An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has...
An investor's utility function is ?(?) = ln ?, where w denotes net wealth. He has $100 for investment. There are two assets, a “safe” one and a “risky” one. The safe asset yields 10% return with certainty. The risky asset yields 19% return with probability 0.5, and 2% return with probability 0.5.
a.) How much money should the investor invest in each asset? 2.
b.) Now suppose instead of 2% it is changed to 1%, while all other information stays the same. Redo the problem.
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An investor's utility function is ?(?) = ln ?, where w denotes
net wealth. He has...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the...
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount...
econ
In a year from now, there may be two states of the economy - “good” and “bad.” Assume that the probability of “good” state is 1/3, and the probability of “bad” state is 2/3. There are two investment opportunities: (i) risky asset will return you $1.32 in a year from now on each $1 you invest “today” if the economy is in “good” state, and $0.90, if the economy is in “bad” state; (ii) safe asset will return you $1.02...
ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a...
ubariho Julius’ utility function is U(W)=ln(W). His current wealth is $5,000. He is now given a chance to buy a futures contract on Nickel that gives him 75% chance of winning $5,000, and 25% chance of losing $4,000. What is his, Julius’ certainty equivalent for holding the futures contract?
1. Suppose that an individual has a wealth of $50,000 and the utility of U(W) =...
1. Suppose that an individual has a wealth of $50,000 and the utility of U(W) = VW. This individual has the option of investing all wealth in risky stock, which is worth $100 per share, which will be worth $105 per share in a good state with probability 1/2 and $95 per share in a bad state with probability 1/2. Assume, the interest rate is zero. (a) Find the expected value and the expected utility of investing all wealth in...
Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A)....
Suppose Peter Brown’s utility for total wealth (A) can be represented by the utility function U(A)=ln(A). He currently has $1,000 in cash. A business deal of interest to him yields a reward of $100 with probability 0.5 and $0 with probability 0.5. If he owns this business deal in addition to the $1,000 and considers selling the deal, what is the smallest amount for which he would sell it (i.e., the amount of the deal such that he is indifferent...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset and a risky asset. Let xs denote the quantity (dollars) of wealth invested in the safe asset. Let X, denote the quantity (dollars) of wealth invested in the risky asset. The safe asset has an interest rate of rs = 0. The risky asset has a probability n of earning an interest rate rr = -1 and a 1 – 1 probability of earning...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset and a risky asset. Let xs denote the quantity (dollars) of wealth invested in the safe asset. Let Xr denote the quantity (dollars) of wealth invested in the risky asset. The safe asset has an interest rate of rs = 0. The risky asset has a probability n of earning an interest rate rr = -1 and a 1 – a probability of earning...
6. (+2) Suppose that the happiness, or "utility", associated with additional wealth w, is u(w)V, and...
6. (+2) Suppose that the happiness, or "utility", associated with additional wealth w, is u(w)V, and consider two investments: Investment 1 produces S0 with probability 0.5 and $1000 with probability 0.5. The second produces $500 with probability 1. Which investment provides greater utility, in expectation?
Suppose an investor has exponential utility function U(x) = −exp(−ax) and an initial wealth level of...
Suppose an investor has exponential utility function U(x) = −exp(−ax) and an initial wealth level of W. The investor is faced with an opportunity to invest an amount w ≤ W and obtain a random payoff x. show that his evaluation of this incremental investment is independent of W.
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w....
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probability %, and 4 with probability %. Calculate my certainty equivalent for this gamble: CE=_ . Calculate my risk premium p for this gamble p=
Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the choice of investing in a safe asset or a risky asset. $1 invested in the safe asset returns $1 with certainty. $1 invested in the risky asset returns $1.25 when the market state is "good" and returns $0.8 when the market state is "bad". The good state occurs with probability 2/3 and the bad state occurs with probability 1/3. Let x be the amount...
1. Suppose that an individual has a wealth of $50,000 and the utility of U(W) = VW. This individual has the option of investing all wealth in risky stock, which is worth $100 per share, which will be worth $105 per share in a good state with probability 1/2 and $95 per share in a bad state with probability 1/2. Assume, the interest rate is zero. (a) Find the expected value and the expected utility of investing all wealth in...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset and a risky asset. Let xs denote the quantity (dollars) of wealth invested in the safe asset. Let X, denote the quantity (dollars) of wealth invested in the risky asset. The safe asset has an interest rate of rs = 0. The risky asset has a probability n of earning an interest rate rr = -1 and a 1 – 1 probability of earning...
4) Consider an agent with initial wealth W to be allocated between a safe (risk-free) asset and a risky asset. Let xs denote the quantity (dollars) of wealth invested in the safe asset. Let Xr denote the quantity (dollars) of wealth invested in the risky asset. The safe asset has an interest rate of rs = 0. The risky asset has a probability n of earning an interest rate rr = -1 and a 1 – a probability of earning...
6. (+2) Suppose that the happiness, or "utility", associated with additional wealth w, is u(w)V, and consider two investments: Investment 1 produces S0 with probability 0.5 and $1000 with probability 0.5. The second produces $500 with probability 1. Which investment provides greater utility, in expectation?
My von Neumann Morgenstern utility function is U (W) = 32 + (9/5)w1/2 for wealth w. I face a gamble that pays 1 with probability %, and 4 with probability %. Calculate my certainty equivalent for this gamble: CE=_ . Calculate my risk premium p for this gamble p=
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