Chapter 7 Probability and Risk
$125 will be received with probability .2 $100 will be received with probability .3 $50 will be received with probability .5 A. What is the expected value of the lottery? B. What is the variance of the outcome? C. What would a risk-neutral person pay to play the lottery?
A:EV = 0.2*125 + 0.3*100 + 0.5*50 = 80 B. Variance = 0.2*(125-80)2 + 0.3*(100-80)2 +0.5*(50-80)2 = 975 C. A risk-neutral person would pay the expected value of the lottery: 80
Risk Neutral
Condition of being indifferent between a certain income and an uncertain income with the same expected value
Risk Loving
Condition of preferring a risky income with the same expected value Prefer a gamble over an assurred value
Consider the following utility function: U(x) = X^1/2 A lottery pays nothing in state 1 and $100 in state 2. The probabilities of these states are 3/8 and 5/8, respectively. a)Calculate the expected utility of the lottery. Calculate the expected value of this lottery, and the utility of receiving this expected value with certainty. Which is larger - the expected utility of the lottery, or the utility of the expected value of the lottery? What does this tell you about this persons attitude toward risk? b)Calculate the certainty equivalent of the lottery. c)Calculate the risk premium for the lottery.
A)EV=62.5 EU=6.25 U(EV)=7.9 Since the utility of receiving this EV w/certainty is more than the expected utility of the lottery therefore they are more risk averse. B)39.06 C)23.44
The financial reward in each state of nature is called
A Payoff
Risk Premium is
The maximum a risk averse person is willing to pay for insurance
Scenario 2 Hakan just bought a house for $250,000. The utility he gets from wealth is given by: U(w) = 5w^(0.5). Hakan estimates that the probability of a major earthquake in the coming year is 10%, and that in the event of such a quake, the property would be worth $40,000. Pt. 1 Assume insurance is available for $30,000. Should Hakan buy the insurance? a. Yes. b. No. c. Hakan is indifferent. d. We need more information on Meryem's attitude toward risk. Pt2. What is the maximum Hakan would pay for insurance? a. $18,500 b. $29,100 c. $36,900 d. $50,250 Pt3. If Yasemin's marginal utility of income function is given as: MU(I) = 2I, where I represents income, she is a. risk averse. b. risk loving. c. risk neutral. d. none of the above.
1)B 2)B 3)B
What reduces Risk?
1)Diversification 2)Insurance 3)Obtaining more information
Which of the following is an example of a subjective probability? A. Based on many years of data, an automobile insurance company estimates the probability that a randomly chosen 20-year old driver will have an accident during his 20th year as 0.001. B. After examining a coin to determine that it is an unaltered coin produced by the U.S. Mint, a gambler says the probability of a coin flip coming up heads is 1/2. C. After examining a deck of cards to determine that there are 52 cards of the correct suits and values, a card player says the probability of drawing the 7 of hearts is 1/52. D. Although College A has never played College B in basketball, a sports analyst believes there is a 0.8 probability that A will beat B in their upcoming game
D
Which of the following is not a way to reduce risk? A. Buying insurance. B. Obtaining more information about choices and payoffs. C. Diversifying investments. D. By considering fewer alternatives.
D
Risk Averse
Is the condition of preferring a certain income to a risky income with the same expected value (Avoid Risk)
Subjective probability
Is the gut feeling of the person making the risky decision
Which utility functions represent a risk neutral, averse, and loving individual? U(I)=I^(3) U(I)= 4I U(I)=I^.5
MU(I)=3I^(2) -Risk Loving -Exponential MU(I)=4 -Risk Neutral Linear MU(I)=.5I^(-.5) -Risk Averse -The other one
Variance is the
Measure of riskiness or uncertainity
EV(Expected Value) equals
Price of X times the probability of getting X plus the Price of Y times the probability of of getting Y and etc
STDEV =
Square root of the variance ].
Suppose that Natasha's utility function is given by U(I)= (10I)^.5, where I represents annual income in thousands of dollars. Suppose that Natasha is currently earning an income of $40,000 (I = 40) and can earn that income next year with certainty. She is offered a chance to take a new job that offers a 0.6 probability of earning $44,000 and a 0.4 probability of earning $33,000 Should she take the new job? Natasha should ________ the new job because her expected utility of ______ is _________ her current utility. (Round expected utility to three decimal places.) Suppose for some reason Natasha takes the new job. Would she be willing to buy insurance to protect against the variable income associated with the new job? If so, how much would she be willing to pay for that insurance? (Hint: What is the risk premium?) Natasha would be willing to pay ____for insurance. (Round your answer to the nearest penny.)
not take 19.852 less than $189.8
Variance =
π1 x (P1 -EV)^2 + π2 x (P2 -EV)^2
