Mean variance utility defines risk using certainty equivalent wealth. The lower the certainty equivalent wealth, the lower the mean variance utility. uestion Select one: O True O False
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Mf.
Mean variance utility defines risk using certainty equivalent wealth. The lower the certainty equivalent wealth, the lower the mean variance utility.
uestion
Select one:
O True
O False
Under constant relative risk aversion, the lower the certainty equivalent wealth is than the average wealth of a lottery the riskier the lottery.
Select one:
O True
O False
Given a
Select one:
O True
O False
Greater risk aversion means a plot of utility vs. wealth would look less
Select one:
O True
O False
The greater the wealth, the less the utility of the next dollar of wealth.
Select one:
O True
O False
People don't like risk because it means they get poorer when they're poorer and richer when they're rich. In fact, a financial security that does the opposite of that would be negatively risky and be even better than risk free.
Select one:
O True
O False
People don't like risk because it is uncertain. Certain things are always preferable to uncertain things.
Select one:
O True
O False
Given the opportunity to buy a 50% at $2 for $1, most people would be indifferent
Select one:
O True
O False
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- Microeconomics Wilfred’s expected utility function is px1^0.5+(1−p)x2^0.5, where p is the probability that he consumes x1 and 1 - p is the probability that he consumes x2. Wilfred is offered a choice between getting a sure payment of $Z or a lottery in which he receives $2500 with probability p = 0.4 and $3700 with probability 1 - p. Wilfred will choose the sure payment if Z > CE and the lottery if Z < CE, where the value of CE is equal to ___ (please round your final answer to two decimal places if necessary)Prospect Y = ($6, 0.25 ; $15, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of CE(Y) for Will? (In other words, what is Will's certainty equivalent for prospect Y?) (The certainty equivalent represents the maximum amount a person would be willing to pay to acquire a risky prospect, and equivalently, the lowest price for which they would be willing to sell a risky prospect if they already owned it) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)2 Prove rigourously, "Constant relative risk aversion (CRRA) implies decreasing absolute risk aversion (DARA), but the converse is not necessarily true."
- Givenu(x)=x0.5 Lottery A Probability 0.50 0.25 0.25 Outcome 64 16 0 For automatic grading, give all numerical answers to exactly two decimal places. Do not include currency signs 1) What is the expected value? (Give the answer as 36.00, not 36) 2) What is the expected utility? 3) What is the certainty equivalent? (Number only) 4) What is the risk premium? 5) Would this person rather receive 20 for sure than play Lottery A? (Answer should be Y or N for auto-grading to work) 6) (Harder) In many applications of expected utility, it is possible to lose money. The usual way of handling this is to interpret utility in terms of final wealth. Suppose it costs money to play this lottery. If starting wealth is 100, calculate the expected utility of playing lottery A if the price of playing is 15. Your answer should be to two decimal places. (Note: calculating the certainty equivalent of the lottery would be a little different than we've done in class. Squaring your EU result would give…Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?a. Suppose that you took part in a lottery that has a chance to increase, decrease or have no effect on your level of income. With probability 0.5, your income remains at it original level K500; with 0.2 probability, your income increases to K700; and with probability 0.3, your income decreases to K400. The utility function is.u（1） =I^0.7where I denote income leveli.Using the utility function show that the consumer's risk preference is averse. (2marks)ii.Calculate both the EU and EV of the income. (4marks)iii.Using the results in (il) above, indicate the attitude to risk of this consumer. (2marks)
- Prospect Y = ($4, 0.25 ; $16, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of U(EV(Y)) for Will? (In other words, how much utility would Will get were he to receive the expected value of Y?) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Given u(x)=x^0.5 and Lottery A (below) Lottery A Probability 0.50 0.25 0.25 Outcome 64 16 0 For automatic grading, give all numerical answers to exactly two decimal places. Do not include currency signs 1) What is the expected value? (Give the answer as 36.00, not 36) 2) What is the expected utility? 3) What is the certainty equivalent? (Number only) 4) What is the risk premium? 5) Would this person rather receive 20 for sure than play Lottery A? (Answer should be Y or N for auto-grading to work) 6) (Harder) In many applications of expected utility, it is possible to lose money. The usual way of handling this is to interpret utility in terms of final wealth. Suppose it costs money to play this lottery. If starting wealth is 100, calculate the expected utility of playing lottery A if the price of playing is 15. Your answer should be to two decimal places. (Note: calculating the certainty equivalent of the lottery would be a little different than we've done in class. Squaring…Uncertainty and willingness to pay for insurance. Utility = (Wealth)1/3 Prob(flood) = .04 Prob(no flood) = .96 Total wealth if flood = $100,000. Total Wealth if no flood = $800,000. Find: (i) expected value, (ii) expected utility, (iii) certainty equivalent, and (iv) maximum willingness to pay for a policy that provides 100% flood insurance coverage. Draw the utility function and include all solved values on the diagram. What is the average gross profit per insurance customer, if each customer is charged his own maximum willingness to pay?
- Prospect Y = ($10, 0.25 ; $13, 0.75) If Will's utility of wealth function is given by u(x)=x0.25, what is the value of EU(Y) for Will? (In other words, what Expected Utility does Will receive from prospect Y?) (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)Suppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds.CombinationFraction of Portfolio in Diversified StocksAverage Annual ReturnStandard Deviation of Portfolio Return (Risk)(Percent)(Percent)(Percent)A 0 1.50 0B 25 3.00 5C 50 4.50 10D 75 6.00 15E 100 7.50 20There is a relationship between the risk of Caroline's portfolio and its average annual return.Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase…Kindly assist on the questions below 1) Dan is an expected utility maximizer with a utility function over wealth given by : u(w) = 2√w +10 Dan faces a gamble of where there are equal chances to win $9 or $16. The certainty equivalent of this gamble is a) 3.5 b) 17 c)2√13 +10 d) not enough information to compute e) 20 2) Consider a expected utility maximizing consumer with preferences represented by u(w)= w2 If they face a loss that occurs with a 15% probability (select all that applies) a) fair insurance will be priced at 15% per dollar b) fair insurance will leave them with wealth equal to their certainty equivalent c)they will choose to fully insure themselves with fair insurance d)they will always buy more insurance than a risk neutral person