Introduction
The given report pertains to an investment company (XYZ Investment Advisors) which collects funds from various clients and invests the same in a host of global assets and securities in accordance with the stated risk appetite of the investors. The customers use the company’s services as they believe that the company driven by its experience and professional skill could actually generate superior returns in comparison with investors managing their own funds. For the purposes of the given report, the data pertaining to 100 clients of the firm has been drawn which provides information about various parameters such as amount invested, returns generated, age, fee paid along with the type of asset in which the money has been invested. Statistical analysis of the provided sample data has been performed in order to draw some conclusions about the population data. Further, based on findings, new recruits are offered some advice which would help them outperform in their jobs.
Literature Review
From the investor perspective, investing is a mystery but that can be codified using two key attributes which every security belonging to any asset class would follow. These two attributes are returns delivered and risk assumed. The objective of a prudent investor is to maximise returns earned while minimising risk assumed. But typically risk and return go hand in hand and for an asset that delivers higher returns, typically the risk is also higher. Thus, there is a risk return tradeoff where the investor needs to make prudent choices where an optimal solution is found which results in outperformance. Thus, while making portfolio choices the investors should look at ways to achieve the above stated target. The above objective can be assisted through the practice of diversification which can potentially lead to significant decrease in risk while improve returns per unit risk. However, it is essential that the same must be practised with caution (Mollik and Bepari, 2015).
Section 1
There are three options with regards to conducting bivariate analysis based on the underlying choices of the variables i.e. categorical and numerical variables. For this exercise, option 3 has been chosen which tends to focus on both numerical variables. Bivariate analysis and hypothesis test for the investor data is conducted below:
After selecting option 3, these are the things which need to be performed.
- Scatter plot to find the association between the selected variables.
- Determination of mean and standard deviation for the selected variables.
The selected variables for the analysis are highlighted below:
- Fees paid ($) (Dependent variable)
- Annual Returns ( in $ per $1,000 investment) (Independent variable)
Scatter plot
From the scatter plot, it can be concluded that the variables i.e. fees paid and returns do not have any strong association with each other. Further, it can be said that the relationship between the variables is quite weak consider the scatter observed which fails to outline any linear pattern to describe the relationship (Flick, 2015)..
The below highlighted table is for indicating the mean and standard deviation of the selected variables.
To check the claim regarding the significance of the slope, hypothesis testing would be used. The hypothesis to be put to test is outlined below.
Regression output by considering fee paid as dependent variable and the returns per $1,000 investment as an independent variable has been computed and pasted below.
Value of t stat = 0.29 (corresponding to the slope coefficient)
Also, p value = 0.77 for the above t statistic of 0.29
Assuming 5 % = alpha (level of significance)
From the above, it is apparent that p value is much higher than the level of significance (0.77 > 0.05). Therefore, null hypothesis would not be rejected. Hence, the final conclusion can be made that the slope is not significant and can be assumed to be 0.00 (Hillier, 2006).
Section 2
“Investigate the variable returns (in $ per $ 1,000 investment)”
Construction of 95% confidence interval
The number of observation is 100 which is greater than 30 and as per central limit theorem the distribution would be normal. However, the value of standard deviation for the population mean is unspecified. Therefore, t value would be taken into account in place of z value (Hair et. al., 2015).
Confidence interval formula:
Level of significance
Therefore, t stat for the above stated input is 1.98.
Lower limit
Upper limit
95% confidence interval = [36.24 42.05]
Interpretation:
It can be said with 95% confidence that annual returns on investment (in $ per $ 1,000 investment) would lie between the interval $36.24 and $42.05 (Flick, 2015).
Hypothesis testing
- µ ≤ 30 i.e. value of average annual returns on investment would not exceeds $30.
- µ > 30 value of the average annual returns on investment would exceeds $30.
The number of observations is 100 which are greater than 30 and as per central limit theorem the distribution would be normal. However, the value of standard deviation for the mean is unspecified. Therefore, t value would be taken into account in place of z value (Hillier, 2006).
, degree of freedom = 99,
For the above inputs, the p value is 0.00001.
Level of significance = 5%
It is apparent from the above that p value is lower than the level of significance. Hence, null hypothesis would be rejected. Therefore, “value of the average annual returns on $1,000 investment would exceed $30” (Flick, 2015).
Basic Advice
One of the key concerns for the new employees is the usage of sample data for deriving conclusions about population through the use of hypothesis testing as not only the correct hypothesis test has to be employed but it needs to be backed with an appropriate choice of sampling method thus ensuring that the given sample is representative. For reducing the risk associated with choosing a biased sample, it makes sense that the method deployed for obtaining the sample should be the stratified sampling which would assure representation from various key attributes in the same proportion as they occur in the population. Further, a minimum sampling size must also be chosen based on the overall population size and the homogeneity present in the population (Hastie, Tibshirani and Friedman, 2011).
Conclusion
Based on the analysis carried out above, it is apparent that the relationship between the fee given by the client does not seem to be associated with the returns that they make on the investment done by the company. However, there is a catch which warrants that a naïve conclusion should not be drawn. This factor which works in the background is the nature of assets in which funds have been invested. The returns would typically be driven by the type of investment and it would be incorrect to interpret the same in the absence of the underling risk. Also, the given sample data lends support to the conclusion that the average annual return earned by the investor is more than 3% p.a. This is also reflected from the value obtained in the confidence interval which tends to lend support to the conclusion drawn. Additionally, for the investors, it becomes imperative that they must appreciate the inherent tradeoff between risk and return and make prudent choices aimed at maximising the returns per unit risk. Further, the new employees need to demonstrate caution with the usage of samples for deriving conclusions about population.
References
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research project, 4th ed., New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015). Essentials of business research methods, 2nd ed., New York: Routledge.
Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning, 4th ed., New York: Springer Publications.
Hillier, F. (2006), Introduction to Operations Research, 6th ed., New York: McGraw Hill Publications.
Mollick, A. and Bepari. M.K. (2015), Risk-Return Trade-off in Emerging Markets: Evidence from Dhaka Stock Exchange Bangladesh, Australasian Accounting, Business and Finance Journal, Vol. 9, No.1, pp. 70-82
