Investor Data Analysis For XYZ Investment Advisors

Literature Review

Presently, investors are becoming more aware of their personal financial future because of the combination of higher self responsibility for retirement along with an aging population. Thus, the requirement to invest for supporting the retirement is extremely important. Considering the statistically significant impact of current investment choices on future living conditions (Browning and Crossley, 2001), it is extremely important to know the theory of effective management of asset to optimize the investment return for achieving our investment aim. Business statistics is very helpful to companies in finding the optimal quantity of investment needed for a firm to yield profitable returns at different time lags. In this assignment, we would try to analyze an investment data on the basis of certain hypothesis testing.

The first section introduces our topic and the second section gives a literature review of an academic journal surveyed for this topic. Third and fourth section gives the analysis part of the topic. Fifth section gives the recommendations and suggestions on the basis of the research findings and the sixth section concludes the topic with certain proposals for future research on this topic.

Rolf W. Banz highlighted the empirical relation between the total market value of common stocks of NYSE and their returns. As per the author, the smaller companies, that is companies having lower quantity of investment or lower market value, is observed to posses an average, a higher risk adjusted returns that the large firms have having huge investments and larger market value. It is viewed from the existing literature that the capital asset pricing model have sometimes been unspecified and the size effect of all these companies prevails and had been non-linear in the market value. This is reviewed from the fact that the most significant impact occurs for every small firms and there is a very small difference between large and average sized firms.

Before going forward to bivariate analysis, we need to construct our hypothesis that there is no major impact of investment on the income of the company. In other words, our null hypothesis is H₀: β = 0 against our alternative hypothesis, H₁: β ≠ 0. So our dependent variable is the income and the independent variable is the amount invested.

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Regression Statistics
Multiple R	0.704771
R Square	0.496702
Adjusted R Square	0.491567
Standard Error	12536.29
Observations	100
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.52E+10	1.52E+10	96.71579	0.00
Residual	98	1.54E+10	1.57E+08
Total	99	3.06E+10
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	63741.61	2925.794	21.78609	0.00	57935.47	69547.75	57935.47	69547.75
amount invested	0.147449	0.014993	9.834419	0.00	0.117695	0.177202	0.117695	0.177202

From the result, we can state that income is significantly dependent on the total amount of investment. This can be confirmed from the p-value which is 0 (strictly less than 0.05). The coefficients claim that if the investment amount increases by one unit then the income of the company will increase by 0.147449 units. The intercept term is also statistically significant and it implies the effect on income if the vale of amount invested is 0. Hence we reject our null hypothesis and accept our alternative hypothesis. So our claim of section 2 is achieved here.

Bivariate Analysis and Hypothesis Test

The scatter plot showing the relation between income and amount invested is given below: –

Figure 1

Descriptive Statistics	income	amount invested
Mean	89740	176321.71
Standard Error	1758.133767	8403.483712
Median	90500	171823.5
Mode	106000	20000
Standard Deviation	17581.33767	84034.83712
Sample Variance	309103434.3	7061853850
Kurtosis	-0.602402535	-0.923459107
Skewness	-0.202137829	-0.120203874
Range	76000	328497
Minimum	50000	20000
Maximum	126000	348497
Sum	8974000	17632171
Count	100	100
Largest(1)	126000	348497
Smallest(1)	50000	20000
Confidence Level (95.0%)	3488.518734	16674.3344

In this analysis we have used two numerical variables (i.e. option 3).

In this section, we will compute the 95% Confidence interval of the variable return per $1000. For this, we need the following computations: –

Mean = 38.6

Standard Deviation = 15.2269

No. of observations = 100

Square Root of No. of observations = 10

T-score scaling factor (p,n-1) = 1.9842169

Margin of errors = t-score*(Standard Deviation/Square root of the no. of observations) = 2.984418

Upper Confidence limit = Mean + Margin of errors = 41.58442

Lower Confidence limit = Mean – Margin of errors = 35.61558

Now we shall test claim that the average annual return on investment per $1000 is above $30.

So our null hypothesis is: – H₀: µ = 30

And our alternative hypothesis is: – H₁: µ > 30

The z Critical one-tail value is 1.644854. So we reject the null hypothesis if the z-value is greater than 1.644854. Here our z-value is 23.29377 which is far greater than 1.644854. So we reject the null hypothesis and accept the alternative hypothesis that the average annual return on investment per $1000 is above $30.

From our point of view, after going through the data and the above analysis, we can predict certain factors. Firstly, according to the sample data, we find a statistically significant impact of the amount invested on income with an average return of around $39 per $1000 invested. Hence it is obvious that the company need to attract more and more investment in order to increase its earning. Secondly, using dummy variable approach, we find that the type of investment becomes risky when there is higher return per $1000 and when the individual is young. Here we have defined investment type as 1 if the investment is associated with high risk and 0 if it is associated with low risk. We use STATA software to compute this result. The results are given below: –

Figure 2

In Figure 2, we interpret the regression results as follows: if the age of the investor increases by one unit, then log odds in favor of high risk investment will decrease by 0.0493 units.

Figure 3

In Figure 3, we interpret the regression results as follows: if the number of children of the investor increases by one unit, then logs odds in favor of high risk investment will increase by 0.27531 units.

Figure 4

In Figure 4, we interpret the regression results as follows: if the returns of the project for the investor increase by one unit, then logs odds in favor of high risk investment will increase by 0.085 units.

This research demonstrates the use of business statistics in summarizing a large amount of information related to investment analysis. From our analysis we can say that investment is positively related to income. There is also a big scope of future research on the factors that would affect the type of investment like age of the investors, his/her marital status, number of children they have, the returns obtained etc. This research can also be carried out on the countrywise basis. That is, showing the risk behavior of the individuals from various countries (country 1 and country 2).

References

Jensen, M. (1986). Agency cost of free cash flow, corporate finance, and takeovers, American Economic Review, 76 (2), pp. 323-329.

Drobetza, W., Gounopoulos, D., Merikas, A. & Schröder, H. (2013). Capital structure decisions of globally-listed shipping companies, Transportation Research Part E, 52, pp. 49-76.

Fama, E.F. & French, K.R. (2005). Financing decisions: Who issues stock? Journal of Financial Economics, 76, pp. 549-582.

Fan, J.P.H., Titman, S. & Twite, G. (2012). An international comparison of capital structure and debt maturity choice, Journal of Financial Quantitative Analysis, 47, pp. 23-56.

Faulkender, M., Flannery, M.J., Hankins, K.W. & Smith, J.M. (2012). Cash flows and leverage adjustments, Journal of Financial Economics, 103, pp. 632-646.