Markov chain with the following transition probabilities: To 6% 0.4 Form 5% 7% 5% 0.6 6% 0.2 0.6 0.2 7% 0.1 0.4 0.5 Insert rates were 6% both last year and this year. The probability that they will be 5% years from now is: (a) 0.203 (b) 0.318 (c) 0.282 (d) 0.6
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- Question 3 (Minimum-variance Hedging) A farmer has a crop of grapefruit juice that will be ready for harvest and sale as 150000 pounds of grapefruit juice in 3 months. He is worried about possible price changes, so he is considering hedging - a financial engineering technique that minimizes future uncertainties in the cash flow. Typically, hedging is carried out using futures contract. However, unfortunately, there is no futures contract for grapefruit juice, but there is a futures contract for orange juice. Still, the farmer might consider using the futures contract for orange juice as a replacement for futures contract for grapefruit juice, in the hope that these two contracts are highly correlated due to the similarity of the underlying products. Currently, the spot prices are $1.20 per pound for orange juice and $1.50 per pound for grapefruit juice. The standard deviation of the prices of orange juice and grapefruit juice is about 20% per year, and the correlation coefficient…The Vintage Restaurant, on Captive Island near Fort Meyers, Florida, is owned and operated by Karen Payne. The restaurant just completed its second year of operation. Below are the sales for those two years (in ten thousands of dollars). Month First Year Second Year January 57 61 February 51 75 March 58 54 April 57 56 May 68 62 June 72 71 July 60 59 August 51 75 September 68 68 October 51 50 November 71 64 December 75 58 a) Construct a time-series plot in excel. (Label axes and graph) b) Develop a six month moving average. Compute MSE and forecast the amount of sales for the next month. c) Use α = 0.2 to compute the exponential smoothing values. Compute MSE and forecast for the next month. d) Compare the result for the six month average and exponential smoothing. Which appears to provide a better…When a forecaster uses the ______________ method, she or he assumes that the time series components are changing slowly over time.
- Which of the following are reasons why a process would be considered stochastic? 1. we lack of data on the variable of interest/generating process 2. we lack quantitative understanding of the generating process 3. the generating process itself is random 4. the process can be modelled with certainty 5. the generating process changes over time(b) A milk man buys milk at K10 per litre and sells it at K12 if sold on the same day; if not, it can be sold at K9 per litre the next day. Demand of milk lies between 45 litres and 60 litres per day and its probabilities are uniformly distributed over this demand. If each day’s demand is independent of the previous day’s demand, how many litres should be ordered every day?Consider the bathtub model of unemployment, with a separation rate s=0.1 and a job finding rate f=0.3. These probabilities have been constant for many periods, so the unemployment rate in period t is at its steady-state level. in period t, the separation rate rises to 0.2. what is the unemployment level in period t+1? (a) 0.125 (b) 0.25 (c) 0.375 (d) 0.4 Motivate and Discuss your answer.
- (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…Mike, a lumber wholesaler, is considering the purchase of a (railroad) car- load of varied dimensional lumber. He calculates that the probabilities of reselling the load for $10,000, $9000, and for $8000 are 0.22, 0.33, and 0.45 respectively. In order to ensure an expected profit of $3000, how much can Mike pay for the loadIn the B&K model of Example 18.5-1, suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Suppose further that will add a fourth counter. Counters 1,2, and 3 will open based on increments of two customers and counter 4 will open when there are 7 or more in the store. (a) The steady-state probabilities, for all . (b) The probability that a fourth counter will be needed. (c) The average number of idle counters.
- Please explain the math behind how this went from an expectation value of the commuter of the hamiltonian and the momentum, to just the commuter. (the problem defines Ptot = P1+P2)George Kyparisis owns a company that manufactures sailboats. Actual demand for George's sailboats during each of the past four seasons was as follows: Season 1 2 3 4Winter 1,400 1,240 1,080 920Spring 1,520 1,420 1,640 1,540Summer 1,000 2,140 2,040 1,960Fall 600 750 650 520 George has forecasted that annual demand for his sailboats in year 5 will equal 6,500 sailboats. Based on the given data and using the multiplicative seasonal model, the demand level for George's sailboats in the spring of year 5 will be nothing sailboats (enter a whole number).Hemmingway, Inc., is considering a $5 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $25 million. Under this option, the company would not build the $20 million production facility. The decision tree is shown in Figure 4.16. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $59 million.…
