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A particular investment advice company named XYZ Investment Advisors has clients worldwide and it tends to make investments on their behalf and manages their funds so as to generate superior returns for the customers. The customers tend to avail services offered by the firm as they believe that firm has expertise and experience in making investments and thus could generate superior returns on the amount invested while keeping in mind the individual risk and asset preferences for the client. The given report aims to analyse the sample data concerned with 100 customers in accordance with the statistical techniques available to reach meaningful conclusions about population. Additionally, the customers and new recruits also need to be given useful advice in wake of the analysis along with the literature review.
The two central characteristics that tend to define each investment are referred to as underlying risk along with the returns. For the evaluation of attractiveness of any asset, it is quintessential that these two aspects must be viewed in unison and not independent of each other. Relying only on one aspect can lead to incorrect decision making which must be avoided. This is because if only returns are considered, then an investor may invest in a risky asset and therefore on a risk adjusted basis may earn an inferior return only. Further, if the investor considers only the risk aspect and aims to invest in the asset having the lowest risk, it might be possible that the returns offered are quite dismal. As a result, it is imperative that the choice should be made keeping in mind both the risk return characteristics so that through investment they are able to earn maximum return per unit risk which should be the ultimate objective (Mollik and Bepari, 2015).
Section 3 – “A simple Bivariate Analysis of the investor data and Hypothesis test”
Two non –numeric variables have been selected for the analysis and hypothesis testing.
Variable 1 – Returns in $ per thousand invested
Variable 2 – Fees paid
It has been assumed that the fee paid is a dependent variable which is dependent on the returns in $ per thousand which is considered to be the independent variable.
The scatter plot to find the association between the variables (returns in $ per thousands and fee paid) is furnished below:
From the above scatter plot, it can be seen that fee paid and returns in $ per thousands are not having any significant association. Therefore, it can be concluded that the strength of the association between the variables (fees paid and returns) is very weak (Flick, 2015).
A simple Bivariate Analysis of the investor data and Hypothesis test
For the selected variable, the value of mean and standard deviation has been determined in excel and offered below:
Hypothesis testing
Hypothesis testing would be conducted in regards to determine whether slope is significant or insignificant.
Regression would be run in excel by taking fee paid – dependent variable and returns – Independent variable.
From the regression output, it can be seen that t stat is having a value of 0.27 and the respective p value is 0.78.
Let the significance level is 5%.
It is apparent that p value is greater than significance level (0.75 >0.05). Hence, there is lack of evidence for the rejection of null hypothesis. As a result the slope can be assumed to be equal to zero. Therefore, it can be concluded that slope is insignificant (Hair et. al., 2015).
Section 4 –“Investigate the variable return in $ per thousand”
95% confidence interval
It is apparent that the sample size is 100. As per central limit theorem, the data distribution can be assumed to be normal because the sample size is higher than 30. However, z value would not be used to find the confidence interval because the standard deviation of the population is not given. Therefore, it is fair to use t stat in place of z value (Hillier, 2006).
The table for the mean and standard deviation of the returns in $ per thousand is highlighted below:
Sample size = 100
Confidence interval
Degree of freedom =
Value of t stat for 99 degree of freedom and 5% level of significance is 1.98.
- Lower limit of 95% confidence interval
- Upper limit of 95% confidence interval
95% confidence interval would be [35.96 42.04]
It can be said with 95% confidence that the returns in $ per thousand would lie in the interval [35.96 42.04].
Hypothesis testing would be taken into account to check the validity of the given claim that “the average annual returns on investment per $1000 is above $30.”
Null Hypothesis- µ ≤ 30 i.e. the value of average annual returns on the investment is equal to or lower than $30.
Alternative Hypothesis – µ > 30 i.e. the value of average annual returns on the investment is greater than $30.
As per central limit theorem, when the number of observations is higher than 30, then the data is said to be normally distributed. As the number of observations are 100 and therefore, the distribution would be said to be normal. However, the z stat would not be considered to check the hypothesis because the standard deviation of the population is not given. Therefore, it is fair to conclude that t stat would be used (Flick, 2015).
Investigate the variable return in $ per thousand
Value of degree of freedom would be = 100 – 1 = 99
The p value for 99 degree of freedom and 5.859 t stat value is 0.00001 (Hair et. al., 2015).
Let the level of significance is 5%.
It can be seen that the p value is not higher than the level of significance and therefore, sufficient evidence is available for the rejection of null hypothesis. Hence, the final conclusion can be made and it can be said that the value of average annual returns on the investment is greater than $30 (Hastie, Tibshirani and Friedman, 2011).
For the investors, the key advice is with regards to choice of investment in line with the underlying risk appetite. This is critical as if there is a deviation from the intended risk, then the investor would not feel comfortable and satisfied with the investment no matter what the underlying returns are. A case in point is when a risk averse investor is allocated a risky portfolio which may have some wide fluctuations in value sometimes on a daily basis. This will unsettle the investor and would make him/her nervous. Similarly for an investor who is low risk averse and has been allocated an asset that is not very risky might lead to dissatisfaction owing to lack of significant fluctuations in the stock price (Damodaran, 2010).
Also, for the new recruits it is noteworthy that while working with sample, extreme caution needs to be exhibited as it is quite possible that the sample may not faithfully represent the population and thus the conclusions drawn from such a sample about the population may not be correct. In order to reduce the underlying risk in this regard, it is advisable that instead of using random sampling, stratified random sampling would be more appropriate and lead to more representative sample. This would enhance the overall accuracy of the conclusions drawn based on the sample and enable to firm to do away with the usage of the population data (Hastie, Tibshirani and Friedman, 2011).
Conclusion
The above analysis clearly reflects that there does not seem to be a significant relationship between the returns derived on the invested funds and the underlying fee that the firm charges from clients which prima facie hints at the fee not being return driven,. However, this may be incorrect as the different investors have exposure to different risk asset and it would be futile to compare the returns in isolation of the underlying risk. There is availability of sufficient evidence to indicate that the population annual returns earned on every $ 1,000 investment would exceed $ 30 or 3% p.a. Also, the confidence interval of interval is 95% likely to lie in the range of $ 35.96 – $ 42.04. Besides, for investors, it is critical to note two things, one being the knowledge of risk return tradeoff involved in making asset choice and the second is investing in assets having same risk appetite as their own. Also, the new recruits have to be careful when using sample for drawing population inferences as it is desirable that the sample is representative of population.
References
Damodaran, A. (2008), Corporate Finance, 2nd ed., London: Wiley Publications
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
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