May 2016 Open seminar of Eesti Pank

1. Portfolio Allocation, Background Risk
and Households’ Flight to Safety
Sarah Brown (Sheffield)
Daniel Gray (Sheffield)
Mark N. Harris (Curtin)
Christopher Spencer (Loughborough)
May 2016

2. I. Introduction and Background
 A stylised fact in the household finance literature
is households’ inclination to shun owning risky
assets;
 Observation initially appears uncontroversial, yet
constitutes one of a number of empirical
‘puzzles’ that have traditionally sat
uncomfortably with the predictions of financial
and economic theory;
 Stockholding puzzle has attracted significant
attention, e.g. Fratantoni, 2001; Haliassos and
Bertaut, 1995; Bertaut, 1998.

3. I. Introduction and Background
 What households actually do is often
inconsistent with formal theories prescribing
what they ought to do.
 This highlights a disconnect between ‘positive’
and ‘normative’ household finance (Campbell,
1996).
 To explain such puzzles, many studies have
relaxed the assumptions of standard finance
models, e.g. by including transaction costs,
credit constraints and background risks.

4. I. Introduction and Background
 In classical portfolio theory, assuming complete
markets, background risks should not influence
allocation decisions, as such risks can be fully
insured against.
 Incomplete markets, background risk will cause
households to reduce their total desired risk
exposure by reducing exposure to avoidable
risks (e.g. holding more safe assets).
 This behaviour was termed ‘temperance’.

5. I. Introduction and Background
 In the context of risky asset allocation,
theoretical concept of ‘temperance’
developed to address the inconsistency
identified by Campbell, 1996;
 This concept provides an intuitive basis for
some microeconometric studies which seek
to explain observed asset allocation.

6. I. Introduction and Background
 Temperance (Pratt and Zeckhauser, 1987; Kimball,
1991; Gollier and Pratt, 1996) implies that
households who suffer more from labour market
uncertainty should choose to be exposed to less
financial risk;
 Labour income risk has received considerable
attention;
 In addition – health, housing payments and
unemployment risks are potential sources of
background risk.

7. I. Introduction and Background
 Empirical evidence supporting this prediction
has been found using household-level data:
 Bertaut (1995) and Haliassos and Bertaut
(1995): labour income risk is negatively
associated with stock ownership;
 Fratantoni (2001): labour income risk and
home ownership costs associated with less
risky asset holding.

8. I. Introduction and Background
 Vissing-Jorgensen (2002): larger standard
deviation of nonfinancial income reduces
stock investment;
 Heaton and Lucas (2000): investors invest
less in stocks with more volatile business
income;
 Qi and Wu (2014): labour income, housing
value and business income volatility reduce
stockholding.

9. I. Introduction and Background
 We contribute to this growing microeconometric
literature which aims to test this hypothesis;
 Existing methods: OLS; binary probits and logits;
and tobits (adding in extra explanatory variables
to capture background risk).
 We propose a deflated fractional ordered probit
(DFOP) model;
 ‘Deflated’ refers to the prediction that the fraction
of risky assets held will be lower than would be
in the absence of background risk.

10. I. Introduction and Background
 Notion of background risk is integral to our story: our
statistical model introduces a background risk
equation which allows:
(1) Households to move away from a ‘background risk
neutral’ portfolio composition;
(2) Investigation of the extent to which households re-
allocate resources from high risk to less risky (safe,
medium) asset classes.
 We uniquely combine methods from the literature on
category inflation with methods of compositional data
analysis.

11. II. Method
 Aim to model the share of the household’s
portfolio allocated to each type of asset
(assumed in the absence of background
risk);
 Shares are labelled j = 0, 1, 2
 The shares are decreasing in risk as j
increases.

12. II. Method
 We could model each of the shares as a
linear system:
𝑠𝑖𝑗 = 𝒙𝒊
′
𝜷𝒋 + 𝑢𝑖𝑗
 Such an approach does not ensure:
0 ≤ 𝐸 𝑠𝑖𝑗 𝒙𝒊 = 𝒙𝒊
′
𝜷𝒋 ≤ 1
 Issues handling boundary observations of 0
and 1.

13. II. Method
 Kawasaki and Lichtenberg (2014) suggest the
fractional ordered probit model, which appears an
ideal starting point:
1. it explicitly recognises the limited range of the dependent
variable;
2. all predictions and expected values of the model lie in the
(0,1) interval;
3. number of categories that the dependent variable can take is
finite (and small);
4. zero shares are not problematic;
5. it recognises the ordering of the categories such that larger
values of j correspond to decreasing risk

14. II. Method
 Agents posses an underlying latent variable (𝑦𝑖
∗
)
as follows:
𝑦𝑖
∗
= 𝒙𝒊
′
𝜷 + 𝑢𝑖
 Standard OP model, the outcome j chosen by
household i depends on the relationship between
the latent variable & the boundary parameters, 𝜇 :
𝑦𝑖 =
0 𝑖𝑓 𝑦𝑖
∗
< 𝜇0
1 𝑖𝑓 𝜇1 ≤ 𝑦𝑖
∗
< 𝜇1
2 𝑖𝑓 𝑦𝑖
∗
≥ 𝜇1

15. II. Method
 This gives the corresponding likelihood
function of household i to be:
𝓁𝑖
=
𝑗=0
𝐽−1=2
Φ 𝜇0 − 𝒙𝒊
′
𝜷 𝑑 𝑖0 𝛷 𝜇1 − 𝒙𝒊
′
𝜷

16. II. Method
 OP model, a household can be in only one of
the j=0,1,2 outcomes (given by the indicator
function, 𝑑𝑖𝑗 = 1 𝑦𝑖 = 𝑗);
 Hence, the OP is not sufficient to model
fractional data;
 For fractional data, we are interested in the
effect of the covariates on:
𝐸 𝑠𝑖𝑗 𝒙𝒊 , 𝑗 = 0, 1, 2

17. II. Method
 We can replace 𝑑𝑖𝑗 = 1 𝑦𝑖 = 𝑗 with 𝑠𝑖𝑗 (the
share of total assets in aggregate j for
household i).
 This changes the likelihood function for
household i to be:
𝓁𝑖
=
𝑗=0
Φ 𝜇0 − 𝒙𝒊
′
𝜷 𝑠 𝑖𝑗=0
Φ 𝜇1 − 𝒙𝒊
′
𝜷

18. II. Method
 The allocation equation, 𝑦𝑖
∗
, is given by:
𝐸 𝑠𝑖𝑗=0 𝑥𝑖 = Φ 𝜇0 − 𝒙𝒊
′
𝜷
𝐸 𝑠𝑖𝑗=1 𝑥𝑖 = Φ 𝜇1 − 𝒙𝒊
′
𝜷 − Φ 𝜇0 − 𝒙𝒊
′
𝜷
𝐸 𝑠𝑖𝑗=2 𝑥𝑖 = 1 − Φ 𝜇1 − 𝒙𝒊
′
𝜷
 By construction, all satisfy:
0 ≤ 𝐸 𝑠𝑖𝑗 𝒙𝒊 ≤ 1
 Consistent with the risk ordering of the j asset
bundles in the household’s portfolio.

19. II. Method
 The boundary parameters μ, will be of special
interest: they allocate share bundles into one of
three groups: high, medium and low risk assets.

20. II. Method
 How can we accommodate the relatively low
fraction of high-risk assets?
 Answer: envisage the above model as
explaining, a household’s portfolio allocation
in the absence of background risk.
 This allocation needs to be impacted in some
way, to allow individuals the opportunity to
move away from this (deflate the asset
allocation equation).

21. II. Method
 Two background risk equations:
ℎ𝑖
∗
= 𝒘𝒊
′
𝜹 + 𝜀𝑖
𝑚𝑖
∗
= 𝒘𝒊
′
𝝀 + 𝜑𝑖
 ℎ𝑖
∗
and 𝑚𝑖
∗
represent unobserved latent
propensities to move away from the choice of
risky assets j=0 (high risk) and j=1 (medium
risk).

22. II. Method
 These propensities are also modelled as fractional
OP:
ℎ𝑖 =
0 𝑖𝑓 ℎ𝑖
∗
< 𝜇0
ℎ
1 𝑖𝑓 𝜇0
ℎ
≤ ℎ𝑖
∗
< 𝜇1
ℎ
2 𝑖𝑓 ℎ𝑖
∗
≥ 𝜇1
ℎ
; 𝑚𝑖 =
1 𝑖𝑓 𝑚𝑖
∗
> 0
2 𝑖𝑓 𝑚𝑖
∗
≤ 0
 Consider the tempered expected value of the risky
asset share:
𝐸 𝑠𝑖𝑗=0 𝒙𝑖, 𝒘𝑖 =
Φ 𝜇0 − 𝒙𝒊
′
𝜷 ×
Allocation
Φ 𝜇0
ℎ
− 𝒘𝒊
′
𝜹)
Background Risk

23. II. Method
 The expected values for the medium risk
asset (j=1) bundle is:
𝐸 𝑠𝑖,𝑗=1 𝒙𝑖, 𝒘𝑖
=
{ Φ 𝜇1−𝒙 𝒊
′
𝜷 −Φ 𝜇0−𝒙 𝒊
′
𝜷 ×Φ 𝒘 𝒊
′
𝝀 }
𝑦 𝑖=1×𝑚 𝑖=1
+ {Φ 𝜇0−𝒙 𝒊
′ 𝜷 ×[Φ 𝜇 𝟏
𝒉− 𝒘 𝒊
′ 𝜹 −Φ 𝜇 𝟎
𝒉− 𝒘 𝒊
′ 𝜹 ]}
𝑦 𝑖=0×ℎ 𝑖=1

24. II. Method
 The expected values for the safe risk asset
(j=2) bundle is:
𝐸 𝑠𝑖,𝑗=2 𝒙𝑖, 𝒘𝑖
=
[1−Φ 𝜇1−𝒙 𝒊
′
𝜷 ]
𝑦 𝑖=2
+ {Φ 𝜇0−𝒙 𝒊
′
𝜷 ×[1−Φ 𝜇1
ℎ− 𝒘 𝒊
′
𝜹 ]}
𝑦 𝑖=0×ℎ 𝑖=2
+ { Φ 𝜇1−𝒙 𝒊
′ 𝜷 −Φ 𝜇0−𝒙 𝒊
′ 𝜷 ×[1−Φ 𝒘 𝒊
′ 𝝀 ]}
𝑦 𝑖=1×𝑚 𝑖=2

25. II. Method
 With these modifications the likelihood
function becomes:
𝓁𝑖 =
𝑗
𝐸 𝑠𝑖𝑗=0 𝒙𝑖, 𝒘𝑖) 𝑠 𝑖𝑗=0
𝐸 𝑠𝑖𝑗=1 𝒙𝑖, 𝒘𝑖) 𝑠 𝑖𝑗=1
𝐸 𝑠𝑖𝑗=2 𝒙𝑖, 𝒘𝑖) 𝑠 𝑖𝑗=2
 The choice of variables which enter 𝒙𝑖 and
𝒘𝑖 will be important for identification.

26. DFOP Model: Background risk
affecting all non-safe assets
Household
High
risk
(yi=0)
Safe
(yi=2)
Medium
risk
(yi=1)
Medium
risk
(yit=1;
hi=1ǀ yi=0; mi=1ǀ yi=1)
High
risk
(hi=0ǀ yi=0)
Allocation
equation (y)
Background risk
equations (h,m)
Safe
(yi=2;
hi=2ǀ yi=0; mi=2ǀ yi=1)

27. III. Cross-Sectional Data
 US Survey of Consumer Finances (SCF), 1998-
2013, repeated cross-section survey;
 SCF is sponsored by the Federal Reserve board
in cooperation with the Department of the
Treasury;
 Information on families’ balance sheets,
pensions, income and demographic
characteristics.
 No other US survey collects comparable data.

28. II. Cross-Sectional Data
 Given the high rate of non-response
associated with microdata relating to wealth
information, the SCF provides imputations
which give a distribution of outcomes for
each observation;
 Our sample comprises 28,005 households.
 We use proxies for uncertainty to underline
the impact of different types of uncertainty on
household portfolio composition.

29. III. Dependent Variables
 Low Risk Share: (Value of checking accounts, saving accounts
and bonds, money market accounts, call accounts, certificates
of deposits and US savings bonds) / Total value of financial
assets.
 Medium Risk Share: (Value of state and local bonds, tax free
bonds, fairly safe component of retirement funds and saving
accounts and cash value of life insurance policy) / Total value
of financial assets.
 High Risk Share: (Value of directly held stock, stock mutual
funds and amount of retirement and saving accounts in stocks
in addition to managed accounts including annuities and trust
funds) / Total value of financial assets.

30. Proportion of low risk assets; all households; 0.8%
hold zero low risk assets
05
10152025
Percent
0 .2 .4 .6 .8 1
Proportion of Low Risk Assets

31. Proportion of low risk assets; households holding
low risk assets
05
10152025
Percent
0 .2 .4 .6 .8 1
Proportion of Low Risk Assets: Excluding Zero Shares

32. Proportion of medium risk assets; all households;
33.13% hold zero medium risk assets
0
10203040
Percent
0 .2 .4 .6 .8 1
Proportion of Medium Risk Assets

33. Proportion of medium risk assets; households
holding medium risk assets
02468
Percent
0 .2 .4 .6 .8 1
Proportion of Medium Risk Assets: Excluding Zero Shares

34. Proportion of high risk assets; all households;
47.1% hold zero high risk assets
0
1020304050
Percent
0 .2 .4 .6 .8 1
Proportion of High Risk Assets

35. Proportion of high risk assets; households holding
high risk assets
01234
Percent
0 .2 .4 .6 .8 1
Proportion of High Risk Assets: Excluding Zero Shares

36. III. Household Asset Allocation Variables (y
variables)
Age; gender; ethnicity; marital status; children;
education; employment status; risk attitudes;
home ownership; income expectations;
economic expectations; interest rate
expectations; self-assessed health; past
bankruptcy; household income; net worth; year.

37. III. Background Risk Variables (r
variables)
 Major Financial Exp.: =1 if expects any major
expenses.
 No Health Ins.: =1 if not all individuals are
covered by health insurance policy.
 Inheritance: = 1 if expect to receive a
substantial inheritance or transfer of assets in
the near future.
 Know Inc.: =1 if know what income will be in
next year.

38. III. Background Risk Variables (r
variables)
 Start Business: = 1 if started own business.
 Other Business: = 1 if acquired a business
through other means.
 Positive Inc. Diff: Difference between
expected and actual income from past year
(Income greater than expected income)
 Negative Inc. Diff: Difference between
expected and actual income from past year
(Income less than expected income).

39. IV. Results (Summary of asset
allocation equation)
 Age (-); Age2 (+); White (-); Hispanic (+);
Married (-); Have Children in Household (+);
College Degree (-); Employed (+); Self-
Employed (+); Not in the Labour Force (+);
Risk Attitudes (-); Homeowner (-); Economic
Expectations (-); Interest Rate Expectations
(-); Self-Assessed Health (-); Ever Reported
Bankrupt (+); Total Household Income (-);
and Household Net Wealth (-).

40. Background Risk Coefficients
High Risk Equation
Medium Risk Equation
(Binary Equation)
Major Financial
Exp.
-0.049** 0.025
(0.022) 0.022
No Health Ins.
0.237*** 0.303***
(0.083) (0.039)
Inheritance
-0.189*** -0.058**
(0.029) (0.029)
Know Inc.
-0.018 0.015
(0.024) (0.025)
Other Business
0.060** -0.086*
(0.028) (0.044)
Started Business
0.118*** 0.025
(0.025) (0.032)
Positive Inc. Diff
0.000 -0.004
(0.002) (0.003)
Negative Inc. Diff
0.010*** 0.002
(0.003) (0.003)

41. Background Risk Coefficients
(continued)
High Risk Equation
Medium Risk Equation
(Binary Equation)
2001
0.016 0.064
(0.064) (0.062)
2004
0.226*** 0.226***
(0.063) (0.066)
2007
0.144** -0.537***
(0.065) (0.053)
2010
0.302*** -0.582***
(0.064) (0.051)
2013
0.257*** -0.574***
(0.063) (0.052)

42. Overall Marginal Effects (Background Risk Variables)
High Risk Assets Medium Risk Assets Low Risk Assets
Major
Financial Exp.
0.006** -0.008* 0.002
(0.003) (0.004) (0.005)
No Health Ins.
-0.030*** -0.046*** 0.077***
(0.011) (0.009) (0.010)
Inheritance
0.024*** 0.000 -0.024***
(0.004) (0.006) (0.006)
Know Inc.
0.002 -0.004 0.002
(0.003) (0.005) (0.005)
Other
Business
-0.008** 0.021** -0.014
(0.004) (0.009) (0.009)
Started
Business
-0.015*** 0.002 0.013*
(0.003) (0.006) (0.007)
Positive Inc.
Diff
0.000 0.001 -0.001
(0.000) (0.001) (0.001)
Negative Inc.
Diff
-0.001*** 0.000 0.001*
(0.000) (0.001) (0.001)

43. Overall Marginal Effects (Other Variables)
High Risk Assets Medium Risk Assets Low Risk Assets
2001
0.014 -0.012 -0.002
(0.008) (0.010) (0.010)
2004
-0.018** -0.031*** 0.049***
(0.009) (0.011) (0.010)
2007
-0.039*** 0.118*** -0.079***
(0.008) (0.009) (0.009)
2010
-0.068*** 0.137*** -0.069***
(0.008) (0.009) (0.009)
2013
-0.059*** 0.132*** -0.073***
(0.008) (0.009) (0.009)
ln(Income)
0.658*** 0.014 -0.672***
(0.031) (0.009) (0.031)
IHS(Net
Wealth)
0.077*** 0.002 -0.079***
(0.004) (0.001) (0.004)
Risk
Attitudes
0.092*** 0.002 -0.094***
(0.003) (0.001) (0.003)

44. Purged Marginal Effects
High Risk Assets Medium Risk Assets Low Risk Assets
2001
0.023 -0.011 -0.012
(0.019) (0.009) (0.010)
2004
0.016 -0.008 -0.008
(0.020) (0.009) (0.010)
2007
-0.030 0.014 0.016
(0.019) (0.010) (0.010)
2010
-0.042*** 0.020** 0.022**
(0.018) (0.010) (0.009)
2013
-0.038** 0.018* 0.020**
(0.019) (0.010) (0.010)
ln(Income)
0.958*** -0.459*** -0.499***
(0.053) (0.066) (0.050)
HIS(Net
Wealth)
0.112*** -0.054*** -0.058***
(0.005) (0.007) (0.006)
Risk
Attitudes
0.958*** -0.459*** -0.499***
(0.053) (0.066) (0.050)

45. Purged Marginal Effects (Continued)
High Risk Assets Medium Risk Assets Low Risk Assets
Income
Expectations
0.005 -0.003 -0.003
(0.004) (0.002) (0.002)
Economic
Expectations
0.011*** -0.005*** -0.006***
(0.004) (0.002) (0.002)
Bankrupt
-0.083*** 0.040*** 0.043***
(0.011) (0.007) (0.007)
Homeowner
0.043*** -0.021*** -0.022***
(0.007) (0.005) (0.004)
College
Degree
0.135*** -0.065*** -0.070***
(0.008) (0.009) (0.007)
Male
-0.024** 0.011** 0.012**
(0.011) (0.005) (0.006)
White
0.047*** -0.023*** -0.025***
(0.011) (0.006) (0.005)
Children
Present
-0.045*** 0.022*** 0.024***
(0.007) (0.005) (0.004)

46. Background Risk Marginal Effects
High Risk
Assets
Medium Risk
Assets
Low Risk
Assets
Binary
Equation
Major
Financial Exp.
0.017** -0.009** -0.009** 0.010
(0.008) (0.004) (0.004) (0.009)
No Health Ins.
-0.084*** 0.042*** 0.042*** 0.118***
(0.030) (0.014) (0.015) (0.016)
Inheritance
0.067*** -0.033*** -0.034*** -0.023
(0.010) (0.005) (0.005) (0.011)
Know Inc.
0.006 -0.003 -0.003 0.006
(0.009) (0.004) (0.004) (0.010)
Other
Business
-0.021** 0.011** 0.011** -0.033**
(0.010) (0.005) (0.005) (0.017)
Started
Business
-0.042*** 0.021*** 0.021*** 0.010
(0.009) (0.004) (0.004) (0.012)
Positive Inc.
Diff
0.000 0.000 0.000 -0.002
(0.001) (0.000) (0.000) (0.001)
Negative Inc.
Diff
-0.004*** 0.002*** 0.002*** 0.001
(0.001) (0.001) (0.001) (0.001)

47. Background Risk Marginal Effects
(continued)
High Risk
Assets
Medium Risk
Assets
Low Risk
Assets
Binary
Equation
2001
-0.006 0.003 0.003 0.025
(0.023) (0.011) (0.012) (0.024)
2004
-0.080*** 0.040*** 0.040*** 0.088***
(0.022) (0.011) (0.011) (0.026)
2007
-0.051** 0.025** 0.026** -0.209***
(0.023) (0.011) (0.012) (0.021)
2010
-0.107*** 0.053*** 0.054*** -0.226***
(0.022) (0.011) (0.012) (0.020)
2013
-0.091*** 0.045*** 0.046*** -0.223***
(0.022) (0.011) (0.011) (0.020)

48. Distribution of Asset Allocation
Sample
Proportions
EVs at
X_bar (with
background
risk)
EVs at
X_bar
(without
background
risk)
Reallocation
% (Ordered)
(High)
Reallocation
% (Binary)
(Medium)
High Risk
Asset
0.2729 0.2487 0.3623 0.6865 -
Medium
Risk Asset
0.2497 0.2902 0.5216 0.2111 0.4097
Low Risk
Asset
0.4774 0.4611 0.1161 0.1024 0.5903

49. Distribution of Asset Categories - % of Reallocation
High
risk
(yi=0)
Safe
(yi=2)
Medium
risk
(yi=1)
Medium
risk
(yit=1;
hi=1ǀ yi=0; mi=1ǀ yi=1)
High
risk
(hi=0ǀ yi=0)
Safe
(yi=2;
hi=2ǀ yi=0; mi=2ǀ yi=1)
No Background
Risk
Background
Risk
0.6865
0.2111
0.1024
0.4097
0.5903
0.3623
0.5216
0.1161
0.2487
0.2902
0.4611

50. Distribution of Asset Categories - % of Reallocation
Decomposition of Effects of Background Risk
% high risk remaining high risk 0.6865
% high risk going to medium risk 0.2111
% high risk going to low risk 0.1024
% medium risk remaining medium risk 0.4097
% medium risk going to safe risk 0.5903

51. Distribution of Asset Allocation
Asset
Allocation
Decomposition of Reallocation in the
Presence of Background Risk
High 0.2487 = 0.3623x0.6865
Medium 0.2902 = (0.5216x0.4097)+(0.3623x0.2111)
Low 0.4611 = 0.1161+(0.3623x0.1024)+(0.5216x0.5903)
• 68.65% of the purged high risk asset allocation (0.3623)
remain high risk in the presence of background risks.
• 21.11% of high risk assets are reallocated to medium risk,
whilst 40.97% of medium risk assets (0.5216) remain in
medium risk.
• 10.24% of high risk assets are reallocated to safe assets
and 59.03% of medium risk assets are also reallocated to
safe assets in the presence of background risk.

52. Distribution of Asset Allocation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
High Risk Asset Medium Risk Asset Low Risk Asset
Sample Proportions
EVs at X_bar
Purged EVs at X_bar
Reallocation % (Ordered)
Reallocation % (Binary)

53. V. Panel Data - PSID
 US Panel Study of Income Dynamics (PSID),
1999-2013, panel survey conducted
biennially;
 PSID covers a nationally representative
sample of over 18,000 individuals living in
5,000 families in the United States;
 Wealth survey includes information on a
variety of assets held by the household.

54. V. Panel Data - PSID
 We have an unbalanced panel of around
9,880 household heads with approximately
39,500 observations.
 We define risky, medium and save assets in
a similar way to the SCF;
 Risky assets includes direct and indirect
stock holding, medium risk assets includes
assets such as bonds whilst safe assets
includes checking accounts.

55. Low Risk asset Category
0
1020304050
0 .2 .4 .6 .8 1
Proportion of Low Risk Assets
0
1020304050
Percent
0 .2 .4 .6 .8 1
Proportion of Low Risk Assets: Excluding Zero Shares

56. Medium Risk asset category
0
20406080
0 .2 .4 .6 .8 1
Proportion of Medium Risk Assets
0246
Percent
0 .2 .4 .6 .8 1
Proportion of Medium Risk Assets: Excluding Zero Shares

57. High risk asset category
0
204060
0 .2 .4 .6 .8 1
Proportion of High Risk Assets
02468
Percent
0 .2 .4 .6 .8 1
Proportion of High Risk Assets: Excluding Zero Shares

58. Household Asset Allocation
Variables - PSID
 Age; Gender; Ethnicity; Marital Status;
Children; Education; Employment Status;
Risk Attitudes; Home Ownership; Household
Income; Household Net Wealth; Year; and
Region Dummies.
 Mundlak Variables: Age; Net Wealth; and
Household Income

59. Background risk Variables
 Business Ownership: =1 if household owns a
business.
 No Health Insurance: = 1 if not all household
members are covered by health insurance.
 Inheritance: = 1 if has received an
inheritance in the past year.
 Plus Income Uncertainty Measures

60. Measures of Income Uncertainty
 (1) Coefficient of Variation (Cardak and Wilkins
(2009); Becker and Dimpfl (2014)): standard
deviation of Income/mean income across time
 (2) Household Income Equation (Cross-
Sectional) (Robst et al. (1999), Carroll, 1994,
Carroll and Samwick (1995)):
Ln(YHit) = Xitβ + εit;
 YH is household income; X includes married,
education, race, gender, children and year.
 Uncertainty is the standard deviation of εit.

61. Measures of Income Uncertainty
 Permanent and Transitory Income (Diaz-Serrano
(2004)):
𝐿𝑛 𝑌𝐻𝑖𝑡 = 𝑋𝑖𝑡 𝛽 + 𝜇𝑖 + 𝜀𝑖𝑡
 YH is household income; X includes Married,
education, gender, race, children and year
dummies
- Permanent Income Uncertainty – SD(𝑋𝑖𝑡 𝛽 + 𝑢𝑖)
- Transitory Income Uncertainty – SD(𝜀𝑖𝑡)

62. Panel Results – Summary of Asset
allocation
 Age (-), Age2 (+), White (-), Divorced (+),
Child (+), Homeowner (-), College Degree (-),
Household Income (-), Net wealth (-), Health
Status (-), and Risk Tolerance (-).

63. PSID Overall Marginal Effects - DFOP
High Risk
Assets
Medium Risk
Assets Low Risk Assets
Income 0.097* 0.039* -0.136*
(0.053) (0.021) (0.074)
Net Wealth 0.071*** 0.028*** -0.098***
(0.005) (0.002) (0.007)
Risk Tolerance 0.007*** 0.003*** -0.009***
(0.001) (0.000) (0.002)
Health Status 0.012*** 0.005*** -0.017***
(0.002) (0.001) (0.003)
College Degree 0.023** 0.009** -0.032**
(0.011) (0.004) (0.015)
White 0.084*** 0.033*** -0.117***
(0.005) (0.002) (0.007)
Child -0.029*** -0.011*** 0.040***
(0.004) (0.002) (0.006)

64. PSID Overall Marginal Effects (Background
Risk)
High Risk Assets Medium Risk Assets Low Risk Assets
Own Business
0.010* 0.013 -0.023**
(0.006) (0.008) (0.011)
No Health Ins.
-0.037** 0.001 0.036
(0.018) (0.022) (0.028)
Inheritance
0.026*** 0.025** -0.052***
(0.010) (0.012) (0.014)
CV Income
0.428*** 0.045 -0.473***
(0.076) (0.109) (0.135)
SD Income
Residuals
0.042*** 0.007 -0.049***
(0.007) (0.014) (0.016)
SD Transitory
Income
0.043*** 0.025** -0.067***
(0.008) (0.012) (0.014)
SD Permanent
Income
-0.024 -0.068** 0.092**
(0.024) (0.028) (0.039)
SD Transitory
Income
0.043*** 0.028** -0.071***
(0.007) (0.013) (0.014)

65. Distribution of Asset Allocation
(PSID) – Coefficient of Variation
Sample
Proportions
EVs at
X_bar (with
background
risk)
EVs at
X_bar
(without
background
risk)
Reallocation
% (Ordered)
Reallocation
% (Binary)
High Risk
Asset
0.2189 0.1990 0.2619 0.7588
Medium
Risk Asset
0.1557 0.1673 0.2195 0.1751 0.5489
Low Risk
Asset
0.6254 0.6336 0.5186 0.06608 0.4511

66. Distribution of Asset Allocation
(PSID) – SD HH Income residual
Sample
Proportions
EVs at
X_bar (with
background
risk)
EVs at
X_bar
(without
background
risk)
Reallocation
% (Ordered)
Reallocation
% (Binary)
High Risk
Asset
0.2189 0.1990 0.2618 0.7604
Medium
Risk Asset
0.1557 0.1673 0.2081 0.1722 0.5874
Low Risk
Asset
0.6254 0.6336 0.5302 0.0674 0.4126

67. Distribution of Asset Allocation
(PSID) – SD Transitory income
Sample
Proportions
EVs at
X_bar (with
background
risk)
EVs at
X_bar
(without
background
risk)
Reallocation
% (Ordered)
Reallocation
% (Binary)
High Risk
Asset
0.2189 0.1990 0.2652 0.7498
Medium
Risk Asset
0.1557 0.1673 0.2140 0.1772 0.5622
Low Risk
Asset
0.6254 0.6336 0.5208 0.0730 0.4378

68. Distribution of Asset Allocation
(PSID) – Trans. and Perm. Income
Sample
Proportions
EVs at
X_bar (with
background
risk)
EVs at
X_bar
(without
background
risk)
Reallocation
% (Ordered)
Reallocation
% (Binary)
High Risk
Asset
0.2189 0.1989 0.2657 0.7484
Medium
Risk Asset
0.1557 0.1673 0.2199 0.1763 0.5476
Low Risk
Asset
0.6254 0.6338 0.5143 0.0752 0.4524

69. Distribution of Asset Categories - % of Reallocation:
Transitory and Permanent Income
High
risk
(yi=0)
Safe
(yi=2)
Medium
risk
(yi=1)
Medium
risk
(yit=1;
hi=1ǀ yi=0; mi=1ǀ yi=1)
High
risk
(hi=0ǀ yi=0)
Safe
(yi=2;
hi=2ǀ yi=0; mi=2ǀ yi=1)
No Background
Risk
Background
Risk
0.7484
0.1763
0.0752
0.5476
0.4524
0.2657
0.2199
0.5143
0.1989
0.1673
0.6338

70. V. Conclusion
 We introduce a deflated ordered probit model
(DFOP) to explore the extent to which background
risk factors influence household’s financial portfolio
allocations and hence their financial risk exposure;
 Our findings based on the US SCF suggest that
background risk factors do influence portfolio
allocation;
 Current research introduces a panel estimator with
correlated random errors as well as exploring
household asset allocation in other countries.