2. Let U(w) denote the utility function for an investor.(a) If the investor is non-satiated, what property must U(w) have?(b) If the investor is risk-neutral, what property must U(w) have?(c) Let X be a fair gamble. Suppose that an investor is risk-seeking. What would theinvestor prefer between X and the empty portfolio (i.e. making no investment)?

a) When we say the investor is not satisfied, it means they always want more wealth. They are never…

Answered: 2. Let U(w) denote the utility function…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section11.5: Simulating Games Of Chance

Problem 36P: A martingale betting strategy works as follows. You begin with a certain amount of money and...

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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.
Consider two equity market investors. The first investor is a hedge fund manager that relies on very active trading, and borrows from investment banks in order to leverage their investment. Their remuneration depends on total base fee earned by their fund as a percentage of net assets under management, plus a yearly bonus based on returns generated above a hurdle rate. The second investor is a high net-worth individual who is investing for their own retirement, which they anticipate to occur in 10 years or more. Identify three dimensions of risk that are likely to have significantly different impact on thesetwo investors. Explain the nature of the difference. Suggest aspects that each investor might monitor in order to control the risks most relevant to them.
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Suppose a risk-neutral power plant needs 10,000 tons of coal for itsoperations next month. It is uncertain about the future price of coal. Theprice of coal today is $60 a ton but next month it could be either $40 or$68 (with equal probability). How much would the power plant be willingto pay today for an option to buy a ton of coal next month at today’sprice? (Ignore discounting over the short period of a month.)
If a $900,000 30-year fully amortizing fixed rate mortgage loan from City National Bank has an annual interest rate of 6.25% with a monthly payment of $5,541.45, and a $900,000 15-year fully amortizing fixed rate mortgage loan from Wells Fargo Bank has an annual interest rate of 5.25% with a monthly payment of $7,234.90, a borrower should: a. Choose the 30-year fixed rate loan from City National Bank because of the lower monthly payments b. Make a careful analysis of all the terms and conditions of the available loans to determine which loan is better for that borrower under the circumstances, or if another loan or lender should be considered c. Choose a 7-year adjustable rate interest-only loan from PNC Bank instead with a low teaser interest rate of 1.0% for the first loan year d.Choose the 15-year fixed rate loan from Wells Fargo because of the lower interest rate
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Two 9-year-old boys are watching a television replay of a boxing match between Muhammad Ali and Joe Frazier on a program called “Great Fights of the Century.” Since the fight took place before they were old enough to remember the outcome, neither knows who won and they bet on the outcome. Tom bets on Ali and Tim bets on Frazier. Does risk exist in this situation? Defend your answer.
A homebuyer recently obtained a loan to purchase a house. The lender offered a lower interest rate because the loan is secured. Why would a real estate loan be considered a secure loan? О The loan is backed by the property itself. If the borrower defaults on the loan, the lender can sell the property to get their money back. O In order to qualify for a home loan, the borrower must have good credit. Good credit is a form of security for the lender. O All real estate loans are considered unsecure. O Most home loans are long-term loans, which are considered low-risk from the lender's perspective.
On Monday, a certain stock closed at $10 per share. Before the stock market opens on Tuesday, you expect the stock to close at $9, $10, or $11 per share, with respective probabilities 0.3, 0.3, and 0.4. Looking ahead to Wednesday, you expect the stock to close 10 percent lower, unchanged, or 10 percent higher than Tuesday’s close, with the following probabilities. Tuesday's Close 10 Percent Lower Unchanged 10 Percent Higher $9 0.4 0.3 0.3 10 0.2 0.2 0.6 11 0.1 0.2 0.7 Early on Tuesday, you are directed to buy 100 shares of the stock before Thursday. All purchases are made at the end of the day, at the known closing price for that day, so your only options are to buy at the end of Tuesday or at the end of Wednesday. You wish to determine the optimal strategy for whether to buy on Tuesday or defer the purchase until Wednesday, given the Tuesday closing price, to minimize the expected purchase price. Develop and evaluate a decision tree. a-1. Determine the optimal…

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