You are a risk-averse investor with a CRRA utility function. You are faced with the decision to invest your total wealth W of £1,000,000 into a riskless asset which generates a return of 5% or into a risky asset which either generates a return of 20% or a loss of −4% with equal probability. Find the optimal investment allocation with a coefficient of relative risk aversion η=2, and comment on your results.
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You are a risk-averse investor with a CRRA utility function. You are faced with the decision to invest your total wealth W of £1,000,000 into a riskless asset which generates a return of 5% or into a risky asset which either generates a return of 20% or a loss of −4% with equal probability.
Find the optimal investment allocation with a coefficient of relative risk aversion η=2, and comment on your results.
Total wealth= £1000000
Returns from investing in riskless asset= 5%
Risky asset which either generates a return of 20%
Loss from investing in risky asset= -4%
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- Consider two investors A and B.If the Certainty-Equivalent end-of-period wealth of A is less than the Certainty-Equivalent end-of-period wealth of B for the same portfolio choice,then A. Risk aversion of A > Risk aversion of B B. Risk aversion of A = Risk aversion of B C. Risk aversion of A< Risk aversion of B D. Not enough Information Justify your choice in a sentence or two:Find the Pratt - Arrow risk - aversion function for a utility function U(W) = log(0.5-W + 500), where W is the amount of wealth in €. Suppose that an investor's wealth is subject to outcomes -800 €, 500 €, 500 € and 1, 000 € which affect the initial amount of 2,500 € with probabilities of their occurrence 40%, 15%, 15% and 30%, respectively. a) Using the Taylor approximation to certainty equivalent, calculate an approximate expected utility value. b) Calculate the certain equivalent of the investor's uncertain wealth. Interpret.You are considering two portfolios. Portfolio A has an expected return of 15% and a standard deviation of 30%. Portfolio B has an expected return of 6% and a standard deviation of 19%. What is the certainty equivalent of these portfolios, specifically when your risk aversion is such that you are indifferent between portfolio A and portfolio B?
- Suppose Investor A has a power utility function with γ = 1, whilst Investor B has a power utility function with γ = 0.5 (i) Which investor is more risk-averse(assuming that w > 0)? (ii) Suppose that Investor B has an initial wealth of 100 and is offered the opportunity to buy Investment X for 100, which offers an equal chance of a payout of 110 or 92. Will she choose to buy Investment X?Leo owns one share of Anteras, a semiconductor chip company which may have to recall millions of chips. The stock currently trades at $100/share. Leo believes the probability that they have to recall the chips is 50%. If the chips have to be recalled, the stock price will be cut in half, but otherwise it will remain $100. The expected value of Leo's share is ______ Assume Leo has the utility function, U(X)=√X. The minimum price Leo would accept to sell his share is _______ Leo's risk premium is ________Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = X^n/n . There is a safe asset (such as a US government bond) that has a net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth?
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