Question 1: A risk averse agent, whose utility is given by U(r) = In r and whose wealthis 50,000 is faced with a potential loss of 10,000 with a probability of 0.1. What is themaximum premium he would be willing to pay to protect himself against this loss? Whatis the minimum premium that an insurer, with the same utility function and wealth1,000,000 will be willing to charge to cover this loss? Explain the difference beteen thetwo figures.

Given: Utility function of risk averse agent is u(x)=ln(x) and wealth is 50,000 is faced with a…

Answered: Question 1: A risk averse agent, whose…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 1SE: What term is used to express the likelihood of an event occurring? Are there restrictions on its...

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What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.
3. Suppose Chelsea has the following utility function over sure wealth: v (y) = In y (a) Consider the lottery that yields the outcome $2 with probability and the outcome $8 with probability . What is Chelsea's certainty equivalent for this lottery? 2 3* (b) For the lottery in (b), how much would Chelsea pay to have her risk taken away? (c) What is Chelsea's probability premium at $25 for a lottery that could swing her wealth $20 up or down? What about $15 up or down?
1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Returns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock. Consider the case of Celestial Crane Cosmetics Inc. (CCC): Five years of realized returns for CCC are given in the following table. Remember: 1. While CCC was started 40 years ago, its common stock has been publicly traded for the past 25 years. 2. The returns on its equity are calculated as arithmetic returns. 3. The historical returns for CCC for 2014 to 2018 are: 2014 2015 2016 2017 2018 Stock return 18.75% 12.75% 22.50% 31.50% 9.75% Given the preceding data, the average realized return on CCC’s stock is . The preceding data series represents of CCC’s historical returns. Based on this conclusion, the standard deviation of CCC’s historical returns is . If investors expect the…
Returns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock. Consider the case of Happy Dog Soap Inc. (HDS): Five years of realized returns for HDS are given in the following table. Remember: 1. While HDS was started 40 years ago, its common stock has been publicly traded for the past 25 years. 2. The returns on its equity are calculated as arithmetic returns. 3. The historical returns for HDS for 2014 to 2018 are: 2014 2015 2016 2017 2018 Stock return 8.75% 5.95% 10.50% 14.70% 4.55% Given the preceding data, the average realized return on HDS's stock is The preceding data series represents historical returns is of HDS's historical returns. Based on this conclusion, the standard deviation of HDS's If investors expect the average realized return from 2014 to 2018 on HDS's stock to continue into the future, its…
Suppose that we are interested in explaining the equity pre- mium puzzle using prospect theory. Suppose also that the probability weighting function is linear and the utility function under prospect theory is given by x0.5 if x ≥ 0 (domain of gains) v (x) = — (−x) 0.5 if x < 0 (domain of losses) Evaluate the following statement. ”Under the assumptions given in the question we can explain the equity premium puzzle.” (A) True. (B) False. (C) There is insufficient information to answer this question.
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Question 2: A risk averse agent, whose utility is given by u(a) = In(x) and his wealth is 50, 000 is faced with a potential loss of 10,000 with a probability of p = 0.1. What is the maximum premium he would be willing to pay to protect himself against this loss?

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