073 3.23 0.0247 13.81 0.0162 6.19RSK_AVS �0.0291 �7.01 �0.0271 �5.20 �0.0612 �12.71 �0.0442 �7.30BRW_CTR �0.0045 �0.50 �0.0016 �0.14 �0.0583 �5.52 �0.0238 �1.80BUS/NW �0.0791 �6.63 �0.0790 �6.60 �0.0658 �4.75 �0.0623 �4.49RE/NW �0.0064 �3.48 �0.0063 �3.44 0.0064 3.00 0.0066 3.10PEN/NW 0.0187 3.50 0.0185 3.46 �0.0196 �3.16 �0.0202 �3.25PLN_HRZ 0.0013 1.39 0.0038 3.40SPD_HRZ �0.0035 �0.59 – – �0.0041 �0.60PEC_HRZ 0.0069 0.64 – – 0.0597 4.77Adjusted R2 0.12 0.12 0.12 0.12

Note: This table documents the effect of the planning horizon and its two components on household direct and

indirect stockholdings. Indirect stockholdings are through mutual funds, trusts, or annuities. We study this effect in

the sub-sample of ‘‘savers.’’ We report the coefficients and their t-statistics for the OLS regressions; the adjusted R2

for the OLS regressions are also reported.


DOI: 10.1002/rbf.10

100 P. He and X. Hu

18% for regression (1). With these concerns, we calculate the residuals from regression (1),

denoted as RES_HRZ, to check whether the residual has any explaining power in the

household portfolio variation. The standard deviations of RES_HRZ are around 3.2 in both

full sample and sub-sample of savers. The regression results are reported in Table 11.

In Table 11, the coefficients on RES_HRZ in all regressions are significant. This confirms

our conjecture that some other factors, which are not included in regression (1), can also

affect household planning horizons. To compare the effect of different constructed horizon

variables on household portfolios, we first calculate the standard deviations of each horizon

variable:

STD Full sample Savers

SPD_HRZ 0.62 0.59PEC_HRZ 1.18 1.12RES_HRZ 3.24 3.20

The product of the standard deviation and the corresponding OLS coefficient is also

calculated. The absolute value of this product is reported below, in order to compare the

relative importance of each horizon variable.

Full sample Savers

SPD_HRZ 0.005 0.005PEC_HRZ 0.074 0.077RES_HRZ 0.010 0.017

Table 10. Cross-asset diversification and time diversification

VariablesOLS(1) OLS(2)

Coeff. t-stat Coeff. t-stat

CST �0.1853 �4.52 �0.1599 �3.70Log(INC) �0.0083 �2.81 �0.0124 �4.06Log(NTW) 0.0314 12.02 0.0121 2.58AGE 0.0008 2.52 0.0006 1.80EDU 0.0306 16.04 0.0204 7.35RSK_AVS �0.0876 �17.14 �0.0675 �10.52BRW_CTR �0.0602 �5.38 �0.0193 �1.38BUS/NW �0.1301 �8.83 �0.1255 �8.50RE/NW 0.0005 0.24 0.0007 0.33PEN/NW �0.0026 �0.39 �0.0031 �0.48NMF 0.0148 14.40 0.0151 14.77PLN_HRZ 0.0038 3.24 – –SPD_HRZ – – �0.0049 �0.67PEC_HRZ – – 0.0699 5.26Adjusted R2 0.30 0.30

Note: This table documents the effect of the planning horizon and its two components on household portfolio choice

while controlling the effect of cross-asset diversification by adding the number of mutual funds (NMF) in the

regression. We study this effect in the sub-sample of ‘‘savers.’’ We report the coefficients and their t-statistics for the

OLS regressions; the adjusted R2 for the OLS regressions are also reported.


DOI: 10.1002/rbf.10


As we can see, the constructed subjective mental accounting variable, PEC_HRZ, has the

largest impact on household portfolio decisions compared with other horizon variables.

Although the constructed residual horizon, RES_HRZ, is statistically significant, its impact on

household portfolios is not as important as the risk perceiving factors we identify in this study.

Other robustness checksWe also conduct some other robustness checks, which can be summarized below16. We run

the regressions within two age groups: The working households, or households younger than

65; and the retired households, or households older than 65. The main results are similar to

those in Table 5, namely, the effect of the planning horizon remains significant for each age

group, and the proxy for the risk-perceiving horizon is significant but the proxy for

the spending horizon is less so. One interesting observation is that, in the younger group, the

age effect is positive and significant while in the older group, negative and insignificant. This

confirms the results in Heaton and Lucas (2000) as we pointed out earlier. This result

demonstrates that age is not a perfect proxy for investment horizon, especially for younger

households. We also find that the coefficient on borrowing constraints is large in absolute

value in older households. This implies that without labor income, borrowing constraints

become much more restrictive in limiting the risk-taking behavior for retired households.

Table 11. Robustness check using residual horizons

Full sample Subsample-savers

VariablesOLS Tobit OLS Tobit

Coeff. t-stat Coeff. p-value Coeff. t-stat Coeff. p-value

CST �0.2604 �10.31 �0.9474 0.00 �0.2579 �5.93 �0.8242 0.00Log(INC) �0.0039 �2.07 �0.0234 0.00 �0.0131 �4.20 �0.0254 0.00Log(NTW) 0.0170 6.30 0.0378 0.00 0.0195 4.11 0.0348 0.00AGE 0.0006 2.63 0.0000 0.98 0.0005 1.52 0.0006 0.26EDU 0.0182 12.17 0.0326 0.00 0.0232 8.26 0.0383 0.00RSK_AVS �0.0691 �18.33 �0.1034 0.00 �0.0712 �10.92 �0.0999 0.00BRW_CTR �0.0085 �1.06 �0.0267 0.05 �0.0233 �1.64 �0.0574 0.01BUS/NW �0.0580 �7.35 �0.0948 0.00 �0.1396 �9.33 �0.2180 0.00RE/NW 0.0006 2.00 0.0017 0.00 �0.0001 �0.04 �0.0080 0.13PEN/NW �0.0005 �0.33 �0.0002 0.93 �0.0006 �0.08 �0.0398 0.03SPD_HRZ �0.0082 �1.60 �0.0171 0.04 �0.0079 �1.07 �0.0061 0.56PEC_HRZ 0.0625 8.38 0.1354 0.00 0.0692 5.13 0.1208 0.00RES_HRZ 0.0030 4.35 0.0058 0.00 0.0052 4.30 0.0088 0.00Adjusted R2 0.28 0.28

Note: This table documents the effect of the residual component of the planning horizon on household portfolio

choice. The planning horizon is decomposed into three parts: the Spending Horizon (SPD_HRZ), the Risk Perceiving

Horizon (PEC_HRZ), and the Residual Horizon (RES_HRZ). We study this effect in both the full sample and the sub-

sample of ‘‘savers.’’ We report the coefficients and their t-statistics or p-values for the OLS and Tobit regressions; the

adjusted R2 for the OLS regressions are also reported.

16Tables and details can be obtained from the authors upon request.


DOI: 10.1002/rbf.10

102 P. He and X. Hu

The other robustness check is that we replace the dependant variable in Equation (2) with

ST/NW, or the value of stocks divided by net worth. The main results remain robust: The

coefficient on the planning horizon is positive and significant, while the proxy for the risk-

perceiving horizon has more explanatory power than the proxy for the spending horizon.

CONCLUSION

Investors have a limited capacity to make fully rational investment decisions, and they tend to

simplify a complicated information processing and decision making problem into several

manageable dimensions. The way an investor structures his decision problem can frame his

perception of risk. In this study, we find empirical evidence that the horizon matters—

households with longer planning horizons invest more in stocks. We further explore the

interaction between a household’s spending/investment horizon and its mental accounting, or

risk-perceiving horizon. We argue that a household’s reported planning horizon reflects a

combination of its investment horizon and its risk-perceiving horizon. Our empirical results

show that the household planning horizon has a significant and positive effect on household

risk-taking behavior, and this effect is mainly driven by the mental accounting component, or

the risk perceiving horizon. Therefore, in practice individuals make investment decisions

based on the horizon at which the risk is perceived rather than the horizon at which cash is

needed. Our results are consistent with the myopic loss aversion explanation proposed by

Thaler et al. (1997), and/or the cognitive bias explanation proposed by Samuelson (1994).

An interesting question that this study raises is the following: Is the difference in relative

stockholdings across planning horizons due to the over-investment in stocks by households

with longer horizons or under-investment in stocks by households with shorter horizons?

Further research is needed to identify the answer to this question.

In addition, the perception of investment risk consists of two parts: The perception of risk

dynamics across time and the perception of the non-dynamic aspect of risks. Our study

focuses mainly on the first part of a household’s risk-perceiving behavior, though we

understand individuals may blend cross sectional risks and dynamic risks together. It is up to

future research to further study these two parts separately and/or jointly.

The authors thank Gib Bassett, Michael Brennan, Robert Chirinko, and Debbie Lucas for

their comments and suggestions. Financial supports from the University of Illinois at Chicago

and Tsinghua University are gratefully acknowledged.

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LIST OF FORESEEABLE EXPENDITURES

EXP1: Education of children

EXP2: Education of others (including self and spouse/partner)

EXP3: Health care for self and spouse/partner

EXP4: Health Care for others (including elderly parents/disabled child)

EXP5: Health care/medical expenses—not available for whom

EXP6: General support for self/spouse/partner in retirement or old age

EXP7: General support for child/grandchild

EXP8: General support for parents

EXP9: General support for others or not available for whom

EXP10: Baby

EXP11: Purchase of new home (including vacation home)

EXP12: Purchase of car or other large durable goods


DOI: 10.1002/rbf.10

104 P. He and X. Hu

EXP13: Burial expenses

EXP14: Taxes

EXP15: Home repairs or improvements

EXP16: Weddings, vacations, moving, and other special expenditures

EXP17: Business and investment; start/expand own business

EXP18: Investment, major purchase

EXP19: Charitable expense

EXP20: Bills and living expenses

EXP21: Other major financial obligations


DOI: 10.1002/rbf.10


household investment—the horizon effect

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