MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL

MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
lower-risk-tolerance
 z-scores   self-reported-questionnaire

 FinaMetrica
  risk-tolerance distribution
                                       measure


            risk-tolerance-test individuals
Technical         Manual
  25-questions financial-advice
      scoring-algorithm mean data
            sub-scales population-of-interest
            world-scale age-20-to-80
    standard-deviation              2018
  norm-reinforced
                  risk-tolerance-scale
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

                                                    FinaMetrica Technical Manual
February 2018
Dr Myrsini Katsikatsou, Research Fellow at the London School of Economics, Department of
Statistics
Stuart Erskine, Commercial Economist


                                                                           Contents
1.  Introduction.................................................................................................................................................... 3
2.  Executive Summary ....................................................................................................................................... 5
3.  Cleaning the Data .......................................................................................................................................... 7
4.  Demographic Profile ..................................................................................................................................... 8
5.  Data Analysis – Association of Risk Tolerance with Demographics ....................................................... 15
    Differences in Risk Tolerance across Countries ....................................................................................... 15
    Differences in Risk Tolerance over Time ................................................................................................... 17
    Differences in Risk Tolerance by Gender .................................................................................................. 18
    Differences in Risk Tolerance across Personal Income Groups ............................................................. 19
    Differences in Risk Tolerance across Age Groups .................................................................................... 20
    Differences in Risk Tolerance across Education Levels ........................................................................... 21
    Differences in Risk Tolerance across Net Assets Groups ........................................................................ 22
    Differences in Risk Tolerance by Gender Controlling for Personal Income.......................................... 23
    Differences in Risk Tolerance across Age Groups Controlling for Personal Income ........................... 23
    Differences in Risk Tolerance across Education Levels Controlling for Personal Income................... 25
6. Construct Validity ......................................................................................................................................... 27
    Associations of the 25 Risk Tolerance Questions ..................................................................................... 27
    Factor Analysis ............................................................................................................................................. 30
7. Reliability Analysis........................................................................................................................................ 32
    Internal-consistency Reliability .................................................................................................................. 32
    Test-retest Reliability ................................................................................................................................... 33
8. Risk Tolerance Scales and Scoring Algorithm........................................................................................... 35
    Global Norm Group and Scoring Algorithm – Equal Weighting ............................................................. 36
    Global Scoring Algorithm – Different Weightings .................................................................................... 38
9. Comparing the 10-question Score with the 25-question Score.............................................................. 40
10. Development of 3-question Profile ............................................................................................................ 41




Copyright © PlanPlus Global Inc. All Rights Reserved.                                                                                               Page 1
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

                                                                         Table of Tables
Table 1: Descriptive Statistics for Distribution of Risk Tolerance Scores by Country........................................................ 17
Table 2: Descriptive Statistics for Distribution of Risk Tolerance Scores by Year .............................................................. 18
Table 3: Mean Differences in Risk Tolerance Scores between Adjacent Years .................................................................. 18
Table 4: Descriptive Statistics for Distribution of Risk Tolerance Scores by Gender......................................................... 19
Table 5: Descriptive Statistics for Risk tolerance Scores across Personal Income Classes .............................................. 20
Table 6: Mean Differences in Risk Tolerance Scores between Adjacent Income Classes ................................................ 20
Table 7: Median Risk Tolerance Scores across Income Classes by Country....................................................................... 20
Table 8: Descriptive Statistics for Risk Tolerance Scores across Age Groups .................................................................... 21
Table 9: Mean Differences in Risk Tolerance Scores between Adjacent Age Groups ....................................................... 21
Table 10: Descriptive Statistics for Risk Tolerance Scores across Education Levels ......................................................... 22
Table 11: Mean Differences in Risk Tolerance Scores between Adjacent Education Levels ............................................ 22
Table 12: Gender Means of Risk Tolerance Scores across Income Classes........................................................................ 23
Table 13: Descriptive Statistics for Risk Tolerance Scores across Age Groups and Income Classes .............................. 24
Table 14: Mean Differences in Risk Tolerance Scores between Adjacent Age Groups across Income Classes ............ 25
Table 15: Means of Risk Tolerance Scores across Education Levels and Income Classes................................................ 26
Table 16: Mean Differences of Risk Tolerance Scores between Adjacent Education Levels across Income Classes ... 26
Table 17: Goodman and Kruskal's Gamma Coefficient for 25 Risk Tolerance Questions ................................................ 28
Table 18: Pearson Correlations for 25 Risk Tolerance Question ......................................................................................... 29
Table 19: Principal Component Analysis for First Five Components ................................................................................... 30
Table 20: Correlation of Risk Tolerance Questions with First Component ......................................................................... 30
Table 21: Correlation of Risk Tolerance Questions with Factor in One-factor Latent Variable Model ........................... 31
Table 22: Reliability Coefficients ............................................................................................................................................... 32
Table 23: Split-half Reliability Coefficients .............................................................................................................................. 33
Table 24: Cronbach's Alpha when the Respective Question is Deleted .............................................................................. 33
Table 25: Percentage of Cases with Different Time Lags between Assessments ............................................................. 33
Table 26: Correlation of Risk Tolerance Scores Measured at Two Time Points ................................................................. 34
Table 27: New Scoring Algorithm Using Questions 1 – 10, 12 – 22, and 25 ....................................................................... 37
Table 28: Empirical Percentiles of New World Distribution against the Normal Distribution ......................................... 38
Table 29: Mean, Median and Standard Deviation of New Risk Tolerance Scores by Risk Group .................................... 38
Table 30: Question Weights by Principal Component Analysis ........................................................................................... 39
Table 31: Question Weights by Principal Component Analysis Sorted from Largest to Smallest ................................... 39
Table 32: Difference between 10Q Scores and New Total Scores ....................................................................................... 40
Table 33: Difference between 10Q Scores and New Total Scores by Risk Group.............................................................. 40
Table 34: Reliability Coefficients of the 10Q Score ................................................................................................................ 40
Table 35: Difference between 3Q Scores and New Total Scores ......................................................................................... 41
Table 36: Difference between 3Q Scores and New Total Scores by Risk Group ................................................................ 41


                                                                        Table of Figures
Figure 1: Distribution of Risk Tolerance Scores by Countries .............................................................................................. 16
Figure 2: Distribution of Risk Tolerance Scores by Year ....................................................................................................... 17
Figure 3: Distribution of Risk Tolerance Scores by Gender .................................................................................................. 18
Figure 4: Distribution of Risk Tolerance Scores by Personal Income Classes .................................................................... 19
Figure 5: Distribution of Risk Tolerance Scores across Age Groups ................................................................................... 21
Figure 6: Distribution of Risk Tolerance Scores across Education Levels ........................................................................... 22
Figure 7: Gender Means and 95% CI for Risk Tolerance Scores across Income Classes .................................................. 23
Figure 8: Age Group Means and 95% CI for Risk Tolerance Scores across Income Classes ............................................ 24
Figure 9: Mean Score and 95% CI for Risk Tolerance Scores across Education Levels and Income Classes ................. 25
Figure 10: Demographic Profile of the Updated Norm Group ............................................................................................ 36
Figure 11: Histogram of the New World Scores ..................................................................................................................... 38




Copyright © PlanPlus Global Inc. All Rights Reserved.                                                                                                            Page 2
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

1. Introduction
The objective of this report is to review the FinaMetrica risk tolerance scale and the scoring algorithm to
ensure they are relevant to the contemporary data and update the scale if necessary. Risk tolerance is
measured following completion of the 25-question self-reported questionnaire1. The test approach is
norm-referenced, therefore the scores are interpreted relative to other people’s scores. In other words,
the test reports how much lower or higher the level of risk tolerance of a respondent is compared to
the average level of risk tolerance of the population of interest. In this report, the population of interest
is defined as being adults of age 20-80 who have sought financial advice from a financial
advisor/planner. To estímate the average level of risk tolerance in the population, a sample of
FinaMetrica data is used (this is the norm group).
Currently there is a world scale and two sub-scales: one for UK and a common one for Australia, New
Zealand, Canada, and USA. The data for the three norm groups is predominately from UK, USA,
Australia, New Zealand and Canada for the period January 2010 – July 2011. The scoring algorithm uses
24 of the 25 questions (question 24 is excluded) and consists of the following steps:
    1. After the norm group /data having been specified, the mean and standard deviation for 24
       questions are computed to be used in step 2.
    2. The z-scores for the 24 questions for all individuals in the norm group are computed, where z-
       score in question A of individual X = (answer of individual X to question A – mean of question A) /
       standard deviation of question A.
    3. For all individuals in the norm group, the sum of their z-scores is computed as well as the
       standard deviation of the sums of the z-scores. The latter is used in step 4.
    4. For all individuals the z-score of their sum of z-scores is computed by dividing their sum of z-
       scores with the standard deviation2 of the sums calculated in step 3. Let us refer to the z-score
       of the sum of the z-scores as the total z-score.
    5. For all individuals in the norm group, the total z-score is multiplied by 10 and then 50 is added
       to the product. Let us refer to the transformed total z-score as the total score. The last step is
       done so that the total scores have mean 50 and standard deviation 10.
The distribution of the total scores of the norm group is used in order to interpret the total score of a
new respondent. For example, if a new respondent scores 60, we can say that they exhibit higher risk
tolerance by one standard deviation compared to the average level of the norm group (which is 50); if
the score is 45 then it is lower by half a standard deviation compared to the average level of the norm
group. For this, the norm group needs to be representative of the potential future test takers.
Since the current norm groups are based on older data, from January 2010 - July 2011, it is preferable to
ensure ongoing validity to use contemporary data, from September 2011 – July 2016. Furthermore, data
from India, DACH (Germany, Austria and Switzerland), South Africa, and Ireland has increased
significantly to warrant further investigation. Therefore, the “new” countries need to be represented by
the norm group as well. Also a review of the scoring algorithm was viewed as necessary too. For
example, are the questions still indicators of risk tolerance? Do they all measure risk tolerance
consistently? Can we improve the scoring by assigning different weights on the questions depending
on their reliability to measure risk tolerance? The current report has attempted to answer these
questions.



1 http://www.riskprofiling.com/Downloads/Questionnaire_AUSNZ.pdf, this is the Australian version of the
questionnaire. Other versions are identical except for terminology differences, e.g. stocks vs shares.
2 The variance (which is the square root of the standard deviation) of the sum of the z-scores is equal to the sum of

the variances of the 24 questions’ z-scores plus the covariance of all pairs of the 24 z-scores.



Copyright © PlanPlus Global Inc. All Rights Reserved.                                                    Page 3
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

The target audience of the report is financial advisors and those undertaking due diligence of the
FinaMetrica risk tolerance toolkit. The report, in addition to Introduction, consists of 8 sections. Each
section starts with a summary of the section’s findings followed by a detailed discussion of the analysis
and the results. A brief outline of each section is given below.
     Section 2 summarises the main findings of the rest of the sections.
     Section 3 introduces the available data and the part of which is kept for analysis.
     Section 4 describes the demographic profile of the analysed data (gender, age, education level,
      income, marital status, value of net assets, number of family members financially dependent on
      the respondent, country of residency, year of taking the risk tolerance test).
     Section 5 focuses on identifying associations of risk tolerance with demographic characteristics.
      This is mainly to a) spot major differences across countries which will lead to separate risk
      tolerance scales, b) investigate differences over time so that we will select the data for the norm
      group accordingly, c) determine the cases to be included in the norm group data, and d)
      describe associations of risk tolerance with different demographics which may inform financial
      advice and decisions.
     Section 6 carries out a construct validity analysis to confirm that the questions still do measure
      risk tolerance.
     Section 7 conducts a reliability analysis to assess whether and to which degree the
      questionnaire consistently measures risk tolerance.
     Section 8 proceeds with the update of the norm groups and scoring algorithm.
     Section 9 compares the risk tolerance scores based on the 10-question version of the
      questionnaire with the scores derived by the full version of the questionnaire (25 questions) to
      assess whether the shorter version of the questionnaire, which is already administered to some
      clients, measures the risk tolerance as accurately as the full version of the questionnaire.
     Section 10 discusses whether the risk tolerance scores computed on the full version of the
      questionnaire can be well approximated by a score computed on a 3-question short form of the
      questionnaire.




Copyright © PlanPlus Global Inc. All Rights Reserved.                                         Page 4
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

2. Executive Summary
The contemporary data, that covers the period Sep 2011 - Jul 2016, was cleaned removing duplicated
cases, non-relevant cases, and cases with non-legitimate variable values (e.g. age out of the range 20-
80 including). We were left with 407016 cases from the initial 541549 cases.
Describing the data at high-level
The data originates geographically from UK, Australia/New Zealand, USA, India, DACH, Canada, South
Africa, Ireland, Hong Kong, China, Sweden, Finland, Malaysia, and Kuwait (the countries are listed in
order of data size) and is predominantly sourced from clients of financial advisors/planners who have
completed a FinaMetrica risk tolerance profile. The bulk of the data, 91%, comes from UK, Australia-
New Zealand and USA, while 8.7% from India, DACH, Canada, South Africa, and Ireland. 82% of the data
spans just 4 years, 2012-2015, and is almost evenly distributed to the respective years.
The data is:
     Slightly male-dominated (56.7% male respondents).
     70% are 40-69 years old, and 60% are university graduates or post-graduates.
     Three-quarters are married or in a relationship.
     63% supported financially (fully or partially) none or one family member.
     Half of the respondents have $50,000-199,999 total personal income before tax and report net
      assets of value $500,000-1,999,999.
It is worthwhile noting that about one-third of the respondents did not provide their demographic
characteristics and subsequently they are not included in the above numbers. It is also worth noting
that India has a distinctive demographic profile where the respondents appear the youngest, most
educated (about 90% have university degree or higher) and male in majority (78.5%).
For further analysis, only data from UK, Australia/New Zealand, USA, India, DACH, Canada, South Africa,
and Ireland, that is 99.7% of the 407016 cases was retained. Based on the analysis, there are no
practically significant differences in the distribution of risk tolerance scores across countries and over
time. Zooming in the country score averages, they all hover around 50 with UK having the lowest
average score, 47.8, and India and South Africa the highest average scores, 53.5.
With respect to the rest of the demographics, higher levels of risk tolerance are found to be associated
with men, younger ages, and people with higher income and higher education. Men on average score
higher than women by around 5 and this difference roughly remains after controlling for income (i.e.
for a given income category). The average score of the highest income category is around 9 higher than
the average score of the lowest income. This difference roughly remains the same when the analysis is
done country-wise with the exception of Ireland and India where the differences of the average scores
are 14 and 5, respectively.
The average risk tolerance score of age group 20-29 is about 7 higher than the average score of age
group 70-80. There is a small interaction though between age and income. The age effect on risk
tolerance is slightly more intense in the lower income classes and tends to be less strong as we move to
the higher income classes. A similar pattern is observed for education. The average score of the most
educated people is higher by 6 compared to the average score of the least educated people. However,
due to the interaction between education and income, the effect of education on risk tolerance tends to
decrease as income increases.
The construct validity analysis shows that all questions, except for questions 11, 23 and 24, measure the
same concept that can be interpreted as risk tolerance. Questions 1 – 10, 12 – 22, and 25 are all found
to be reliable indicators measuring risk tolerance consistently. Questions 11, 23, and 24 present nearly


Copyright © PlanPlus Global Inc. All Rights Reserved.                                          Page 5
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

no association with the rest of the questions and the risk tolerance factor. Thus, these three questions
are excluded from the new scoring algorithm, but otherwise the steps of scoring remain the same as
those detailed in Introduction. The average difference between the 24-question score (all questions but
question 24) and the 22-question score (all questions but questions 11, 23, 24) is 0.19 and the maximum
absolute difference is 3.85, both suggesting no practical material difference between the two scores
with regard to its use and purpose for guiding investment. Though continuing to ask these questions or
alternative questions does feed into other analyses that FinaMetrica may wish to undertake.
In consultation with FinaMetrica, a general world scale is considered sufficient for scoring purposes
because the maximum absolute difference between a score on a regional sub-scale and a score on the
world scale is 5.66. The largest difference mean occurs in India and it is 4.10 (i.e. a score on India scale
is on average 4.10 higher than the same score on the world scale). The regional differences are
considered small for practical application purposes and so further subscales were not developed.
The score ranges that define the risk groups remain the same. The table below gives a brief summary
of the seven risk groups.

 Risk Group      Score Range       Percentage in Risk Group    Brief Description of Risk Group
      1             0 – 24                   1%                People with extremely low risk tolerance.
      2            25 – 34                   6%                People with very low risk tolerance.
      3            35 – 44                  24%                People with low risk tolerance.
      4            45 – 54                  38%                People with average risk tolerance.
      5            55 – 64                  24%                People with high risk tolerance.
      6            65 – 74                   6%                People with very high risk tolerance.
      7            75– 100                   1%                People with extremely high risk tolerance.


The new scoring algorithm gives equal weights to the z-scores of all 22 questions (as the previous
scoring does to all 24 questions). A weighted scoring algorithm with larger weights to the z-scores of
questions with higher reliability to measure risk tolerance has also been examined. The conclusion is
that it is not needed as, on average, the weighted score was the same as the unweighted one.
The scores produced using a 10-question short form (questions 1, 2, 3, 6, 10, 13, 14, 16, 18 and 21) are
found to be very close to the scores based on 22 questions (questions 1 – 10, 12 – 22, and 25). The 10-
question score is within 5 units from the 22-question total score for 90.6% of cases of the new world
norm group while 76.7% of cases are assigned to the same risk group by both scores (22-question and
10-question).
Finally, we investigated the viability of a 3-question discovery version (questions 10, 14 and16). These
questions were chosen on the basis of their reliability level, easiness to understand and answer, that
they capture different aspects of risk tolerance and that they are a subset of both the 22-question and
10-question versions. The 3-question score is found to be a close approximation of the total score. For
68.5% of the cases of the world norm group, the two scores are within 5 units apart from each other
while 61.5% cases are assigned to the same risk group by both scores.




Copyright © PlanPlus Global Inc. All Rights Reserved.                                            Page 6
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

3. Cleaning the Data
The contemporary data set available to FinaMetrica covers the period Sep 2011 – Jul 2016 and consists
of 541549 registers. Out of the complete data, we retain only cases that meet the following criteria:
     Clients of financial advisors.
     Completed the 25-question version of the questionnaire.
     For better data integrity, age range is limited to 20-80, inclusive.
     Ensured legitimate values in all variables. Only one case was found with non-legitimate value for
      variable “Combined before-tax income” and removed.
     Ensure Client Code is not missing and appears only once in the data set. Client Codes appearing
      more than five times in the course of five years, Sep 2011-July 2016 were regarded as
      problematic because multiple measurements taking place too close in time (e.g. within the
      same year) or the answers to the questions differ substantially.
After the cleaning procedure, there were 407016 cases (from 541549) left.




Copyright © PlanPlus Global Inc. All Rights Reserved.                                       Page 7
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________

4. Demographic Profile
The section describes the demographic profile of the data by providing graphs accompanied by brief
explanations. The current demographic profile is compared to that described in the last technical report
(2012) matching that which the latter provides.
Before proceeding with a detailed description, a snapshot of the demographic profile of the
contemporary data is given below.
     The bulk of the data (91%) comes from UK, Australia-New Zealand (ANZ) and USA.
     82% of the data relates to 2012-2015 and are almost evenly distributed to the respective years.
     70% of the respondents were aged between 40-69 years old when they completed the
        questionnaire.
     Gender; Male slightly outnumber female (56.7% men).
     60% of the respondents have a university degree or attained higher education level.
     56% of the respondents have $50,000-199,999 total personal income before tax.
     80% of the cases have combined (within partners) income before tax between $50,000-499,999.
     46% of the individuals report net assets of value $500,000-1,999,999 (when married/in a
        relationship the share in jointly owned assets is included).
     77% report that they are married or in a relationship.
     63% of the cases support financially (fully or partially) at most one person in their family while
        92% support at most 3 people.
Note that all aforementioned percentages and the graphs below are with respect to the total number of
cases for which the related demographic has been reported. The percentage of cases out of the
complete data set with missing value in each of the demographic variables is as follows: 32% for age,
31% for gender, 39% education level, 39% for personal before-tax income, 33% for marital/relationship
status, 39% for value of net assets, and 40% for number of family dependants.




                                           DACH




Copyright © PlanPlus Global Inc. All Rights Reserved.                                          Page 8
MANUAL TECHNICAL FINAMETRICA - PLANPLUS GLOBAL
________________________________________________________________________________________




Copyright © PlanPlus Global Inc. All Rights Reserved.                          Page 9
________________________________________________________________________________________




Country
91% of the data comes from UK, Australia-New Zealand (ANZ) and USA with UK being the largest group
(43.0%), while ANZ and USA data is of similar size (24.1% each). The rest of the data comes from India
(2.7% - 11058 cases), DACH (2.2% - 8903 cases), Canada (1.8% - 7307 cases), South Africa (1.5% - 6083),
Ireland (0.5% - 1939 cases), Hong Kong, China, Sweden, Finland, Malaysia and Kuwait. For the last six
countries the sample size ranges from 611 cases (for Hong Kong) to 5 (Kuwait). Compared to the last
technical report, we notice the following differences: a) the UK relative data size has grown
substantially, b) the India and DACH relative data size has increased, and c) new countries have been
added such as Sweden, Finland, and Ireland.
Year
82% of the data refers to 2012-2015 and are almost evenly distributed to the respective years (2012 -
17%, 2013 - 21%, 2014 - 22%, 2015 - 22%) while, as expected, less data comes from 2016 (13%) and 2011
(5%). Recall that 2016 covers approximately the first half of the year (up to July) and 2011 covers only
September-December.
Age
70% of the cases in the data set are people of age 40-69 years old. The age groups 50-59 and 60-69 are
the largest ones (26% each) followed by the 40-49 group (19%). The smallest group is that of age 20-29
(7%) while the groups 30-39 and 70-80 are of similar size (12% and 10%, respectively). Compared to the
last technical report, the age profile of the data set is roughly the same.
Gender
Males (56.7%) slightly outnumber females. The gender profile is about the same as reported in the last
technical report.
Education
60% of the respondents have at least a university degree while together with those that have a trade or
diploma they make up 79% of the data. The rest 21% is divided almost evenly into those who completed
high school and those who did not.
Marital / Relationship Status
Three-quarters of the respondents in the data (77%) report that they are married or in a relationship.


Copyright © PlanPlus Global Inc. All Rights Reserved.                                        Page 10
________________________________________________________________________________________

Total Personal Before-tax Income
A bit more than half of the respondents in the data set (56%) have $50,000-199,999 total personal
income before tax with the category $50,000-99,999 being the largest (32%). The next largest income
categories are $20,000-49,999 (17%) and $200,000-499,999 (13%). The categories “under $20,000” and
“$500,000 or over” comprise 14% of the data.
Combined (Within Couple) Before-tax Income
The picture remains similar when combined before-tax income is considered. One-third of the cases
(33.5%) fall into the class $100,000-199,999 while 80% of the cases have combined before-tax income
between $50,000-499,999. The $50,000-99,999 and $200,000-499,999 categories are of about the same
size. The smallest is that of “under $20,000” (2.8%).
Value of Net Assets
A bit less than half of the cases in the data (46%) report net assets of value $500,000-1,999,999. The
next largest categories are $200,000-499,999 (16%) and $2,000,000-4,999,999 (12%). Hence three-
quarters of the data has assets of value $200,000-4,999,999. Note that when a respondent is married or
in a relationship, they have included in their answer their share in jointly owned assets.
Number of Family Members Financially Supported (Fully or Partially) by Respondent
63% of the respondents support financially (fully or partially) none or one person in their family while
29% of respondents support 2-3 family members. Hence, 92% of the data supports at most 3 people.


Demographic Profile over Time
Within each year, the distribution of the data to the three major countries, UK, Australia- New Zealand,
and USA, is about the same. The main difference over the years is that the data sets of India and DACH
seem to grow but still represent a less than 5% of the total data in a given year. Moreover, the
distributions of age, gender, education level, and personal before-tax income remains about the same
over time. Hence, with respect to these variables, the demographic profile of the data remains roughly
the same in the course of the period September 2011 - July 2016. Note that these results are based only
on the cases for which the related demographic characteristics have been provided.




                                            DACH




Copyright © PlanPlus Global Inc. All Rights Reserved.                                          Page 11
________________________________________________________________________________________




Demographic Profile across Countries
It is important to be aware of any differences in the demographic profile of the countries. This section
presents the age, gender, personal income, and education profile of the countries that comprise 99.7%
of the data set, i.e. UK, Australia/New Zealand (ANZ), USA, India, DACH, Canada, South Africa, and
Ireland.
The graphs below show that the profile of Indian data is fairly different to that of the rest of the
countries. Respondents from India are in comparison the youngest, most educated, and men in
majority but with the lowest average personal income in face value (note that caution is needed when
comparing the distribution of personal income across the countries as the purchasing power may differ
substantially). For the remaining countries, we observe the following:
     ANZ, US, Canada have almost the same age profile, while UK’s profile is slightly older, Ireland’s
      slightly younger, and much younger that of South Africa and DACH.
     Gender-wise, UK, ANZ, Canada, and South Africa exhibit are similar, while Ireland’s and DACH’s
      data is more male-dominated.




Copyright © PlanPlus Global Inc. All Rights Reserved.                                        Page 12
________________________________________________________________________________________

     When it comes to education level, UK presents the largest percentage in the lowest education
      level (high school not completed), while US presents the largest, after India, percentage in the
      highest level (“university degree or higher”).



                                DACH




                                                                                DACH
                         DACH




                                                                                   DACH




Gender Demographic Profile
In the literature, gender has been found to be associated with risk tolerance (i.e. males are associated
with higher levels of risk tolerance than females). However, a question that may be raised is whether
the two genders differ in their demographic characteristics which in turn, could be the causality of the
different risk tolerance levels. Hence, the first step is to register any cross-gender demographic
differences. Based on the graphs below, we see that women tend to have lower personal and combined
income, and net assets of lower value. In particular, 70% of the income class “under $20,000” is women.
The percentage of women steadily falls as the income class represent higher income, to reach 21% in
the upper class “$500,000 or over”. The picture for women slightly improves when the combined
income is considered or the value of net assets. However, still, in all classes of both variables (combined
income, net assets) women are underrepresented (45% or lower), especially on the higher end. These
demographic differences warrant further investigation in Section 5: Comparison of Risk Tolerance Score
across Personal Income (i.e. do the average scores of males and females differ given they are both in
the same income category). When it comes to marital/relationship status, women make up 57% of the
single category and 39% of the married/in relationship category.


Copyright © PlanPlus Global Inc. All Rights Reserved.                                          Page 13
________________________________________________________________________________________




Income Profile across Age Groups
Age has also been found to associate with risk
tolerance in the literature. Is this because the income
is different across age groups? To answer this we first
need to register the income differences across ages.
The lower income classes, “under $20,000” and
$20,000-49,999 are relatively larger in the younger
ages (20-29) and older ages (60-80), while the upper
income classes, $100,000-199,999 and $200,000-
499,999 are larger in the middle ages. The age group
40-49 seems to have the highest average personal
income; 57% of the respondents of this age group
report personal income of at least $100,000. In
Section 5, we study the effect of age on risk tolerance
after controlling for income.



Copyright © PlanPlus Global Inc. All Rights Reserved.                          Page 14
________________________________________________________________________________________

5. Data Analysis – Association of Risk Tolerance with Demographics
To determine the norm group, we need to investigate whether the distribution of risk tolerance differs
over time (from Sep 2011 to Jul 2016) and across countries and to identify the demographic
characteristics that are associated with risk tolerance.
For the analysis, we use the global risk tolerance scores included in the data set. These scores have
been computed by using the norm group / data that comes from predominately Australia, New
Zealand, Canada, USA, and UK and cover the period Jan 2010 – Jul 2011. Note these scores on the global
scales are almost identical to the scores computed on the UK subscale and the ANZCUS subscale
(ANZCUS refers to Australia, New Zealand, Canada, and USA).
For the contemporary data set (Sep 2011 – Jul 2016) we keep the data from UK, Australia/New Zealand,
USA, India, DACH, Canada, South Africa, and Ireland as these countries make up 99.7% of the data
(405828 cases in total). The data size for each of the aforementioned countries is at least 1900 cases. It
ranges from 1939 cases for Ireland to 174383 for UK. We will refer to this data as the Working Data Set.
The data of Hong Kong, China, Sweden, Finland, Malaysia, and Kuwait has been excluded from the
Working Data Set. Hong Kong data size is 611 cases but do not seem to be representative of the region
as 97% of “Hong Kong” respondents are believed to be expats. The data sets of China, Sweden, Finland,
Malaysia, and Kuwait are still fairly small with 344, 162, 36, 30, and 5 cases, respectively.
The main results of the analysis presented in this section are:
     The differences in average risk tolerance score across countries are of no practical importance.
      They all hover around 50, the mean value of the risk tolerance scale. India and South Africa
      exhibit the highest average score, 53.5, while UK the lowest average, 47.8.
     There is essentially no difference in the annual average score for the time period Sep 2011 – Jul
      2016. The annual average score is 49.
     Men, younger ages, and people with higher income and higher education tend to have higher
      level of risk tolerance on average.
     Men on average score higher than women by about 5 and this difference roughly remains after
      controlling for income (i.e. for a given income class).
     The average score of the highest income category is around 9 higher than the average score of
      the lowest income. This difference roughly remains the same when the analysis is done country-
      wise with exception of Ireland and India where the differences of the average scores are 14 and
      5, respectively.
     The average risk tolerance score of age group 20-29 is about 7 higher than the average score of
      age group 70-80. Due to interaction between age and income, the age effect on risk tolerance is
      slightly more intense in the lower income classes and tends to be less strong for the higher
      income classes.
     The average score of the most educated people is higher by 6 compared to the average score of
      the least educated people. However, there is interaction between education and income. The
      effect of education on risk tolerance tends to decrease as income increases.
     The value of net assets owned and risk tolerance are not found to be associated.
     For most sub-groups defined by the value of various demographic characteristics, the average
      score falls into the middle risk group 4.


Differences in Risk Tolerance across Countries
Our analysis below suggests that there are no differences of practical importance in the distribution of
risk tolerance across countries. The country distributions can be considered roughly the same.



Copyright © PlanPlus Global Inc. All Rights Reserved.                                          Page 15
________________________________________________________________________________________




                                  DACH




Figure 1: Distribution of Risk Tolerance Scores by Countries


The graph above presents the boxplot3 of risk scores for each country. The distributions look similar
with small differences in the score means. The table below summarises the mean, median, standard
deviation, minimum, maximum, skewness and kurtosis for the observed distribution of risk tolerance
by country. The standard errors of skewness and kurtosis are provided in parenthesis. Based on the
table, there are small differences in the score means with UK exhibiting the smallest mean, 47.79, and
India the largest, 53.34, but the difference is barely of 6. Such differences may be considered of no
practical importance when regarding the investment implications, especially if it is taken into account
that the score means are close to 50 (the mean of the scale) and fall into the same risk group, group 4,
which represents people with average level of risk tolerance.
The country means are almost identical to the country medians suggesting that the distribution of risk
scores is close to symmetrical for all countries. The standard deviation for all countries is very close to
10 which is the standard deviation of the scale. The differences of the standard deviations are less than
a unit. The country minimum and maximum values of risk score are almost identical. The skewness is a
very small positive number for UK, Australia/ New Zealand, USA, Canada, and South Africa. This
indicates an almost symmetrical distribution with a slightly longer tail to the right, i.e. slightly more
values to the top end of the risk tolerance scale rather than to the bottom end of the scale. India, DACH
and Ireland have a symmetrical distribution. The kurtosis is a small positive number for all countries
implying that there are more observations in the ends of the risk scale (i.e. fatter tails) compared to a
normal distribution with mean 50 and standard deviation 10. The Indian data seems to have more
observations in the ends of the risk scale than in any other country while the data of Australia/New
Zealand practically follows a normal distribution with mean 50 and standard deviation 10.




3
  A boxplot displays the distribution of a variable where the median is reported by the solid line inside the box and
the lines on the bottom and top of the box show the value range of the middle 75% of the data. The circles
represent extreme values. Very roughly a boxplot can be seen as a “flat” histogram.



Copyright © PlanPlus Global Inc. All Rights Reserved.                                                    Page 16
________________________________________________________________________________________

  Country     Data Size Mean Median Std. Dev. Min                  Max       Skewness             Kurtosis
      UK       174383      47.79        48      10.053       13     95     .130  (.006)         .388  (.012)
   AUS/NZ       98244      49.46        49       9.916       13     95     .155  (.008)         .377  (.016)
      USA       97911      50.55        50       9.699       13     95     .128  (.008)         .359  (.016)
     India      11058      53.75        54       9.838       14     95     -.047 (.023)         .633  (.047)
     DACH        8903      51.81        52      10.550       13     95     .088  (.026)         .180  (.052)
    Canada       7307      50.57        50      10.607       14     95     .131  (.029)         .429  (.057)
 South Africa    6083      53.34        53      10.568       15     95     .113  (.031)         .155  (.063)
    Ireland      1939      49.32        49      10.838       17     85     -.082 (.056)         .026  (.111)
 standard errors in parenthesis
Table 1: Descriptive Statistics for Distribution of Risk Tolerance Scores by Country


An ANOVA analysis (where the independent variable is risk score and factor is country) rejects the
hypothesis of equality among country score means at any conventional significance level (p-
value=0.000). However, we should bear in mind that large data sets like ours will almost always reject
the hypothesis of equality as the power of the ANOVA test to detect small differences across groups’
increases substantially with the size of the data. In other words, the data size is so large that the test
picks up on very minor differences. Same reasoning applies to country pairwise comparisons where
differences of less than 1.67 units are found to be statistically significant. In particular, the mean
differences of the following pairs of countries are found to be statistically significant (p-value0.5) but these
differences are only 0.13 and -0.03, respectively.


Differences in Risk Tolerance over Time
Distribution of risk tolerance score over time shows no practical difference. Figure 2 provides the
boxplots of risk score per year and Table 2 the corresponding descriptive statistics. We observe that in
all years the score mean and median coincide and are between 48 and 50. There is no observable trend
over time.




Figure 2: Distribution of Risk Tolerance Scores by Year



Copyright © PlanPlus Global Inc. All Rights Reserved.                                            Page 17
________________________________________________________________________________________

  Year Data size Mean         Median      Std. Dev.   Min     Max      Skewness                Kurtosis
  2011    19414      48.44       48        10.244      14      95    .171   (.018)          .313    (.035)
  2012    70819      48.27       48        10.034      13      95    .131   (.009)          .282    (.018)
  2013    85638      49.11       49        10.013      13      95    .131   (.008)          .330    (.017)
  2014    89361      49.87       50        10.112      13      95    .114   (.008)          .408    (.016)
  2015    88678      49.61       49        10.018      13      95    .107   (.008)          .382    (.016)
  2016    51918      49.42       49        10.102      13      95    .130   (.011)          .402    (.021)
 standard errors in parenthesis
Table 2: Descriptive Statistics for Distribution of Risk Tolerance Scores by Year


Although Table 3 reports the mean differences of adjacent years being statistically significant (p-
value
________________________________________________________________________________________

Figure 3 presents the boxplots of risk tolerance scores by gender and Table 4 gives the descriptive
statistics as well as the test of equal means. The mean score is 52.11 and 46.44 for men and women,
respectively. The medians are almost identical to the means and along with the skewness values
indicate that the distributions are symmetrical for both genders. The standard deviations are very close
and the kurtosis is a bit higher for women (slightly more extreme observations for women than men).

 Gender Data size Mean            Median     Std. Dev.   Min     Max       Skewness            Kurtosis
   Male      158691     52.11       52         9.965      13      95    .074   (.006)       .379    (.012)
  Female     121189     46.44       46         9.245      13      95    .086   (.007)       .434    (.014)
 Difference in means = 5.68, p-value=0.000, standard errors in parenthesis
Table 4: Descriptive Statistics for Distribution of Risk Tolerance Scores by Gender


Differences in Risk Tolerance across Personal Income Groups
Personal income (before tax) is positively associated with risk tolerance, i.e. larger income is associated
with higher levels of risk tolerance. The average score of the highest income category is around 9
higher than the average score of the lowest income. The average level of risk tolerance increases by a
maximum of 3.5 between adjacent income classes. The difference is less than one between the two
lower categories (“Under $20,000” and “$20,000-$49,999”) and between the two higher categories
(“$200,000-$499,999” and “$500,000 or over”). Note that the analysis is based on the cases for which
personal income has been reported, 61% of the Working Data set.
Figure 4, which presents the boxplot of risk tolerance score for each income class, shows that there is
an increasing tendency of the median score and of the range of the middle 75% of the values (the lines
on the bottom and top of the box tend to move upwards) as income increases. This is more apparent
across the middle income classes ($20,000 up to $499,999) rather than between the first two and the
last two income classes. Table 5, that provides the descriptive statistics of risk tolerance for each
income class, conveys the same message. The score means increase with the income, from 45.68 for
the lowest income class to 54.60 for the highest income class. However, they all fall just about in the
middle risk group 4 (which represents people with average level of risk tolerance). Table 6 shows that
differences in means between adjacent income classes are statistically significant at any conventional
significance level (p-value
________________________________________________________________________________________

In all income classes, the mean and median coincide and along with the close-to-zero values of
skewness we understand that all distributions are almost symmetrical. The standard deviations,
minimum, and maximum values only slightly differ across income classes. The slight positive kurtosis
for all distributions suggests that there are more observations in the ends of the risk scale (i.e. fatter
tails) compared to a normal distribution.

   Income Class        Data Size    Mea      Median       Std.      Min     Max     Skewness         Kurtosis
                                      n                   Dev.
   Under $20,000      22621         45.68   46           9.846
                                                             13     95    .065 (.016) .428                (.033)
   $20,000-$49,999    41617         46.08   46           9.527
                                                             14     95    .217 (.012) .499                (.024)
   $50,000-$99,999    80101         48.65   48           9.616
                                                             14     95    .158 (.009) .365                (.017)
 $100,000-$199,999    58877         52.00   52           9.529
                                                             13     95    .139 (.010) .421                (.020)
 $200,000-$499,999    32747         54.11   54           9.550
                                                             16     95    .087 (.014) .319                (.027)
  $500,000 or over    12318         54.60   55           10.005
                                                             14     95    .112 (.022) .814                (.044)
 standard errors in parenthesis
Table 5: Descriptive Statistics for Risk tolerance Scores across Personal Income Classes


         Pairwise Category Comparisons            Mean Difference   Std. Error  p-value
      “Under $20,000” vs “$20,000-$49,999”             -0.40           .079      .000
     “$20,000-$49,999” vs “$50,000-$99,999”            -2.57           .058      .000
    “$50,000-$99,999” vs “$100,000-$199,999”           -3.35           .052      .000
  “$100,000-$199,999” vs “$200,000-$499,999”           -2.12           .066      .000
   “$200,000-$499,999” vs “$500,000 or over”           -0.49           .102      .000
Table 6: Mean Differences in Risk Tolerance Scores between Adjacent Income Classes


Doing a similar analysis in each country separately we find that the effect of income on risk tolerance
remains in all countries, i.e. an increase in income is associated with an increase in risk tolerance score.
Table 7 presents the median risk tolerance scores across the income classes for each country separately
and for all countries together. The range of median in each country is around 10 apart from Ireland and
India where the ranges are 14 and 5, respectively. The patterns remains the same if instead of medians
we consider means; in all countries the mean and median of risk tolerance are almost identical within
each income category.

   Income Class          All       AUS/NZ   Canada      DACH      Ireland   India     UK       USA      S. Africa
   Under $20,000      46      46       47       47      43       51                   44       48          48
  $20,000-$49,999     46      46       47       47      46       53                   44       47          50
  $50,000-$99,999     48      49       50       49      47       54                   47       50          52
 $100,000-$199,999    52      52       53       53      50       54                   51       52          56
 $200,000-$499,999    54      55       58       56      54       55                   53       54          58
  $500,000 or over    55      55       56       56      57       56                   54       54          59
Table 7: Median Risk Tolerance Scores across Income Classes by Country


Differences in Risk Tolerance across Age Groups
The score mean seems to increase as we move from age group 20-29 to group 30-39 but decreases as
age increases beyond 39. A similar pattern is observed in score variance. The average risk tolerance
score of group 20-29 is about 7 higher than the average score of group 70-80. The means for all age
groups fall into the middle risk group 4 and the differences of the means between adjacent age groups


Copyright © PlanPlus Global Inc. All Rights Reserved.                                                Page 20
________________________________________________________________________________________

are of maximum 3. The differences in standard deviation are minimal as well, 1.3 at most. The results
come from 67.9% of the Working Data for which age is reported. All these can be seen in Figure 5 and in
Table 8. Table 9 shows that the differences in score means between adjacent age groups are
statistically significant (p-value
________________________________________________________________________________________

levels is 6.1. The means for all education levels fall into the average risk group 4. The result is based on
61.3% cases of the Working Data which have reported their education level. Later in this section we
investigate whether, controlling for income, the differences across education levels remain.
Figure 6 and tables 10 and 11 below detail the analysis. The mean differences for the first two
education levels (High school not completed versus completed) and for the last two (trade or diploma
versus university degree or higher) seem to be similar, 2.6 in absolute value, while the difference
between the two middle levels (completed high school versus trade/diploma) is smaller, 0.93 in
absolute value.




Figure 6: Distribution of Risk Tolerance Scores across Education Levels


  Education Level Data size        Mean      Median     Std. Dev.   Min   Max     Skewness         Kurtosis
   High school not
                       23512       45.14        45       10.124     13    95     .154   (.016)   .389   (.032)
    competed (1)
    High school
                       28850       47.72        47       9.869      14    95     .189   (.014)   .360   (.029)
   completed (2)
 Trade/diploma (3)     46675       48.65        48       10.029     14    95     .171   (.011)   .310   (.023)
 University degree
                      149539       51.24        51       9.761      13    95     .158   (.006)   .370   (.013)
    or higher (4)
 standard errors in parenthesis
Table 10: Descriptive Statistics for Risk Tolerance Scores across Education Levels



 Pairwise comparisons    Mean Difference      Std. Error p-value
 Category 1 vs 2               -2.57             .087     .000
 Category 2 vs 3               -0.93             .074     .000
 Category 3 vs 4               -2.59             .052     .000
Table 11: Mean Differences in Risk Tolerance Scores between Adjacent Education Levels


Differences in Risk Tolerance across Net Assets Groups
Risk tolerance is not found to be associated with the value of net assets owned. The average risk
tolerance score hovers around 50 for all categories of net asset values.




Copyright © PlanPlus Global Inc. All Rights Reserved.                                            Page 22
________________________________________________________________________________________

Differences in Risk Tolerance by Gender Controlling for Personal Income
In Section 4 we have reported that females tend to earn less than males in general. Above we found
that males’ score mean is about 5 higher than that of females. Controlling for income, the gender score
difference of about 5 remains in each income class. The result is based on the analysis of 60.9% of the
Working Data for which both demographic variables have been reported.
Figure 7 shows gender means along with their 95% confidence interval for a given income class. The
solid horizontal line denotes score 50 while the dashed lines show the bounadries of risk group 4 (45
and 54). Table 12 presents the means for each sub-group defined by gender and income, the gender
mean differences for each income class, and the corresponding p-value. All means just about fall into
the middle risk group 4. The smallest mean difference is observed for the income class $50,000-$99,999
(3.9) while the largest for the class “$500,000 or over” (6.19). All differences are statistically significant (p-
values
________________________________________________________________________________________

based on 60.4% of the Working Data for which both demographic variables (age and income) have been
reported.
Figure 8 presents the mean risk score and its 95% confidence interval for all age groups within each
income class. The solid horizontal line denotes score 50 while the dashed lines the boundaries for risk
group 4 (45 and 54). The 95% confidence intervals are short in almost all cases because of the large
data size of each sub-group (defined by age and income). Table 13 provides the mean risk tolerance
score for each age group by income sub-class. The mean scores for the older ages with lower income
just about fall into the risk group 3, while the mean scores for younger ages with higher income just
about fall into risk group 5. The rest of the mean scores fall into the average risk group 4.
Table 14 gives the differences in score means between adjacent age groups given a certain income
class and the corresponding p-value is provided in parenthesis only if it is larger than 0.01 (i.e. when the
difference is statistically significant at 1% significance level). The largest differences are systematically
found when the age group 40-49 is compared to that of 50-59. However, the difference in mean score
between adjacent age groups given an income class is not more than 3 on average. Given an income
class, the maximum mean difference across age groups is between 7 to 10.




Figure 8: Age Group Means and 95% CI for Risk Tolerance Scores across Income Classes


    Age Group        Under       $20,000-     $50,000-   $100,000- $200,000-   $500,000
                    $20,000      $49,999      $99,999    $199,999 $499,999      or over
      20-29          50.94         51.95       53.34      55.56       57.31      55.32
      30-39          48.95         50.08       52.24      55.06       56.81      57.64
      40-49          47.48         48.01       50.58      53.81       55.87      56.00
      50-59          44.77         45.81       48.03      51.32       53.49      54.05
      60-69          42.86        44.32        46.45      49.37       51.34      52.32
      70-80          41.41        43.55        45.87      48.71       50.31      50.97
Table 13: Descriptive Statistics for Risk Tolerance Scores across Age Groups and Income Classes




Copyright © PlanPlus Global Inc. All Rights Reserved.                                            Page 24
You can also read
Next part ... Cancel