Investment Analysis And Performance Evaluation: A Case Study

Literature Review

A particular company with international reach named XYZ Investment Advisors tends to make investments on behalf of their clients who entrust the company with their investments on the basis of the expertise of the company to professionally manage the funds to achieve superior returns while keeping risk under control. It is of immense significance that performance analysis of the client investments needs to be done in regards to various other information relating to the fees charges, nature of investments and client profiles.  A data set of 100 customers seems to have been selected using random sampling for the purpose of analyse and analysing association between certain variables, Additionally, using inferential statistics technique hypothesis testing has been used for drawing conclusions about the likely population. Based on the above mentioned statistical analysis, the new recruits in the company would be given advice along with precautions while using samples to daw conclusion about population.

The investments in which investors tend to take positions have two main aspects i.e. associated risk and return. While risk refers to the underlying volatility in the returns, the returns refers to the underlying capital gain on the asset. There is a close relationship between these two aspects as these typically go hand in hand. The endeavour of the investor is to avoid risk and thus in order to lure the investor into buying a risky asset, it is imperative that associated returns should also be potentially higher so that there is an incentive for the investors to assume the incremental risk. Further, while making prudent investment choice also, it is essential that the investors must assume a holistic position towards analysis. This analysis would not be focused on either risk or return in isolation but would seek to combine both the parameters (Brow, 2011).

This is required so as to work out an optimum combination of risk and return of assets which tends to maximise the returns per unit risk. Additionally, it is imperative that investors while choosing the assets in which there funds should be invested should be mindful of their risk appetite and must ensure that asset allocation is done driven by this concern. This ensures that the risk undertaken in the financial market investment tends to be in line with the preferences of the customers. Further, since the risk appetite and preferences of the customers typically are different, hence the company would offer different investment choices in accordance with the customised preferences of the customers so as to be representative of them(Diggle and Brooks, 2006).

A simple “Bivariate Analysis” of the investor data and Hypothesis test

Selected – Option 3

Two numeric variables:

• Annual Returns ($1,000 investment)
• Fess Paid

In this section in order to perform the bivariate analysis returns ($1,000) is taken as independent variable and fees paid is selected as dependent variable.

Scatter plot: To show the relationship between the variables is highlighted below:

 

It is apparent from the above highlighted scatter plot that the variables (returns in per thousand dollar) and fees paid ($) do not show any pattern or direct relationship. Hence, it can be said that they are weakly associated with each other (Flick, 2015).

Section 3

Mean and standard deviation for the variables has been computed in excel and highlighted below in the tabular form.

Particulars	Mean	Standard Deviation
Returns ($1,000)	38.35	14.18
Fees Charged ($)	183.39	154.20

In order to check whether the slope is significant or not, hypothesis testing needs to be performed.

Null Hypothesis: β = 0

Alternative Hypothesis: β ≠ 0

The output from the regression for the variables is highlighted below:

 

The value of t statistic for the respective slope is -0.53. Further, the p value corresponding to the t statistics is 0.60.

Assuming 5% level of significance, it can be concluded that the p value for the given slope is higher than the level of significance (0.60 >0.05). Therefore, insufficient evidence presents to reject the null hypothesis. Therefore, it can be concluded that the slope would be zero and hence, there is no significance of the slope (Hillier, 2006).

Investigate the variable return per $1000

• 95% confidence interval for annual return on investment per $1000

According to the Central Limit Theorem, the data which is having a sample size of higher than 30 would indicate normal distribution. Additionally, this assumption would become stronger when the sample size is significantly higher.

It is apparent from the given data set that the number of observations (Sample size) is 100.Therefore, it can be decided that the distribution of the data set is normal. From the data it can be seen that standard deviation of population is unknown and hence, t value approach would be used to determine the 95% confidence interval (Needham, 2012)

Particulars	Mean	Standard Deviation
Returns ($1,000)	38.35	14.18

Sample size

Degree of freedom  

Significance level

For degree of freedom (99) and significance level (5%) t value is 1.984.

Now, from the above input data the upper and lower limit of 95% confidence interval can be determined (Hastie, et. al., 2011).

Lower limit of 95% confidence interval

Upper limit of 95% confidence interval

95% confidence interval =

Particulars	Mean	Standard Deviation
Returns ($1,000)	38.35	14.18

 Sample size

It can be concluded from the confidence interval that we can claim or conclude with 95% confidence that average annual returns on $1000 would fall between the range $35.53 and $41.16.

Hypothesis Testing

Claim -The average annual return on investment per $1000 is above $30

Null Hypothesis: µ ≤ 30 the average annual return on investment per $1000 is lower than $30

Alternative Hypothesis: µ > 30 the average annual return on investment per $1000 is higher than $30.

The p value for inputs (t statistics = 5.888) and (degree of freedom = 99) comes out to be zero.

Let the level of significance is 5%.

It can be concluded that p value is lower than the level of significance and therefore, sufficient evidence is available to reject the null hypothesis. As a result, alternative hypothesis would be accepted. Hence, it can be said that the average annual return on investment per $1000 is higher than $30.

Based on the above findings, it is essential that investors tend to understand that the fees charged are not linked with the returns typically earned. This makes sense as the various customers have invested in different risk portfolios and hence it is not possible to compare returns of the customers. It is quite possible that a portion of the fees might be linked with the performance of the fund but the same would be practised only after adjusting for the difference in the risk associated with different investments (Hair, et. al., 2015).

Further, for young recruits, it is imperative to pay attention on the likely distribution and the test statistic to be used in which the population standard deviation knowledge is critical for determining the appropriate method to be used. Further, the inferential statistical technique of hypothesis testing would be true to the extent that the sample is representative of the population. Thus, appropriate sampling technique ought to be used and additionally the appropriate sample size must be used based on the underlying heterogeneity in the population data.

Conclusion

In accordance with the discussion carried out above, it becomes evident that the returns earned on every $ 1,000 of investment does not seem to be related to the fees charged by the company but the same can be on account of the risk difference which leads to the conclusion that such a provision does not exist, when such a provision might exist in real. In accordance with the 95% confidence interval derives, it is 95% likely that the annual returns (average) tend to lie between $ 35.53 and $ 41.16 for every $ 1,000 that is invested. Besides, the test of hypothesis derived inference about population indicates that the annual returns (average) is is excess of $ 30 for every $ 1,000 that is invested. This implies a return in excess of 3% pa. But caution needs to be exhibited with regards to trusting the conclusions being drawn about the population based on the sample data as the underlying sample may be biased and may not be represent the population in a faithful manner. Besides, the investors on their part should be aware of their risk appetite while choosing prudent investment choices and must also be driven by the risk return trade-off.

References

Brown, R. (2011) Risk and Return from Equity Investment in the Australia, Australian Journal of Management, 42(7), pp. 120-122.

Diggle, J. and Brooks, R. (2006) “Risk –return trade -offs from investing in the Australian cash management industry”, Australian Journal of Management, 42(7), pp. 120-122.

Flick, U. (2015) Introducing research methodology: A beginner’s guide to doing a research project, 4^th edn. New York: Sage Publications.  

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and Page, M. J. (2015) Essentials of business research methods, 2^nd edn. New York: Routledge.   

Hastie, T., Tibshirani, R. and Friedman, J. (2011) The Elements of Statistical Learning, 4^th edn. New York: Springer Publications.

Hillier, F. (2006) Introduction to Operations Research, 6^th edn., New York: McGraw Hill Publications.

Needham, D. (2012) A trade-off between risk and return, Morningstar Australia, [Online] Available at

https://www.morningstar.com.au/funds/article/risk-return-tradeoff/4549 [Accessed May 25, 2017]