We are going to invest $1,000 for a period of 6 months.Two potential investments are available: T-bills and gold. Ifthe $1,000 is invested in T-bills, we are certain to end the6-month period with $1,296. If we invest in gold, there is a34chance that we will end the 6-month period with $400 anda 14chance that we will end the 6-month period with $10,000.If we end up with x dollars, our utility function is given byu(x) x1/2. Should we invest in gold or T-bills?

We are going to invest $1,000 for a period of 6 months.Two potential investments are available: T-bills and gold. Ifthe $1,000 is invested in T-bills, we are certain to end the6-month period with $1,296. If we invest in gold, there is a34chance that we will end the 6-month period with $400 anda 14chance that we will end the 6-month period with $10,000.If we end up with x dollars, our utility function is given byu(x) x1/2. Should we invest in gold or T-bills?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 45P: You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that...

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You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet 1. From then on, every time you win a bet, you bet 1 the next time. Each time you lose, you double your previous bet. Currently you have 63. Assuming you have unlimited credit, so that you can bet more money than you have, use simulation to estimate the profit or loss you will have after playing the game 50 times.
A project does not necessarily have a unique IRR. (Refer to the previous problem for more information on IRR.) Show that a project with the following cash flows has two IRRs: year 1, 20; year 2, 82; year 3, 60; year 4, 2. (Note: It can be shown that if the cash flow of a project changes sign only once, the project is guaranteed to have a unique IRR.)
Based on Kelly (1956). You currently have 100. Each week you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g., if you invest 100, you increase your asset position by 300), and, with probability 0.6, the amount you invest is lost. Consider the following investment strategies: Each week, invest 10% of your money. Each week, invest 30% of your money. Each week, invest 50% of your money. Use @RISK to simulate 100 weeks of each strategy 1000 times. Which strategy appears to be best in terms of the maximum growth rate? (In general, if you can multiply your investment by M with probability p and lose your investment with probability q = 1 p, you should invest a fraction [p(M 1) q]/(M 1) of your money each week. This strategy maximizes the expected growth rate of your fortune and is known as the Kelly criterion.) (Hint: If an initial wealth of I dollars grows to F dollars in 100 weeks, the weekly growth rate, labeled r, satisfies F = (I + r)100, so that r = (F/I)1/100 1.)
In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?
You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.
Martha and Ken Allen want to sell their house. At thebeginning of each day, they receive an offer. We assume thatfrom day to day, the sizes of the offers are independentrandom variables and that the probability that a given day’soffer is for j dollars is pj . An offer may be accepted duringthe day it is made or at any later date. For each day thehouse remains unsold, a maintenance cost of c dollars isincurred. The house must be sold within 30 days. Formulatea dynamic programming recursion that Martha and Ken canuse to maximize their expected net profit (selling price -maintenance cost). Assume that the maintenance cost for aday is incurred before the current day’s offer is received andthat each offer is for an integer number of dollars.
We are thinking of filming the Don Harnett story. Weknow that if the film is a flop, we will lose $4 million, andif the film is a success, we will earn $15 million. Beforehand,we believe that there is a 10% chance that the Don Harnettstory will be a hit. Before filming, we have the option ofpaying the noted movie critic Roger Alert $1 million for hisview of the film. In the past, Alert has predicted 60% of allactual hits to be hits and 90% of all actual flops to be flops.We want to maximize our expected profits. Use a decisiontree to determine our best strategy. What is EVSI? What isEVPI?
Barbara Flynn sells papers at a newspaper stand for $0.40. The papers cost her $0.30, giving her a $0.10 profit on each one she sells. From past experience Barbara knows that: a) 20% of the time she sells 150 papers. b) 20% of the time she sells 200 papers. c) 30% of the time she sells 250 papers. d) 30% of the time she sells 300 papers. Assuming that Barbara believes the cost of a lost sale to be $0.05 and any unsold papers cost her $0.30 and she orders 250 papers. Use the following random numbers: 14, 4, 13, 9, and 25 for simulating Barbara's profit. (Note: Assume the random number interval begins at 01 and ends at 00.) Based on the given probability distribution and the order size, for the given random number Barbara's sales and profit are (enter your responses for sales as integers and round all profit responses to two decimal places): Random Number Sales Profit 14 4 13 9 25