Calculation of Expected Profit and Expected Opportunity Loss for Each Portfolio - Statistics Project Example

Statistics & Probability Student’s Name Institution Abstract This paper provides answers to the set of 12 questions ranging from statistics, probability and financial calculations. Most of the calculations are carried out in the excel sheets attached and the answers summarised within this paper. Keywords: chart, performance, satisfaction Statistics & Probability This paper provides answers to the set of 12 questions ranging from statistics, probability and financial calculations. 1. Value of Exports for Bossley Enviro Pty Ltd over last two quarters The data for Bossley Enviro Pty Ltd is provided in the table.1 and the single line graph for this data is in fig.1below respectively.   2009 2010 2011 Quarter Mar Jun Sept Dec Mar Jun Sept Dec Mar Jun Sept Dec Exports ($m) 10.3 10.2 10.2 10.2 10.6 9.4 9.8 10.0 10.4 10.6 10.6 10.9 Table.1 data for Bossley Enviro Pty a. Single Chart Graph Fig.1 Bossley Enviro Pty Ltd value of exports chart From fig.1 above, the value of exports for Bossley Enviro Pty Ltd for the last 12 quarters seems to be increasing but in a rather non-linear manner. In March 2009, the export value was at $10.3M and maintained this level throughout the first quarter. This level shot to 10.6 at the onset of the second quarter which began in March 2010. This level then dropped sharply in the middle of the second quarter to 9.4 as experienced in June 2010. From this time on, this level has been increasing in linearly manner to $10.9 experienced in December 2011. There are high chances that this rate will continue increasing if conditions remain the same. b. Example of Pictorial Presentation Pictorial representations like graphs, bar charts, and so forth; as in the fig.2 below, are often used to summarise data and present it in a more understandable format. Pictorial representations are additionally used to present data visually and bring information to life (Kelley, 2000). Fig.2; extracted from the daily mail newspaper, shows the frequency of birthdays falling in some given months of the year. This figure suggests that majority of the birthdays were falling in the months of July to September, with September recording the highest number of birthdays. The months of January and April had the least numbers of birthdays. Fig.2 How common is your birthday chart (Fleming, 2012). 2. Performance of Two Property Trusts based on Hotel Ownership and Operation The table.2 below provides total return data concerning the performance of two trusts A and B based on their ownership and operation over a period of ten years. Table.3 avails the calculated amounts for these two Trusts’ mean, median, range, standard deviation, and the coefficient of variation.   Total Return %     Period     1 2 3 4 5 6 7 8 9 10 Totals Trust A 9.9 10.6 11.7 6.8 13.9 16.4 23.0 25.5 22.3 16.3 156.4 Trust B 22.0 5.4 3.7 14.6 19.4 27.3 16.2 29.4 24.5 24.0 186.5 Table.2 Data for performance of the two property trusts Table.3 calculations From the calculations in table.3, Trust B seems to performing better than Trust A. Its total returns amounts to 186.5 compared to Trust A’s 156.4, it has a median of 23.4 compared to Trust A’s 15.2. it also has a wider range of 25.7 compared to Trust B’s 18.7, and a standard deviation of 9.27 compared to Trust A’s 7.06. These higher figures indicate that Trust B’s performance is better than Trust A’s and that a significance difference is evident in their performances. 3. Two-Bedroom Unit rental Rates in Sydney Table.4 below provides data relating to frequency distribution of 200 2-bedroom unit rentals in the Sydney Metropolitan area over a span of eight weeks. Weekly Rental ($) Frequency 200-249.99 32 250-299.99 37 300-349.99 44 350-399.99 38 400-449.99 18 450-499.99 21 500-549.99 5 550-599.99 5   200 Table.4 frequency distribution table of 200 2-bedroom unit rentals in the Sydney Metropolitan area a. Histogram of Data and Cumulative Frequency Histogram Weekly Rental ($)  Mid-Points Frequency Cum. Frequency 200-249.99 225 32 32 250-299.99 275 37 69 300-349.99 325 44 113 350-399.99 375 38 151 400-449.99 425 18 169 450-499.99 475 21 190 500-549.99 525 5 195 550-599.99 575 5 200 Table.5 Cumulative frequency distribution table of 200 2-bedroom unit rentals in the Sydney Metropolitan area Fig.3 Histogram for the frequency distribution table of 200 2-bedroom unit rentals in the Sydney Metropolitan area Fig.4 Cumulative Frequency Histogram for the frequency distribution table of 200 2-bedroom unit rentals in the Sydney Metropolitan area b. Calculations Using $ Mid-points Mean 25 Modal class 300-349.99 Median class 250-299.99 Lower boundary of median interval 250 Value form formula 49.275 Estimation of the median 299.275 Standard Deviation 211.201 Coefficient of variation 8.448 Table.6 Calculation of mean, modal class, median class, median estimate, standard deviation, and the coefficient of variation c. Comment on Skewness or Symmetry From the fig.3 above, it can be argued that the data of 200 2-bedroom unit rentals in the Sydney Metropolitan area is left skewed. This is because a greater part of the frequency falls on the left side of the histogram. 4. Part A: Level of Job Satisfaction Among Staff of a 5-Star Hotel Table.7 below provides data about the level of satisfaction among the employees of a 5-star hotel. Levels of Job satisfaction   Satisfied Unsatisfied Totals Female 96 34 130 Male 44 26 70 Totals 140 60 200 Table.7 Data on level of job satisfaction conducted by the 5-star hotel among its staff a. Overall Level of Job Satisfaction The overall level of job satisfaction P(S) is 0.7. b. Probability of a Male Employee Being Satisfied The probability that a male employee is satisfied in his job P(S|M) is 0.22. c. Probability of a Female Employee Being Satisfied The probability that a female employee selected at random is satisfied in her job P(S|F) is 0.48. d. Dependence or Independence of Job Satisfaction and Gender Job satisfaction is an independent variable, while gender is a dependent variable, and varies with the level of satisfaction. Job satisfaction is independent since it is a feature or an aspect that is intangible. Gender on the other hand is dependent since it a tangible feature. Part B: Investment Portfolio Table.8 and table.9 provide data in relation to the estimated profits for three investment alternatives under three different economic conditions. Portfolio Selection   A B C Economy declines 13000 13100 13000 No change 13700 13900 14200 Economy expands 13500 13500 13000 Table.8 Estimated profit for investment portfolio   Economy declines No change Economy expands Probability 0.15 0.5 0.35 Table.9 Assigned Probabilities for the investment portfolios a. The optimum portfolio that this investor should settle for include the following: Investing 13,100 under investment option B when the economy is declining using the maximin investment decision, Investing 13,500 under investment options B or C when the economy is expanding using the maximax investment decision, Investing 13,000 under investment option C when the economy is declining using the minimax investment decision. b. Expected profit and expected opportunity loss for each portfolio Expected Profit   A B C Economy declines 1,950.0 1,965.0 1,950.0 No change 6,850.0 6,950.0 7,100.0 Economy expands 4,725.0 4,725.0 4,550.0 Opportunity Loss   A B C Economy declines 11,050.0 11,135.0 11,050.0 No change 6,850.0 6,950.0 7,100.0 Economy expands 8,775.0 8,775.0 8,450.0 Table.10 Calculation of expected profit and expected opportunity loss for each portfolio From the tables.9 and 10, the investor should select project C under no economic change, economic situation to maximize the expected profits. c. Expected value of perfect information (EVPI) Expected Value of Perfect Information (EVPI)   A B C Economy declines 11,050.0 11,135.0 11,050.0 No change 6,850.0 6,950.0 7,100.0 Economy expands 8,775.0 8,775.0 8,450.0 Table.11 Calculation of expected value of perfect information (EVPI) 5. Currency Exchange Office Mean 20,000 Std. Dev 6,000 Probabilities   a. Pr(X>27,200) 0.8849 b. Pr(X Read More