u w 1.5 < 0 These two results imply that the utility function is concave.

Transcription

1 A person with initial wealth of Rs.1000 has a 20% possibility of getting in a mischance. On the off chance that he gets in a mishap, he will lose Rs.800, abandoning him with Rs.200; on the off chance that he doesn't, he doesn't loses anything. He maximizes expected utility, and his VNM utility function is u(w) = w. Answer questions 1 to 8 based on the data provided. 1. What is the u (w), i.e., the second derivative of this person s utility function? A) The individual is risk-seeker B) The individual is risk-neutral C) The individual is risk-averse D) Cannot be determined from the given data (Ans.: C) Explanation: Notice that u(w) = w can be written as u(w) = w 0.5. Therefore, u (w) = 0.5 w 0.5 > 0 u (w) = w 1.5 < 0 These two results imply that the utility function is concave. 2. What is the expected amount of money he will lose? A) Rs. 800 B) Rs. 200 C) Rs. 160 D) Rs. 0 (Ans.: C) The expected amount of money he will lose is = (0.2)(Rs.800) + (0.8)(Rs.0) = Rs.160: 3. What is his expected wealth? A) Rs B) Rs. 200 C) Rs. 840 D) Rs. 600 (Ans.: C) His expected wealth is: (0.2)(Rs.200) + (0.8)(Rs.1000) = $ What is his expected utility? A) B) C) D) 20.14

2 (Ans.: A) Explanation: Expected Utility = 0.2 u(rs. 200) u(rs. 1000) = = What is his certainty equivalent wealth, i.e., the certain wealth level that gives him an indistinguishable expected utility from his indeterminate circumstance? A) Rs B) Rs C) Rs D) Rs (Ans.: D) Explanation: u(w) = w = w w = = What is the maximum amount he would pay for full insurance, i.e. what is the greatest premium he would pay an insurance agency to cover the majority of his misfortunes? A) Rs B) Rs C) Rs.0.18 D) Rs (Ans.: B) Explanation: The maximum amount he would pay for full insurance is his initial wealth minus his sure thing equivalent wealth, i.e.: Rs.1000 Rs = Rs The story here is basically this: He starts out with base wealth of Rs If he pays Rs to the insurance company in exchange for them covering his loses in case of an accident, his wealth (regardless of whether or not an accident occurs) will always be Rs.1000-Rs = Rs From this we know that he is indifferent between having certain wealth of Rs and facing the uncertain situation he started out with: both give him an expected utility of So, if he pays Rs for full insurance, he ends up with the same expected utility that he started out with. 7. What is his risk premium, i.e., the amount more than his expected loss is he willing to pay for full protection? A) Rs

3 B) Rs C) Rs.0 D) Rs (Ans.: B) Explanation: He s willing to pay a maximum of Rs for full insurance, and his expected loss is Rs.160. So his risk premium is Rs Rs.160 = Rs What can you conclude about the behaviour of the person if the insurance can be purchased for Rs.150? A) Will purchase the insurance. B) Will not purchase the insurance. C) Will change his utility function according to the price of the insurance. D) There is not enough information given in the question to determine an answer. (Ans.: A) Explanation: If he can get full insurance for one Rupee less (i.e., for Rs.207), buying the insurance will increase his expected utility, so he will want to buy the insurance. If he can only get insurance by paying one Rupee more (i.e., for Rs.209), buying the insurance will decrease his expected utility, so he will refuse to buy the insurance.

4 Answer Questions 9 and 10 based on the data provided. If you are given the following utility function U(W) = e aw + b W + c; (a > 0, b 0 and c 0), then: 9. What can you conclude about the Absolute Risk Aversion properties of the Utility Function? A) As the amount of wealth (W) increases the amount held in risky assets decreases. B) As the amount of wealth (W) increases the amount held in risky assets also increases C) As the amount of wealth (W) decreases the amount held in risky assets remains same D) None of the above (Ans.: B) 10. What can you conclude about the Relative Risk Aversion properties of the Utility Function? A) As the amount of wealth (W) increases the % held in risky assets also increases. B) As the amount of wealth (W) increases the % held in risky assets decreases. C) As the amount of wealth (W) increases the % held in risky assets remains same. D) None of the above (Ans.: A) Explanation: U(W) = e aw + b W + c; (a > 0, b 0 and c 0). We are required to find the properties of this utility function: U (W) = ae aw + b and U (W) = a 2 e aw. As U (W) > 0 and U (W) > 0, hence the utility function has the two fundamental property of (i) non-satiation and (ii) risk averseness. Now let us find absolute risk aversion and relative risk aversion properties of this particular utility function: i. A(W) = U (W) U (W) = a2 e aw ae aw +b. Therefore A (W) < 0, which implies decreasing absolute ii. risk aversion property, i.e., as the amount of wealth (W) increases the amount held in risky assets also increases R(W) = W U (W) = W a2 e aw. Therefore U (W) ae aw +b R (W) < 0, decreasing relative risk aversion property, i.e., as the amount of wealth (W) increases the % held in risky assets also increases

5 11. A new project has begun. The project charter has been written and the project manager has been assigned. The project manager is preparing the work breakdown structure for the project. The WBS is typically used for: A) Explaining the scope of the project relevant to the client B) The basis for organizing and defining the total scope of the project C) Showing the resource conflicts that exist in the project D) The logical relationship between tasks in the project (Ans.: B) Explanation: The work breakdown structure approach allows us to visually see the work that is needed in order to complete a project. The bottom line is by using a work breakdown structure it reduces the number of surprises and improves the ability to better estimate future projects. The work breakdown structure can be used to effectively decompose the project scope, to improve estimating, to better control the project execution and to more accurately verify project completion. In addition, using a work breakdown structure approach summarizes project information to improve the opportunity for use of historical information, which, can aid in both speed and accuracy of future projects. The work breakdown structure is a repeatable process that can be used as a template for future projects.

6 12. In a very large project having a budget of $5 million and a project team of over one hundred people, the project manager constructs a work breakdown structure. The project manager will do the WBS to the detail level of which of the following? A. Task B. Activity C. WBS element D. Work package (Ans.: D) Explanation: The following guidelines should be considered when creating a work breakdown structure: The top level represents the final deliverable or project Sub-deliverables contain work packages that are assigned to a organization s department or unit All elements of the work breakdown structure don t need to be defined to the same level The work package defines the work, duration, and costs for the tasks required to produce the sub-deliverable Work packages should not exceed 10 days of duration Work packages should be independent of other work packages in the work breakdown structure Work packages are unique and should not be duplicated across the work breakdown structure

7 13. The highest element in the hierarchical breakdown of the WBS is: A) A work package B) Sub deliverables C) A cost account D) The final deliverable of the project (Ans.: D) Explanation: Please refer the Explanation of Question No. 12

8 14. All of the following are usually included in a work package except: A) The time needed to complete the work B) A single person who is responsible for its completion C) All the costs for the work package D) All of these are included in a work package (Ans.: D) Explanation: Please refer the Explanation of Question No. 12

9 15. The final step in the creation of a Work Breakdown Structure is to: A) Code the WBS for tracking B) Assign the cost account to a manager C) Assign the work package to a manager D) Develop the responsibility matrix (Ans.: A) Explanation: Please refer the Explanation of Question No. 12

10 16. A project manager has been asked by the client to meet the promise date of the project. The project manager analyzes the schedule before promising a date to the customer. The project manager uses the program evaluation and review technique to evaluate the project schedule. She decides that based on the PERT calculations she can promise a delivery date of June 30. The expected value of the project completion date is May 30. If the project manager is willing to accept a 5% probability that the project will be delivered later than June 30, what is the standard deviation of the duration of the activities on the critical path? Assume a five-day workweek. A. Ten days B. Fifteen days C. One-half month D. One month (Ans.: C) Explanation: Rule for normal distribution, 1σ implies 68% 2σ implies 95% 3σ implies 99.7% In the question it is given that 30 June date represents 95% confidence, which is approximately 2 standard deviations (2σ) and therefore 1 SD or σ is half the difference between 30 May and 30 June. Let x = SD or σ since 2x = 1 month therefore x = 0.5 month So the answer is half month.

11 17. Which one of the following is captured in the Work Breakdown Structure (WBS)? A) The life cycle phases. B) The logical order of tasks. C) The scope of the project. D) Project costs. (Ans.: C) Explanation: Please read Explanation for Question no. 11.

12 18. You are the project manager for a high visibility project. The margin on this project is low, and it is extremely important that the cost estimates for the work on the project be accurate. While reviewing the cost estimates for this project you notice that one of the cost estimates for an element in the WBS is 10% higher than two previous projects for very similar work. What should you do? A) Accept the estimate because you trust all of the people on your project team, and they are responsible for estimates B) Reduce the estimate and add the additional budget to the management reserve C) Ask the person responsible for the estimate to explain the difference and bring supporting information to you D) Reduce the estimate and add the additional budget to the contingency reserve (Ans.: C) Explanation: The responsible team member must be asked to justify the estimate with regard to historical information he used.

13 19. Which of the following is true? A. The critical path is the path through the network that has the highest total duration B. The critical path is the path with the least amount of free float C. The critical path is the list of activities that have zero float D. The critical path is the list of activities that have critical risks associated with them (Ans.: C) Explanation: Critical path activities are the project tasks that must start and finish on time to ensure that the project ends on schedule. A delay in any critical path activity will delay completion of the project, unless the project plan can be adjusted so that successor tasks finish more quickly than planned.

14 20. A task was scheduled to use two persons, full time, and take two weeks to complete. Instead, the project manager was only able to assign one person to this task. At the end of two weeks, the person assigned to the task was 75% complete. What is the cost performance index? A B. 1.5 C D. 0.5 (Ans.: B) Explanation: 2 persons X 2 weeks =100 %work. 1 person working for 2 weeks can only complete 50% work...but actual complete is 75%. So, CPI = 75/50 = 1.5

15 21. The main difference between the two types diagramming methods (ADM, arrow diagramming method, and PDM, precedence diagramming method) of the critical path method (CPM) of scheduling is: A. Placement of the activity on the logic diagram line B. Arrow diagramming method (ADM) is a deterministic method, whereas the precedence diagramming method (PDM) is a probabilistic method C. Precedence diagramming method (PDM) is a deterministic method, whereas the arrow diagramming method (ADM) is a probabilistic method D. Precedence diagramming method (PDM) is a more accurate method (Ans.: A) Explanation: The precedence diagram method (PDM) is a tool for scheduling activities in a project plan. It is a method of constructing a project schedule network diagram that uses boxes, referred to as nodes, to represent activities and connects them with arrows that show the dependencies. It is also called the activity-on-node (AON) method. Arrow diagramming method (ADM) is a network diagramming technique in which activities are represented by arrows. ADM is also known as the activity-on-arrow (AOA) method.

16 22. A risk has four possible outcomes. Given the following information, what is the expected value of this risk? Probability Result of Risk , , , ,500 A. -$20,000 B. -$14,500 C. $7,000 D. -$7,500 (Ans.: D) Explanation: Expected Value = (0.4 X 10,000) + (0.3 X 7,500) + (0.2 X 5,000) + (0.1 X 2.500) = 7,500

17 23. The method used to collect information to use through all phases of the project life cycle is called: A) Responsibility matrix B) Organization breakdown structure C) Work breakdown structure D) Priority matrix (Ans.: C) Explanation: Please read Explanation for Question no. 11.

18 24. A project manager is looking at the risk associated with the project schedule. Realizing that if the risks occur the project will be delivered to the stakeholders late, the project manager decides to consider the risk and promise delivery later than the most likely project completion date. He then takes the time between the promise date and the most likely completion date and distributes it among the activities of the project schedule. This creates float in the schedule. This process is called: A. Schedule delay B. Critical chain scheduling C. Buffering D. Contingency scheduling (Ans.: C) Explanation: The Critical Chain/Buffer Management (CC/BM) approach aims at the construction of latest start schedules where the project activities use aggressive time estimates and puts a clear focus on the determination of a realistic project deadline. In order to keep the probability high that the project deadline will be met, the CC/BM approach protects the project duration and the critical chain of the project using various buffers.

19 25. Refer to the table. What is the critical path? A. Start A B C I Finish B. Start A B H I Finish C. Start D E H I Finish D. Start F G I Finish (Ans.: D) Explanation: Start-A-B-C-I-Finish = 11 units Start-A-B-H-I-Finish = 12 units Start-D-E-H-I-Finish = 12 units Start-F-G-I-Finish = 16 units The critical path is the longest one, in this case, Start-F-G-I-Finish