Example 21.4 Calculate expected opportunity loss from the following payoff table: Payoff Table Event Action A, (Rs) A₂ (Rs) A3 (Rs) E₁ 50 -10 -80 E₂ 400 500 600 E3 600 900 800 Event probabilities 0.2 0.5 0.3
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- Question12: In the given payments matrix, the earnings that a business can obtain with different distribution strategies (S1, S2, S3) are given. The probabilities of the natural states are respectively; P(Q1)=0.2, P(Q2)=0.4, P(Q3)=0.4. 1-) What is the expected payment when the information is not received? 2-) What is the expected payment when the information is received? 3-) What is the expected value of additional information?(a) The monthly returns on two securities A and B are both known to be normally distributed, with the following parameters: Security Expected monthly Return, E(Ri) Standard Deviations of monthly Return, SD(Ri)A 3% 4%B 2% 3% Correlation between monthly returns: corr(RA, RB) = rAB = 0.3 An investor intends to create an equally-weighted portfolio by investing equal amounts in securities A and B at the start of each month. (i) What is the probability that the monthly return on security A is negative? (ii) What are the expected monthly return and the standard deviation of the monthly return on the equally-weighted portfolio? (iii) What is the probability that the monthly return on the equally-weighted portfolio is negative? (b) Six prize…Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 9 8 Medium complex, d2 13 3 Large complex, d3 19 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $16 million and as long as the payoff for the weak demand was greater…
- b) You decide to buy 10,000 shares of each company. If the covariance between ABC and XYZ is 0, what is the expected return and standard deviation of your portfolio over the next year? 1Question 4 (Part B a-c)A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. The Petrol station is considering adding a second pump with an attendant to service customers. The station would pay that person the same $10 per hour. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service (Lq)?c. What is the average number of customers in the system (L)? SHOW ALL WORKINGSThe XY Manufacturing Company must decide whether to manufacture acomponent part at its plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in ten thousand of pesos): State of Nature State of Nature State of Nature Decision Alternative Low DemandS_(1) Medium DemandS_(2) High DemandS_(3) Manufacture, d_(1) -100 200 500 Purchase, d_(2) 50 225 350 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether XY Manufacturing Company should attempt to obtain a better estimate of demand. c. A test market study of the potential demand for the product is expected to reporteither a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:What is the probability that the market research report will be favorable?d. What…
- The XY Manufacturing Company must decide whether to manufacture acomponent part at its plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in ten thousand of pesos): State of Nature State of Nature State of Nature Decision Alternative Low DemandS_(1) Medium DemandS_(2) High DemandS_(3) Manufacture, d_(1) -100 200 500 Purchase, d_(2) 50 225 350 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. c. A test market study of the potential demand for the product is expected to reporteither a favorable (F) or unfavorable (U) condition. The relevant conditional probabilities are as follows:What is the probability that the market research report will be favorable?The XY Manufacturing Company must decide whether to manufacture acomponent part at its plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in ten thousand of pesos): State of Nature State of Nature State of Nature Decision Alternative Low DemandS_(1) Medium DemandS_(2) High DemandS_(3) Manufacture, d_(1) -100 200 500 Purchase, d_(2) 50 225 350 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. a. Use a decision tree to recommend a decision. b. Use EVPI to determine whether XY Manufacturing Company should attempt to obtain a better estimate of demand.The following payoff table provides profits based on various posible decision alternativesand various levels of demand at Kmart Print Shop. Alternatives Low High Alternative 1 10,000 30,000 Alternative 2 5,000 40,000 Alternative 3 -2,000 50,000 The probability of low demand is 0.4, whereas the probability of high demand is 0.6.Calculate the expected value of perfect information for this situation.
- Question 5: A department store prints scratch-and-save discount coupons to distribute to its customers. The numbers for each present discount are shown in the table. Present Discount Number of Each type of discount Available 60% 50 50% 25000 30% 50000 10% 500,000 Determine the expected percent discount. Question 6: An examination consists of 50 multiple-choice items, each with 4 possible answers. what is the probability of guessing 25 or more correct answers? Question 7: A. bank found that 25% of its loans to new small business become delinquent. Ten small business are selected randomly from the bank's files. a) what is probability that three of them are delinquent? b) what is the probability that at least three of them are delinquent? c) what is the expected delinquency? B. Geometric Distribution Q8: Explain why rolling a die until 3 shows can be modelled by a geometric distributionQuestion 4b (a-c)A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. If the Petrol station adds a second pump with an attendant to service customers and the station pays that person the same $10 per hour: Using appropriate formula for the multiple channel model, answer the following questions: a. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service (Lq)?c. What is the average number of customers in the…Suppose a world has two risky assets: HotPot and IceCream. The following table shows the holding period returns in each scenario. Suppose the T-bill rate is 5%. Scenario Probability Return (HotPot) Return (IceCream) Rainy 0.02 10% -5% Snowy 0.03 15% -15% Windy 0.9 10% 8% Sunny 0.05 -10% 25% Which answer is the closest value to the fifth-percentile value at risk (VaR) of holding IceCream? A. -15% B. -5% C. 25% D. -10%