ECON1030 – BUSINESS STATISTICS 1 GROUP ASSIGNMENT 1

ECON1030 – BUSINESS STATISTICS 1

GROUP ASSIGNMENT 1

Due: Week 6

Instructions:

This is a group assignment with a minimum group size of two and a maximum group size of four. The total marks for the assignment is 10. All group members will receive the same marks for the assignment.   All group members must be enrolled in the same tutorial.  The assignment must be provided in the form of a (brief) business report. Please submit a softcopy of your assignment via Turnitin and (in the following tute) submit a hardcopy to your tutor.

Group Members:

Please indicate your tutor and tutorial time:

Problem Description:

It is a well known principle of finance that when investing, there is a trade off between risk and return, i.e. in order to earn a higher return, one must assume greater risk[1]. Stock returns are calculated as the percentage change in price over a given period. Risk is measured by the variability (or volatility) of these returns.

You are part of an analytical team working for a large investment bank. Management is considering two investments: A or B. Before doing so, they have asked your team to prepare a report on the risk and return profiles of these two investments. You will use descriptive statistics and your knowledge of continuous distributions to complete this task.

The returns data (measured annually) for the two investments are given in the Excel file: investment4a.xls

Required:

1. Estimate descriptive statistics for each investment via Excel. Compare the two investments. Be sure to comment on the central tendency, variability and shape of these two investments (Note: use the most appropriate measure when comparing the variability of two distributions). Based on your findings, which investment would you choose and why?

Ans: Below table represents descriptive statistics for investment A and investment B –

The mean (SD) for investment B (11.61 (25.52)) is greater than A (9.96 (19.92)). Median value is also greater for investment B (9.79) than investment A (8.99). Similarly, variance is greater for investment B than A, implying that there is more variability among the values in Investment B compared to Investment A. Skewness and kurtosis are the parameters which give estimate regarding the shape of the distribution. For Investment B the data is less skewed (value very close to zero) and more flat curve as compared to Investment A. Both the data are skewed to the right.

From the above data, I would choose investment B as returns are more. The range for investment B is greater than investment A inspite of the fact that minimum of investment B is less than A and difference between maximum of A is not very less than B.

1. For your chosen investment, assume that the returns are normally distributed with a mean and standard deviation (as estimated in (a) rounded to the nearest integer). Answer the following questions:

1.                                 i.            Find the probability that returns will exceed 55%

Ans: z=x-µ/σ = 55-11.61/25.52 = 1.70

p(x>55%) = 1-p(x<=55%) = 1-0.9554 = 0.0446

1.                               ii.            Find the probability that returns will be between 22% and 36%

Ans: z=x-µ/σ = 22-11.61/25.52 = 0.96

p(x<22%) = 0.8315

And

z=x-µ/σ = 36-11.61/25.52 = 0.41

p(x<36%) = 0.6591

Thus, p(22%<x<36%) = 0.8315-0.6591 = 0.1724

1.                             iii.            Find the probability of making a loss

Ans: For loss we will assume x = 0,

z=x-µ/σ = 0-11.61/22.52 = -0.51

p = 0.3050, p(0) = 0.5

For loss p=0.5-0.3050 = 0.195

1.                             iv.            If you are given a choice between the top 3% of returns and a return of 49%, which option would you choose?

Ans: Top 3% of returns.

1.                               v.            Between what two values of returns (symmetrically distributed around the mean) will 48.6% of all possible returns contained?

Ans: The values are µ ± z_p*σ

Where p = 0.486, so z_0.49 = 0.6879

Thus, values are 11.61 ± 0.6879*25.52 ; -5.945 and 29.165.

Therefore, two values of returns that contain 48.6% of all possible returns are -5.945 and 29.165.

1. What are the limitations of your analysis?

Ans: For determination of normality only descriptive analysis was used. Histograms with normal curve provide better presentation. Risk to benefit ratio is equally important when taking decisions regarding investments. This was not performed.

Presentation:

Document all your findings in a professional business report (maximum: 4 pages). You must write concisely and professionally. For the purposes of this exercise, you may assume that management are technically competent, i.e. you may use technical (statistical) terminology. You may provide a brief execute summary if you wish but do not use technical jargon in this summary. Your executive summary is not included in the page count (note: you can access “Business Report Writing” through “MyRMIT”.  It is under “studying and learning”, “Study Smart”).

Allocation of marks: