Mel and Christy Are Co-Workers with Different Risk Attitudes

Essay

Mel and Christy are co-workers with different risk attitudes. Both have investments in the stock market and hold U.S. Treasury securities (which provide the risk free rate of return). Mel's marginal rate of substitution of return for risk (
/ MU R_P, σ_{P) is}


=
where RP is the individual's portfolio rate of return and σ_P is the individual's portfolio risk. Christy's
=
. Each co-worker's budget constraint is R_{P =} R_F +
σ_P, where R_j is the risk-free rate of return, R_m is the stock market rate of return, and σ_m is the stock market risk. Solve for each co-worker's optimal portfolio rate of return as a function of R_j, R_m, and σ_m.