BUSI 123 Worksheet BUSI 123: Mean-Variance Worksheet Name: 1. Suppose you are deciding how to allocate your wealth among three assets: an equity portfolio, E, with E[re] = 0.18 and o E = 0.30, a bond portfolio, B, with E[TB] = 0.08 and ob = 0.15, and a risk-free asset, F, with rp = 0.05. The correlation between the equity and bond portfolios is P=0.15. (a) Assume you decide to invest all of your money into only the risky assets E and B (who needs a risk-free asset anyway). Explicitly define and solve an optimization problem to determine a general expression (i.e. use parameters and not specific values) for the portfolio weight, wmv, of asset E in the minimum variance portfolio. Using this expression, calculate the specific value of Wmv given the values in the problem. What are E[rmu) and Omu? BUSI 123 Worksheet (b) Suppose you decide you want a specific return upi by choosing a portfolio P1, using only the two risky assets. Derive an expression for the portfolio weight of asset E, wpi. What will the weight be if you desire a return of 0.11? What is the standard deviation of Pi in this case? (c) Suppose you decide it is better to consider investing in the risk-free asset in addition to the two risky assets. Setup, but do not solve, the optimization problem that will determine the weights of the tangency portfolio. Be sure to include all relevant constraints. BUSI 123 Worksheet (d) Rather than work out the tedious algebra of the above problem, use Equation (6.10) in the book or the equation from the notes to explicitly solve for the portfolio weights of the tangency portfolio. What are the expected return and standard deviation of the tangency portfolio? (ue-ryo - (MB - rp)po E0B (6.10) (ME-rfos +(uB - rpo - (HE+MB - 21 f) po BOB WE (e) Determine the equation for the optimal CAL. What is the Sharpe Ratio of the tangency portfolio? BUSI 123 Worksheet BUSI 123: Mean-Variance Worksheet Name: 1. Suppose you are deciding how to allocate your wealth among three assets: an equity portfolio, E, with E[re] = 0.18 and o E = 0.30, a bond portfolio, B, with E[TB] = 0.08 and ob = 0.15, and a risk-free asset, F, with rp = 0.05. The correlation between the equity and bond portfolios is P=0.15. (a) Assume you decide to invest all of your money into only the risky assets E and B (who needs a risk-free asset anyway). Explicitly define and solve an optimization problem to determine a general expression (i.e. use parameters and not specific values) for the portfolio weight, wmv, of asset E in the minimum variance portfolio. Using this expression, calculate the specific value of Wmv given the values in the problem. What are E[rmu) and Omu? BUSI 123 Worksheet (b) Suppose you decide you want a specific return upi by choosing a portfolio P1, using only the two risky assets. Derive an expression for the portfolio weight of asset E, wpi. What will the weight be if you desire a return of 0.11? What is the standard deviation of Pi in this case? (c) Suppose you decide it is better to consider investing in the risk-free asset in addition to the two risky assets. Setup, but do not solve, the optimization problem that will determine the weights of the tangency portfolio. Be sure to include all relevant constraints. BUSI 123 Worksheet (d) Rather than work out the tedious algebra of the above problem, use Equation (6.10) in the book or the equation from the notes to explicitly solve for the portfolio weights of the tangency portfolio. What are the expected return and standard deviation of the tangency portfolio? (ue-ryo - (MB - rp)po E0B (6.10) (ME-rfos +(uB - rpo - (HE+MB - 21 f) po BOB WE (e) Determine the equation for the optimal CAL. What is the Sharpe Ratio of the tangency portfolio
