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4. Assume that a risk-free money market account is added to the market described in Q2. The continuously compounded rate of return on the money market account is 0% per period. (i) Use the method of Lagrange multipliers to determine the proportions of wealth invested in the three assets available for the minimum variance portfolio with expected return u. Your answer must express the proportions as a function of μ. (ii) Recall that the market portfolio has highest Sharpe ratio. Formulate the optimi- sation problem which characterises the market portfolio. You don't have to solve this optimisation problem.

4. Assume that a risk-free money market account is added to the market described in Q2. The continuously compounded rate of return on the money market account is 0% per period. (i) Use the method of Lagrange multipliers to determine the proportions of wealth invested in the three assets available for the minimum variance portfolio with expected return u. Your answer must express the proportions as a function of μ. (ii) Recall that the market portfolio has highest Sharpe ratio. Formulate the optimi- sation problem which characterises the market portfolio. You don't have to solve this optimisation problem.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
Transcribed Image Text:2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
4. Assume that a risk-free money market account is added to the market described in Q2. The continuously compounded rate of return on the money market account is 0% per period. (i) Use the method of Lagrange multipliers to determine the proportions of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. Your answer must express the proportions as a function of µ. (ii) Recall that the market portfolio has highest Sharpe ratio. Formulate the optimi- sation problem which characterises the market portfolio. You don't have to solve this optimisation problem.
Transcribed Image Text:4. Assume that a risk-free money market account is added to the market described in Q2. The continuously compounded rate of return on the money market account is 0% per period. (i) Use the method of Lagrange multipliers to determine the proportions of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. Your answer must express the proportions as a function of µ. (ii) Recall that the market portfolio has highest Sharpe ratio. Formulate the optimi- sation problem which characterises the market portfolio. You don't have to solve this optimisation problem.
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