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 σ
P 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