Donna Is Considering the Option of Becoming a Co-Owner in a Business

question 13

Essay

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 R_j and co-ownership of the business, which has a rate of return of R_b and a level of risk of σ_b. Donna's marginal rate of substitution of return for risk
(
/
) is
=
where RP is Donna's portfolio rate of return and σP is her optimal portfolio risk. Donna's budget constraint is given by
RP = Rj +
σP. Solve for Donna's optimal portfolio rate of return and risk as a function of R_j, R_{b and} σ_b. 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

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Definitions:

DuPont Cellophane

A historical reference to the legal case involving the antitrust analysis of DuPont's market dominance in the production of cellophane as a packaging material.

Alcoa Case

A significant legal case involving the Aluminum Company of America (Alcoa) which dealt with issues of monopolistic practices and antitrust law.

Conglomerate Merger

A type of merger in which two companies in unrelated businesses combine their operations.

Horizontal Merger

A business consolidation that occurs between firms which operate in the same industry, often leading to a higher market concentration.