Investment Type And Age Group Analysis - Business Statistics

Variables Defined in the Study

  Business Statistics is an essential tool for financial investment advisors (firm or an individual), agents and other institutions, particularly to understand the investment patterns and nature of the investors, and therefore generate suggestions on investment decisions, portfolio preparation as best suited to their clients’ needs.

In line with the above statement, data collected on investors (recorded by XYZ Investment Advisors) will be analysed to understand significant relationships among various factors measured and thus draw meaningful conclusions relevant to the study.

The dataset used for this study was collected by XYZ Investment Advisors by recording details like personal information, demographics, investment preferences, etc. of the associated investors (by collecting personal information upon registration, and keeping a record of their investment profile accounts). There are other means of collecting data as well, like by experimental studies, interviews, paid market research, etc., however, none of which has been used in the collection of this dataset.

This report is presented on a sample data of 100 respondents (investors) that are assumed to represent the true population for the study. Moreover, like most of the research studies, this research study has some limitations and it is therefore likely stated that the sample is a true representation of the population and was collected with no bias in the study or investors’ responses.

The main aim of this report is to investigate the relationship between the 2 relevant variables ‘Investment type’ and ‘Age group’. It is also required to estimate a 90% interval for the return on investment (measured in annual profit per $1000), and further test the claim that the average annual profit per $1000 for all the investors is above $30.

 Variables Defined in the Study:

Variable Name	Type of Variable	Purpose
Income	Numerical	To assess the income of an investor.
Amount invested	Numerical	To record the amount the investor has invested with the company.
Return in $ per thousand	Numerical	To assess the return on an investment.
Investment type	Categorical	To classify the risk associated with the investment (high/low risk).
Fees paid	Numerical	Fees paid for the services.
Fees too high	Categorical	To assess if the fees paid was too high.
Gender	Categorical	To look for significant differences in investment patterns of male/female.
Age	Numerical	To record age of the investor for further sub-analysis.
Age group	Categorical	To understand the differences in the younger and older peoples investment choices and preferences.
Married	Categorical	To understand if being married/unmarried affects the investment decisions of an investor.
Number of Children	Numerical	To understand if the number of children (responsibilities, future goals) of an investor affects his/her investment decisions.
Have Children	Categorical	To understand if having children or not affects the investment decisions of an investor.
Country	Categorical	Understanding the demographic profile of the investor.

The research on investment decision-making and preferences among older and younger investors by Wang and Hanna (1997) suggests that in the case of potential losses, adult (older) investors may be more risk averse than younger people, given that they have low levels of net worth. However, the risk aversion tends to decrease with age if the investor has a high level of net worth.

For this report, the relationship between risk preference and age group of an investor was investigated and analysed, irrespective of their levels of net worth. It is expected that adult investors are more risk averse than younger investors.

A simple bivariate analysis was performed using the pair of two categorical variables ‘Investment Type’ and ‘Age group’. The results of the analysis are presented below:

Two-way Table:

Count of Investment type	Age group
Row Labels	50 or below	more than 50	Grand Total
high risk	17	9	26
low risk	35	39	74
Grand Total	52	48	100

% share of Investment type for Different Age Group	Age Group
Row Labels	50 or below	more than 50	Grand Total
high risk	65.38%	34.62%	100.00%
low risk	47.30%	52.70%	100.00%
Grand Total	52.00%	48.00%	100.00%

 

Comments:

As read from the tables and chart above, about 65.38% of the investors having a high-risk preference (that is, willing to invest on a risky investment) are aged 50 years or below, while the remaining 34.62% are older than 50 years. It is also observed that among the investors who are risk-averse (one who prefer less risky investment), about 52.7% are adult while the remaining 47.3% are young investors.

Bivariate Analysis of Investment Type and Age Group

This likely indicates that adult investors are more risk-averse than younger investors. In the following sub-section, this hypothesis is tested.

Testing if there is a relationship between the variables investment type (high risk/low risk) and age group (50 or below/above 50) using Chi-Square test of independence.

 The hypotheses are stated as: Null hypothesis            

 Alternative hypothesis

Two way table	Age group
Investment Type	50 or below	more than 50	Grand Total
high risk	17	9	26
low risk	35	39	74
Grand Total	52	48	100

Using an online calculator, the Chi-Square test statistic was computed to be 2.5218, and the p-value was obtained as 0.1123

Comment:

Since the p-value is greater than the assumed significance level of 0.05, that is p-value>0.05, we fail to reject the null hypothesis, concluding that there is insufficient evidence to claim that the two variables are dependent or have a statistically significant relationship between them.

The findings of the above analysis are not as expected or described by the literature review presented in Section 2. A possible explanation of this could be ignorance of other crucial factors like ‘net worth’ which were unaccounted for in the analysis. This variable could have potentially affected the relationship between the defined categorical variables.

Confidence Interval

For the variable ‘return per $1000’, following summary statistics were computed using MS-Excel:

Data
Sample Standard Deviation,	14.70244
Sample Mean,	37
Sample Size,	100
Confidence Level	90%

 

Intermediate Calculations
Standard Error of the Mean	1.4702
Degrees of Freedom	99
t Value	1.6604
Margin of Error	2.4412

Confidence Interval
Interval Lower Limit	34.56
Interval Upper Limit	39.44

 To test the claim if the average return on per $1000 is above $30, a right-tailed (directional) -test is used. It is appropriate to use a -statistic (and not a -statistic) as the population standard deviation is unknown).

Assumption: It is assumed that the data was sampled using simple random sampling and is approximately normally distributed.

The hypotheses are stated as:

         

Here,  is the hypothesized population mean return to investors per $1000 investment.

Decision Rule: The null hypothesis  is rejected if there is statistically sufficient evidence (at a significance level of 5%, i.e. ) to conclude that the true mean return to investors per $1000 investment is above $30.

Computing the -test statistic:

Thus, the right-tailed -value is computed to be  (using a -table)

Since  i.e. , we reject the null hypothesis thus, concluding that there is sufficient evidence (at 5% significance level) to claim that the mean return to investors per $1000 investment is above $30.

It was found that adult investors are more risk averse but the results obtained were not statistically significant. Therefore, general advice about surveys is presented instead of any specific advices on the previous findings.
It is to be taken care of that the survey results might be biased or the respondents did not answer the questions correctly. Such issues arise when the respondent is not really interested in participating in the survey, but is still asked to do so, or the target audience (in relevance to the research study) is poorly selected.

 This report demonstrates how statistics can be used to summarize bulk of  information such as the investors personal information and their personal investment preferences.

Based on the findings, it can be concluded that no significant relationship was observed between the two categorical variables investment type and age group. In other words, the claim that adult investors are more risk averse is not valid.

It was also noted that the mean return to investors per $1000 investment is $37 with a r deviation of $14.7. Further, with 90% confidence, it can be stated that the true population mean return for all the investors is expected to lie within the range $34.56 to $39.44. Lastly, it was concluded that this mean return on investment per $1000, is significantly more than $30.

The research can be more detailed and extended by adding the variable ‘net worth/net income’ to the analysis, to be more in accordance with the research aim presented in the Journal article.

References  

Wang, H. and Hanna, S. (1997). Does Risk Tolerance Decrease With Age?. SSRN Electronic Journal.Appendix”  Wang, H. and Hanna, S. (1997). Does Risk Tolerance Decrease With Age?. SSRN Electronic Journal.

“ Previous researchers have studied the relationship between age and the holding of risky assets. Morin and Suarez (1983) investigated the effect of age on the holding of risky assets using 1970 Canadian Survey of Consumer Finance data. Risky assets were defined as the sum of stocks, bonds, mutual funds, real estate other than owner-occupied home, equity in own business, and loans. Morin and Suarez (1983) concluded that on average, risk aversion increased with age. For those at the low levels of net worth, risk aversion increased with age. In contrast, for households with high net worth, risk aversion decreased with age. The authors concluded that both net worth and age influenced risk aversion.