Asked by Bryan Cakir on May 28, 2024
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Donna is considering the option of becoming a co-owner in a business. Her investment choices are to hold a risk free asset that has a return of and co-ownership of the business, which has a rate of return of and a level of risk of . Donna's marginal rate of substitution of return for risk where is Donna's portfolio rate of return and σP is her optimal portfolio risk. Donna's budget constraint is given by Solve for Donna's optimal portfolio rate of return and risk as a function of , and . Suppose the table below lists the relevant rates of returns and risks. Use this table to determine Donna's optimal rate or return and risk.
Investment Rate of Return Risk
Risk Free 0.06 0
Business 0.25 0.39
Risk Free Asset
An investment that is expected to return its original value without any loss and with a certain rate of interest; considered to have zero default risk.
Rate of Return
The increase or decrease in the value of an investment during a set time frame, represented as a proportion of the investment's original price.
Level of Risk
The degree of uncertainty associated with an investment or decision, often regarding the potential for loss.
- Implement the principle of utility maximization when choosing portfolios.
- Gain insight into how standard deviation functions as an indicator of risk in portfolios composed of risk-bearing and risk-free assets.
- Appraise financial decision-making using the marginal rate of substitution (MRS) to improve the allocation of resources in a portfolio.
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Learning Objectives
- Implement the principle of utility maximization when choosing portfolios.
- Gain insight into how standard deviation functions as an indicator of risk in portfolios composed of risk-bearing and risk-free assets.
- Appraise financial decision-making using the marginal rate of substitution (MRS) to improve the allocation of resources in a portfolio.
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