Problem 4: For each of the following statements, judge if it is true or false, and provide a detailed explanation behind your answers. a) Roll's critique is that the market is never truly in equilibrium and hence one can never truly test whether the CAPM holds. b) The figure below shows the risk and expected return of 4 given assets. E Consider an investor with "Mean-Variance" preferences, and the statement: "If the investor is indifferent between assets A and D, then she prefers C to B; but if she is indifferent between B and C, she prefers A to D.". c) Suppose you make a "scatter plot", each point representing a pair of contemporaneous returns from a time series of returns on the market portfolio and a single asset. If the CAPM holds, you would expect all
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- 2. Three agents are characterized by the following utility functions: Al: 4,(x)= In(x) A2: и,(х) %3D 10х ? АЗ: и, (х) %— 2* +1 a) Calculate the expected rate of return and risk for the following assets: x, = (4,2 2,6/0,48 0,52) x, = (1,7 3,5/0,27 0,73) b) What asset will the agents with the previous utility functions choose?4) Consider investors with preferences represented by the utility function U = E(r) – Ao². (a) Draw the indifference curve representing a utility level of 10% for an in- vestor with a risk aversion parameter A = 3 in expected return-standard deviation space. (b) In the same graph, draw the indifference curve representing a utility level of 15% for an investor with a risk aversion parameter A = 3. (c) In the same graph, draw the indifference curve representing a utility level of 10% for an investor with a risk aversion parameter A = 5.please explain clearly
- 10. Which one of the following measures may be used to measure the risk of an investment on its own? a) Expected return of the investment. b) Expected utility of the investment for an investor. c) Standard deviation of the possible outcomes of the investment. d) The Bernoullian utility function's value of a good investment outcome.ANSWER C AND D PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth?Suppose an asset has a return of $416 with probability of 85% and a return of $980 with probability 15%. What is the expected return (i.e. expected value) of the asset? а. b. If a risk averse person were given a choice between the above gamble and $400 guaranteed, which one would they pick?
- 5) A person with a current wealth of $100,000 who faces the prospect of 25 percent chance of losing his or her $20,000 automobile through theft during the next year. Suppose this person's utility function is U(Y) = InY. a). If this person takes no action, what is the expected utility? b). What is the actuarially fair premium? What is his expected utility if he purchase this insurance. c). Suppose that now the insurance company provides a new type of insurance. This insurance costs $4900 and requires the individual to incur the first $1000 of the loss from theft would yield. That is expected utility of this new insurance? Will the person choose the insurance in b) or c)?ANSWER E PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth? e) Calculate relative risk aversion for this investor. How does relativerisk aversion depend on wealth?Please answer question on screenshot (which of the folowing statements....) q1) Janet offers her friend Sam (who has identical preferences and initial wealth) the following proposition: They buy the ticket together, and share the cost and proceeds equally.
- Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) /n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w.