This document describes a fractional ordered probit (DFOP) model to analyze how background risks affect households' allocation of financial assets into risky and safe asset classes. The model accounts for the fact that background risks like labor income volatility should cause households to "deflate" or reduce their holdings of risky assets. It models the expected share of a household's portfolio allocated to high, medium, and low risk asset classes based on observed characteristics and two background risk equations representing the propensity to move away from high and medium risk assets. The model is estimated on US Survey of Consumer Finances data from 1998-2013 to investigate how different types of uncertainty influence household portfolio composition.
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1. The document discusses risk management trends for pension plans, including evolving techniques like liability-driven investing and dynamic asset allocation.
2. It explains how negative returns can impact long-term returns more than their arithmetic average suggests, due to the geometric nature of compound returns. Diversification across asset classes is important to manage this risk.
3. The article advocates establishing investment goals and benchmarks, then using tools like asset-liability modeling to evaluate portfolio alternatives and their risk exposures in order to implement solutions that improve the risk profile over time through dynamic asset allocation.
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This document provides an overview of the key concepts to be covered in Chapter 5 on risk and return. It begins with learning objectives for the chapter, which include understanding the relationship between risk and return, defining and measuring risk and return, investor attitudes toward risk, risk and return in portfolio context, the capital asset pricing model, and efficient financial markets. It then covers definitions of return, examples of calculating return, definitions of risk, and how to determine expected return and standard deviation using probability distributions to measure risk. Other topics summarized are risk attitudes, risk and return for portfolios, diversification, the capital asset pricing model, and systematic versus unsystematic risk.
This document discusses using the markovchain package in R to model and analyze long-term care (LTC) insurance policies. It presents transition probabilities for disabled, ill, and dead states for Italian males. The package is used to simulate life trajectories and cash flows to calculate policy premiums and reserves. Simulation allows for stochastic analysis of benefits and reserves over many simulated policyholder lives.
Behavioral Economics and the Design of Agricultural Index Insurance in Develo...BASIS AMA Innovation Lab
UC Davis Professor Michael Carter presented, "Behavioral Economics and the Design of Agricultural Index Insurance in Developing Countries" at the 2014 International Agricultural Risk, Finance, and Insurance Conference (IARFIC).
1. The document discusses risk management trends for pension plans, including evolving techniques like liability-driven investing and dynamic asset allocation.
2. It explains how negative returns can impact long-term returns more than their arithmetic average suggests, due to the geometric nature of compound returns. Diversification across asset classes is important to manage this risk.
3. The article advocates establishing investment goals and benchmarks, then using tools like asset-liability modeling to evaluate portfolio alternatives and their risk exposures in order to implement solutions that improve the risk profile over time through dynamic asset allocation.
The document discusses actuarial risk processes and ruin probability. It introduces the classical risk model and compound Poisson model used to analyze ruin probability. The compound Poisson model assumes claim amounts are independent and identically distributed, and claims follow a Poisson process. The ruin probability is defined as the probability that the insurer's surplus falls below zero. Different formulas are presented for calculating the ruin probability in the compound Poisson model, including the Pollaczek-Khinchin formula, differential equation formula, and Laplace transform formula. Approximations of the ruin probability are also discussed.
This document discusses allocating risk capital across portfolios in a coherent manner. It proposes that an allocation principle should satisfy three properties to be considered coherent: 1) No portfolio should be allocated more capital than its individual risk, to avoid undercutting. 2) Symmetrical portfolios should receive equal allocations. 3) A riskless portfolio should receive a negative allocation equal to its risk measure. The document models the allocation problem using concepts from game theory, with portfolios as players and risk capital as the cost function. It suggests the Aumann-Shapley value provides a coherent approach to risk capital allocation.
This is a pretty broad exploration and tutorial of basic econometrics modeling techniques. It includes an introduction to quite a few multiple regression methods. It also includes an extensive coverage of model testing to ensure that your model is quantitatively sound and statistically robust using state of the art peer reviewing protocol.
A Short Glimpse Intrododuction to Multi-Period Fuzzy Bond Imunization for Con...NABIH IBRAHIM BAWAZIR
A Short Glimpse Intrododuction to Multi-Period Fuzzy Bond Imunization for Construct Active Bond Portofolio, this paper is made to fullfill Fixed-Income securities mid semester exam
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Risk Parity, a relatively new portfolio construction method, took Wall Street by storm overcoming the traditional mean-variance and 60/40 methods. Why this method is better and when?
This document discusses factor investing beyond traditional factors to harvesting alternative risk premia. It finds that replicating hedge fund performance using traditional and alternative factors achieves relatively low explanatory power. Replication strategies have in-sample R-squared values up to 60% but out-of-sample values are much lower, indicating overfitting. Alternatively, risk parity strategies applied to alternative risk factors could better harvest alternative premia in an efficient passive manner.
Eesti Pank Economic Statement 12 December 2013Eesti Pank
The document provides an economic statement from Eesti Pank (the central bank of Estonia) summarizing the Estonian economy and forecast for coming years. Key points include:
- The Estonian economy grew more slowly than forecast in 2013 due to weaker external demand, especially from Finland.
- Rapid wage growth and high domestic demand have caused some imbalances as productivity growth was negative.
- Growth is forecast to pick up in 2014 and 2015 as external demand and investments increase, but risks include continued wage pressures and uncertainty in export markets.
- Inflation will remain moderate while unemployment falls and the budget deficit remains small.
Madis Müller. Estonian financial sector – recent developments and the changin...Eesti Pank
The document summarizes recent developments in Estonia's financial sector and the changing role of Eesti Pank (the central bank of Estonia). It notes that Estonia's banking sector is dominated by Nordic banks and that credit growth is slowing while the real estate market is recovering. It discusses Eesti Pank taking on new responsibilities for macroprudential supervision and the implications of the new Single Supervisory Mechanism for oversight of Nordic bank subsidiaries in Estonia. Close cooperation will be needed between Nordic and Baltic authorities and the European Central Bank as financial supervision responsibilities are merged.
Karsten Staehr. The Euro Plus Pact: Competitiveness and External Capital Flow...Eesti Pank
The document summarizes a presentation on the relationship between competitiveness and external capital flows in EU countries. It discusses the Euro Plus Pact, which assumes that weak competitiveness, as measured by increasing unit labor costs, leads to current account deficits. However, the presentation finds that empirical evidence does not support this relationship. Granger causality tests and VAR models instead indicate that increased capital inflows lead to a short-term real exchange rate appreciation and deterioration of competitiveness. The findings suggest the Euro Plus Pact has the causal relationship backwards and that relative wages are highly dependent on credit availability.
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Konstantīns Beņkovskis, Julia Wörz. Evaluation of Non-Price Competitiveness o...Eesti Pank
The document evaluates the price and non-price competitiveness of exports from Central, Eastern and South-Eastern European countries to the EU market. It outlines limitations of traditional real effective exchange rate indicators and proposes a theoretical framework to assess changes in relative export prices adjusted for quality or taste using elasticities of substitution. Estimates of elasticities are obtained through a system of demand and supply equations estimated with GMM. The results suggest median elasticities of substitution between 4.9-6.2 for large EU countries.
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Measuring and allocating portfolio risk capital in the real worldAlexander Decker
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This document discusses the key concepts and applications of econometrics. It provides an overview of econometrics methodology, including statement of theory, specification of mathematical and statistical models, obtaining data, estimation of parameters, hypothesis testing, forecasting and using models for policy purposes. It also discusses regression analysis and the classical normal linear regression model, addressing topics like interval estimation, hypothesis testing, and issues like multicollinearity.
Optimal Risky Asset Proportion in the Presence of correlated Background RriskTakafumi SHIRATORI
This study derives the optimal investment proportion for financial assets in the presence of background risk by maximization of expected utility in a single period framework. To simplify the problem, I assume that there exist only two financial assets, one risky and one risk free. The optimal proportion says that she should increase her exposure to financial risky asset when financial risky asset and background risk is negatively correlated. This paper is the first analysis to derive this surprising result. Under such a situation, to increase exposure to financial risky asset is optimal even if there exists background risk.
I obtained Master of Business Administration of Waseda University Graduated School with this study in 2012. I researched under Dr. Masayuki Ikeda.
The document discusses correlation in investment management. It defines correlation as a statistical measure of how investment returns move in relation to each other. Anticipating correlations correctly is key for investment decisions and risk management, as falsely predicting low correlations can result in unexpectedly high portfolio risk if correlations rise. While past or ex-post correlation can be observed, ex-ante or future correlation is difficult to predict and requires sophisticated risk models as relationships between assets may change over time.
This document proposes using a family of nested power EWMA estimators based on an exponential power distribution to estimate VaR. It summarizes previous research showing that asset returns are often fat-tailed rather than normally distributed. The power EWMA model nests standard EWMA, robust EWMA, and power EWMA estimators. The document empirically evaluates the conservativeness, accuracy, and efficiency of these models when estimating the VaR of several stock market indices, using measures that address each criterion. The results show that power EWMA and related estimators offer superior coverage of extreme risks compared to standard EWMA, and accurate VaR estimation.
This document discusses using extreme value theory (EVT) to model policyholder behavior in extreme market conditions using variable annuity lapse data. EVT allows predicting behavior in the extremes based on nonextreme data. The paper applies EVT by fitting bivariate distributions to lapse and market indicator data above a large threshold. This provides insights into policyholder behavior in extreme markets without direct observations. The goal is a dynamic lapse formula capturing different characteristics than traditional methods.
Scenario generation and stochastic programming models for asset liabiltiy man...Nicha Tatsaneeyapan
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Macroeconomic fluctuations with HANK & SAM ADEMU_Project
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2. Probability distributions assign probabilities to possible outcomes using subjective probabilities estimated from historical data.
3. The normal distribution is commonly used, characterized by its mean and variance, with outcomes ranging from negative to positive infinity in a symmetric bell curve shape.
4. Utility functions represent investor preferences with increasing but concave curves, and the expected utility criterion selects the portfolio with the highest expected utility.
This document discusses key concepts in portfolio analysis and optimization including:
1. Portfolio possibilities sets define the combinations of assets an investor can hold based on constraints like total weights summing to 1.
2. Probability distributions assign probabilities to possible outcomes using subjective probabilities estimated from historical data.
3. The normal distribution is commonly used, characterized by its mean and variance, with outcomes ranging from negative to positive infinity in a symmetric bell curve shape.
4. Utility functions represent investor preferences with increasing but concave curves, and the expected utility criterion selects the portfolio with the highest expected utility.
Similar to Sarah Brown. Portfolio Allocation, Background Risk and Households’ Flight to Safety (20)
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Sarah Brown. Portfolio Allocation, Background Risk and Households’ Flight to Safety
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
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)
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.
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.
Editor's Notes
Part of research on household finances;
Technical paper – methodological contribution;
Work in progress – comments and suggestions very much appreciated.
Flight to safety – Deutche Bank
Which is also what we do in this paper.
Definition of background risk – risk beyond the household’s control (e.g. labour income uncertainty)
You cannot do anything about background risk, but you can invest less in risky financial assets to reduce your overall exposure to risk.
i.e. you can decide what to do with your savings, but not redundancy if your firm goes bust.
Existing models – very basic;
We draw on the discrete choice literature where ‘inflated’ models are used to account for a build-up of observations in a particular choice category.
Inflate on safe category or deflate on the risky category
Paper: introduces a theoretical framework to motivate our statistical contribution.
DEFLATE ON RISKY ASSETS
INFLATE ON SAFE ASSETS
Existing studies reveal an inverse association between background risk and risky financial investments – but not much more.
X – matrix of covariates and u is a random error term
£100 = wealth
10 – risky; 40 medium; and 50 – safe.
Modelling 10/100 etc.
Y is related to observed characteristics (x) with unknown weights (beta) and a random normally distributed error term, u
Example – ordered index
Health = poor (0), medium health (1), good health (2)
E – expected value.
Some households – all safe assets; some all risky assets; many hold a combination of assets types.
So far – nothing said about background risk;
Application FOP to household finances would still be a contribution – but we want to extend this further ….
FOP (asset allocation equation) and background risk equations are all estimated jointly
Dotted lines depict flights to safety from risk to safer assets.
NOTE – NOT TWO STAGES …. JOINTLY ESTIMATED
The survey oversamples the wealthiest households in the population to account for the skewed nature of assets held within the population.
We use the sampling weights to make our sample representative of the US population
SCF used a lot in household finance literature
The multiple imputations increase the efficiency of the estimation;
We take an average across the 5 imputations.
We follow Carroll (2002) and Hurd (2002) in how we classify assets into three categories based on risk exposure.
Risky assets comprise of both direct and indirect stockholding and are defined following the SCF website
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
Inflation at 1
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
Inflation at 0; deflation at 1
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
Inflation at zero; deflation at 1
Spikes of 0.5 due to half of certain asset categories being allocated to each asset category.
An index, increasing in risk tolerance, based on responses to the question: Which of the following statements comes closest to describing the amount of financial risk that you are willing take when you save or make investments? 0 =Not willing to take any financial risks, 1= Take average financial risks expecting to earn average returns, 3 = Take above average financial risks expecting to earn above average returns, 4 = Take substantial financial risks expecting to earn substantial returns.
Close as possible to the existing literature – focus on the methodological contribution.
INCREASING IN RISK TOLERANCE
2 = low risk, 1 = medium risk and 0 = high risk;
Positive coefficient – positively related to low risk
Negative coefficient – negatively related to low risk, positively related to high risk.
For the Tempering Fractional OP parameters, and the Tempering Fractional Binary (middle) parameters, are both of these relative to the low risk assets. So a positive coefficient in the Tempering Fractional OP parameters indicates a movement away from the Risky asset category to Low risk assets, whilst a positive in the coefficient in the Tempering Fractional Binary (middle) parameters means movement away from the middle asset category to low risk assets.
Index is decreasing in risk – 2 = safe assets
Positive coefficients in the tempering equations imply a movement from risky to less risky assets. That is, positive coefficients imply a "flight to safety".
Negative coefficients – movement towards high risk.
Positive coefficients in the tempering equations imply a movement from risky to less risky assets. That is, positive coefficients imply a "flight to safety".
Negative coefficients – movement towards high risk.
Omitted year =1998
Includes all variables in the model
ME – positive effect for that category – interpretation – straightforward.
Omitted year - 1998
Effects omitting background risk
The marginal effects of the tempering equations. Plus the Binary Equation indicates the marginal effect of the tempering variables of the binary equation (ie movement from middle risky assets to safe assets). Positive coefficients indicate more likely to move towards safe assets.
The more negative the coefficient is, the less likely we are to move out of a category (which means staying in a high risk, or alternatively, medium risk category)!
Binary Equation – Movement from Medium and to Safe assets.
Particularly important feature of our model is that we can decompose the asset re-allocation effects.
Our statistical framework allows us to unpack the portfolio reallocation into its constituent parts;
Not only like the existing literature can we say that background risk affects asset allocation – but we can give a detailed answer regarding HOW it affects the portfolio.
Mundlak – averages of the time varying variables to proxy a fixed effect
Pooled cross-section results with Mundlak variables
For example, Heaton and Lucas (2000) use variation in income growth, whilst Cardak and Wilkins (2009) use a measure of coefficient of variation.
Both the Mincer and Income equation can be estimated through RE or FE models.
Mincer equation is similar to that used in Robst et al. (1999).
(2) OLS cross-section regressions; use predictions to get the residuals;
Standard deviation of the residuals for each household over time.
Time invariant measures.
Random effects can recover estimates the systematic component:
(ui ) due to unobserved individual level factors such as ability, effort. Hence, this systematic component
can also be netted out of the estimated residuals (εit ) and added to the fitted values
(Xitβ + ui ) to proxy permanent income (net out
We include permanent and Transitory both individually and jointly.
Includes all variables in the model
ME – positive effect for that category – interpretation – straightforward.
Particularly important feature of our model is that we can decompose the asset re-allocation effects.
Example from pooled cross section – still developing the panel estimator.
Particularly important feature of our model is that we can decompose the asset re-allocation effects.
Example from pooled cross section – still developing the panel estimator.
Particularly important feature of our model is that we can decompose the asset re-allocation effects.
Example from pooled cross section – still developing the panel estimator.
Particularly important feature of our model is that we can decompose the asset re-allocation effects.
Example from pooled cross section – still developing the panel estimator.