sarah brown. portfolio allocation, background risk and households’ flight to safety

Portfolio Allocation, Background Risk and Households’ Flight to Safety

Sarah Brown (Sheffield)Daniel Gray (Sheffield)Mark N. Harris (Curtin)

Christopher Spencer (Loughborough)

May 2016

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.


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.


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’.


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.


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.


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.


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.


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.


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.

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.

II. Method

We could model each of the shares as a linear system:

Such an approach does not ensure:

Issues handling boundary observations of 0 and 1.

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

II. Method

Agents posses an underlying latent variable () as follows:

Standard OP model, the outcome j chosen by household i depends on the relationship between the latent variable & the boundary parameters, :

II. Method

This gives the corresponding likelihood function of household i to be:

II. Method

OP model, a household can be in only one of the j=0,1,2 outcomes (given by the indicator function, ;

Hence, the OP is not sufficient to model fractional data;

For fractional data, we are interested in the effect of the covariates on:

II. Method

We can replace with (the share of total assets in aggregate j for household i).

This changes the likelihood function for household i to be:

II. Method

The allocation equation, , is given by:

By construction, all satisfy:

Consistent with the risk ordering of the j asset bundles in the household’s portfolio.

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.

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).

II. Method

Two background risk equations:

and represent unobserved latent propensities to move away from the choice of risky assets j=0 (high risk) and j=1 (medium risk).

II. Method

These propensities are also modelled as fractional OP:

Consider the tempered expected value of the risky asset share:

II. Method

The expected values for the medium risk asset (j=1) bundle is:

II. Method

The expected values for the safe risk asset (j=2) bundle is:

II. Method

With these modifications the likelihood function becomes:

The choice of variables which enter and will be important for identification.

DFOP Model: Background risk affecting all non-safe assets

Household

Highrisk

(yi=0)

Safe(yi=2)

Mediumrisk

(yi=1)

Mediumrisk(yit=1;

hi=1ǀ yi=0; mi=1ǀ yi=1)

High risk

(hi=0ǀ yi=0)

Allocationequation (y)

Background riskequations (h,m)

Safe(yi=2;


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.

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.

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.

Proportion of low risk assets; all households; 0.8% hold zero low risk assets

05

1015

2025

Per

cent

0 .2 .4 .6 .8 1Proportion of Low Risk Assets

Proportion of low risk assets; households holding low risk assets

05

1015

2025

Per

cent

0 .2 .4 .6 .8 1Proportion of Low Risk Assets: Excluding Zero Shares

Proportion of medium risk assets; all households; 33.13% hold zero medium risk assets

010

2030

40P

erce

nt

0 .2 .4 .6 .8 1Proportion of Medium Risk Assets

Proportion of medium risk assets; households holding medium risk assets

02

46

8P

erce

nt

0 .2 .4 .6 .8 1Proportion of Medium Risk Assets: Excluding Zero Shares

Proportion of high risk assets; all households; 47.1% hold zero high risk assets

010

2030

4050

Per

cent

0 .2 .4 .6 .8 1Proportion of High Risk Assets

Proportion of high risk assets; households holding high risk assets

01

23

4P

erce

nt

0 .2 .4 .6 .8 1Proportion of High Risk Assets: Excluding Zero Shares

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.

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.

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).

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 (-).

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 Business0.060** -0.086*(0.028) (0.044)

Started Business 0.118*** 0.025(0.025) (0.032)

Positive Inc. Diff0.000 -0.004

(0.002) (0.003)

Negative Inc. Diff0.010*** 0.002(0.003) (0.003)

Background Risk Coefficients (continued)

High Risk Equation Medium Risk Equation (Binary Equation)

20010.016 0.064

(0.064) (0.062)

20040.226*** 0.226***

(0.063) (0.066)

20070.144** -0.537***

(0.065) (0.053)

20100.302*** -0.582***

(0.064) (0.051)

20130.257*** -0.574***

(0.063) (0.052)

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)

Inheritance0.024*** 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)

Overall Marginal Effects (Other Variables)High Risk Assets Medium Risk Assets Low Risk Assets

20010.014 -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)

Purged Marginal EffectsHigh Risk Assets Medium Risk Assets Low Risk Assets

20010.023 -0.011 -0.012(0.019) (0.009) (0.010)

20040.016 -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)

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)

Homeowner0.043*** -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)

White0.047*** -0.023*** -0.025***(0.011) (0.006) (0.005)

Children Present

-0.045*** 0.022*** 0.024***(0.007) (0.005) (0.004)

Background Risk Marginal EffectsHigh Risk

AssetsMedium Risk

AssetsLow 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)

Inheritance0.067*** -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)

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)

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

Distribution of Asset Categories - % of Reallocation

Highrisk

(yi=0)

Safe(yi=2)

Mediumrisk

(yi=1)

Mediumrisk

(yit=1; hi=1ǀ yi=0; mi=1ǀ yi=1)

High risk

(hi=0ǀ yi=0)

Safe(yi=2;


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

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

Distribution of Asset AllocationAsset Allocation

Decomposition of Reallocation in the Presence of Background Risk

High 0.2487 = 0.3623x0.6865Medium 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.

Distribution of Asset Allocation

High Risk Asset Medium Risk Asset Low Risk Asset0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Sample Proportions EVs at X_bar Purged EVs at X_barReallocation % (Ordered)Reallocation % (Binary)

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.

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.

Low Risk asset Category

010

2030

4050

Per

cent

0 .2 .4 .6 .8 1Proportion of Low Risk Assets

010

2030

4050

Per

cent

0 .2 .4 .6 .8 1Proportion of Low Risk Assets: Excluding Zero Shares

Medium Risk asset category 0

2040

6080

Per

cent

0 .2 .4 .6 .8 1Proportion of Medium Risk Assets

02

46

Per

cent

0 .2 .4 .6 .8 1Proportion of Medium Risk Assets: Excluding Zero Shares

High risk asset category

020

4060

Per

cent

0 .2 .4 .6 .8 1Proportion of High Risk Assets

02

46

8P

erce

nt

0 .2 .4 .6 .8 1Proportion of High Risk Assets: Excluding Zero Shares

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

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

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.

Measures of Income Uncertainty

Permanent and Transitory Income (Diaz-Serrano (2004)):

YH is household income; X includes Married,

education, gender, race, children and year dummies

- Permanent Income Uncertainty – SD(- Transitory Income Uncertainty – SD()

Panel Results – Summary of Asset allocation

Age (-), Age2 (+), White (-), Divorced (+), Child (+), Homeowner (-), College Degree (-), Household Income (-), Net wealth (-), Health Status (-), and Risk Tolerance (-).

PSID Overall Marginal Effects - DFOPHigh 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)

PSID Overall Marginal Effects (Background Risk) High Risk Assets Medium Risk Assets Low Risk Assets

Own Business0.010* 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)

Inheritance0.026*** 0.025** -0.052***(0.010) (0.012) (0.014)

CV Income0.428*** 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)

Distribution of Asset Allocation (PSID) – Coefficient of Variation

Sample Proportions


risk)

EVs at X_bar

(without background

risk)



High Risk Asset 0.2189 0.1990 0.2619 0.7588


Low Risk Asset 0.6254 0.6336 0.5186 0.06608 0.4511

Distribution of Asset Allocation (PSID) – SD HH Income residual

Sample Proportions


risk)

EVs at X_bar

(without background

risk)



High Risk Asset 0.2189 0.1990 0.2618 0.7604


Low Risk Asset 0.6254 0.6336 0.5302 0.0674 0.4126

Distribution of Asset Allocation (PSID) – SD Transitory income

Sample Proportions


risk)

EVs at X_bar

(without background

risk)



High Risk Asset 0.2189 0.1990 0.2652 0.7498


Low Risk Asset 0.6254 0.6336 0.5208 0.0730 0.4378

Distribution of Asset Allocation (PSID) – Trans. and Perm. Income

Sample Proportions


risk)

EVs at X_bar

(without background

risk)



High Risk Asset 0.2189 0.1989 0.2657 0.7484


Low Risk Asset 0.6254 0.6338 0.5143 0.0752 0.4524

Distribution of Asset Categories - % of Reallocation: Transitory and Permanent Income

Highrisk

(yi=0)

Safe(yi=2)

Mediumrisk

(yi=1)

Mediumrisk

(yit=1; hi=1ǀ yi=0; mi=1ǀ yi=1)

High risk

(hi=0ǀ yi=0)

Safe(yi=2;


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

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.

sarah brown. portfolio allocation, background risk and households’ flight to safety

Economy & Finance