There are two portfolios available: A: Get $4 for sure B: 70% gaining $10 and 30% losing $10. The expected value of A is $ The expected value of B is $ The standard deviation of A is $ The standard deviation of B is $ (enter all answers with two decimal places.) Amanda is risk neutral, she would choose portfolio О А. В. B. Not enough information to determine. С. А. O D. Aor В.
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- Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.For a given option portfolio, you are long vega (value increases as volatility goes up), and short theta (as time passes your options portfolio loses money). Are you net long or short options? Net long, because as volatility goes up and it increases in value and as time passes you lose value. Net short, because as volatility goes up and it decreases in value and as time passes you increase value. not consistent you are long one and short the other, so can't tell completely independent derivatives, its apples and oranges and no reflection on your portfolioConsider the expected return and standard deviation of the following two assets: Asset 1: E[r1]=0.1 and s1=0.2 Asset 2: E[r2]=0.3 and s2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) r12=-1, (ii) r12=0. (b) Suppose r12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio? (c) Derive the formula for the variance of a portfolio with four assets.
- When you are long an option and you delta hedge, you want A. traders talking a lot about other asset classes and ignore your underlying B. volatility to increase and the underlying to move around a lot C. the cost of carry to narrow D. volatility to decrease and the underlying to just stop movingJamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. a. b. c. d. Graph Jamal’s utility function. Is he risk averse? Explain. (2+2) Does A or B offer Jamal a higher expected prize? Explain your reasoning with appropriate calculations. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why?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?
- 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?B. Richard's nickname is "No-Risk Rick" because he is an extremely risk-averse individual. His utility function is given by U(W) = √W. where W represents his current wealth in dollars. He currently has $100 worth of property, but there is a 50% chance that all of it will be stolen. What is Richard's expect wealth and expected utility of wealth? An insurance company offers to reimburse Richard for his loss if the money is stolen. What is the most that Richard would pay for such a policy? Explain. Please solve this with in 1 hourConsider 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.
- 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. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?6. Risk-averse people will choose different asset portfolios than people who are not risk averse. Over a long period of time, we would expect thatA.every risk-averse person will earn a higher rate of return than every non-risk averse person.B.every risk-averse person will earn a lower rate of return than every non-risk averse person.C.the average risk-averse person will earn a higher rate of return than the average non-risk averse person.D.the average risk-averse person will earn a lower rate of return than the average non-risk averse person. 7.The real exchange rate equals the relative A.price of domestic and foreign currency.B.price of domestic and foreign goods.C.rate of domestic and foreign interest. D.None of the above is correct. 8.According to the theory of liquidity preference, an increase in the price level causes theA.interest rate and investment to rise.B.interest rate and investment to fall.C.interest rate to rise and investment to fall.D.interest rate to fall and…