2019 exam

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School

University of New South Wales *

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Course

9710

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Business

Date

Jun 24, 2024

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Uploaded by MagistrateHorsePerson1146

Page 1 UNSW Sydney CVEN9710 – Management of Risk Term 3 2019 Examinations Instructions: 1. TIME ALLOWED – 2 hours 2. READING TIME – 10 minutes 3. THIS EXAMINATION PAPER HAS 12 PAGES (NOW 8 PAGES, SINCE QUESTIONS 1-20 WERE REMOVED) 4. TOTAL NUMBER OF QUESTIONS – 27 5. TOTAL MARKS AVAILABLE – 100 6. MARKS AVAILABLE FOR EACH QUESTION ARE SHOWN IN THE EXAMINATION PAPER 8. THIS PAPER MAY NOT BE RETAINED BY CANDIDATE 9. CANDIDATES MAY BRING TO THE EXAMINATION: UNSW approved calculators, drawing instruments or rulers 10. CANDIDATES WILL BE PROVIDED: A generalised answer sheet and formula sheet 11. ALL ANSWERS MUST BE WRITTEN IN INK. EXCEPT WHERE THEY ARE EXPRESSLY REQUIRED, PENCILS MAY BE USED ONLY FOR DRAWING, SKETCHING OR GRAPHICAL WORK 11. Answer questions 1-20 on the additional answer sheet provided. Answer questions 21-27 in the spaces provided on this paper. If you need additional space use the back page of the question paper and indicate clearly on the original question page or the back page will not be marked. Question 1: (1 Mark) Questions 1 – 25 were multiple choice questions, with one correct answer each. Each of these questions was worth 1 mark and questions were selected from all parts of the course. A generalised answer sheet (fill in the circles) was provided for answering these questions. These questions are not provided.

Page 2 Question 21: (2 Marks) The diagram below shows the efficient frontier for all investments in a particular security universe when risk free investments are unavailable. The government then issues a new security that has a risk free rate of 2%. Determine the return on the market portfolio after the introduction of this new risk free security. Show your working below. Question 22: (2 Marks) A certain country has a risk free rate of 2% and a market portfolio return of 6%. Penny decides to invest 30% of her money at the risk free rate and the other 70% in the market portfolio. Of the risk that Penny has on her investments what is the percentage that is systematic risk and what is the percentage that is unsystematic risk? Working space: Percentage that is Systematic Risk: Percentage that is Unsystematic Risk: Question 23: (6 Marks) What are the three major types of risk involved with securities? Explain each type. First type: _________________________________________________________________________ Second type: _______________________________________________________________________ Third type: ________________________________________________________________________ 6% 4% 2% 0% 8% Return on market portfolio: Efficient frontier

Page 3 Question 24: (10 Marks) A farmer decides to use part of his farm for growing grapes and olives. Since these involve long lived plants the farmer wants to carefully choose how much of each type of plant to grow. Investigation reveals that the average returns for the two types of crop over many years are the same per hectare for both crops on his soil type, but that two markets have different patterns of fluctuation. The return for grapes is expected to have a standard deviation of 0.8, while the return for olives is expected to have a standard deviation of 0.4. Also, the correlation between the returns for the two types of crop at different times is 0.6. (a) Determine the relative proportions of land that should be devoted to each type of crop to minimise the fluctuation in the farmer’s return from year to year. Percentage devoted to grapes: Percentage devoted to olives: (b) Determine the standard deviation for the return of the total crop if these proportions are adopted Standard deviation of total crop return:

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Page 4 Confidence interval for variance: < 2  < Circle your conclusion: Mean tile length is 423mm Mean tile length is NOT 423mm Statistic calculated from above data: Boundary of critical region: Question 25: (15 Marks) A roof tile manufacturing company makes tiles that it claims have an average length of 423mm. There have been complaints that the tile length is incorrect and too variable. The company has collected and measured a sample of tiles and the measurements are provided in the table below. 424 420 420 423 426 414 426 414 430 416 420 419 Solution: a) What is the 95% confidence interval for the variance of the tile length? b) Test the hypothesis that the mean tile length is not 423mm using a level of significance of 5%.

Page 5 Circle your conclusion: Data fits Poisson Data does not fit Poisson Statistic calculated from above data: Boundary of critical region: Question 26: (15 Marks) A tiling company has been collecting data on the number of roof tiles broken by the installation team for each of 200 houses. The data is provided in the table below. The company is wondering if this data fits a Poisson distribution. Carry out a ‘goodness of fit test’ to determine whether a Poisson distribution is applicable, using a significance level of 5%. x f 0 15 1 56 2 39 3 35 4 27 5 17 6 9 7 2

Page 6 Question 27: (30 Marks) Good Hill Constructions has been approached to be part of a joint venture tunnelling project because the previous tunnelling partner went out of business. The joint venture has already been awarded the job, but they are in negotiations to change the alignment of the tunnel to encourage increased traffic flow. If Good Hill does sign up with the joint venture then there are two construction techniques that they can use. One method is a tunnel boring machine. This is expected to result in a profit of $15 million if the long alignment is built, or $10 million if the short alignment is built. The other method is to use road headers. However, the profit from using road headers is greatly affected by the ground conditions. For the long alignment good ground conditions would result in a profit of $30 million, while poor ground conditions would result in a loss of $10 million. For the short alignment, good ground conditions would result in a profit of $20 million, while poor ground conditions would result in a loss of $5 million. It is believed that the probability of the long alignment being selected is 0.6, which has a probability of 0.7 for good ground conditions. The probability of the short alignment having good ground conditions is 0.8. Good Hill Constructions needs to decide now whether or not to join the joint venture, without knowing which alignment will be built. However, it can put off deciding which type of equipment to use until it does know which alignment. It will not know what the ground conditions are like until it starts construction and the equipment cannot be changed. (a) Draw the decision tree for this situation and clearly label it with all probabilities and EMVs. Write the best strategy using EMV in the box at the bottom of the page. Best strategy using EMV:

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Page 7 The company has developed a utility curve given by U = 1 – e –x/10,000,000 where x is the profit or loss in dollars (b) Redraw your decision tree on this page and clearly label it with all probabilities and utility values. Write the best strategy using utility in the box at the bottom of the page. Best strategy using utility:

Page 8 Extra Workspace Question number: If you needed to use this extra workspace then indicate clearly on the original question page or it will not be marked End of Exam Paper

2019 exam

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