Question

As a portfolio manager, you are considering three mutual funds: a stock fund, a bond fund, and a money market bond that yields a sure rate of         2.45           %. Below is the information concerning the two risky funds: (Total 50 points)

	Expected return	Standard deviation
Stock fund	0.22	0.56
Bond fund	0.06	0.25

The correlation between fund returns is     0.26­­     .

1. Find the weights of the minimum-variance portfolio and calculate its expected return and its standard deviation. Show all work. (You can use Solver to verify your solution, but you need to present formulas with plugged-in numbers to receive full credit.) (12 points)

ω_mv(stocks)=

ω_mv(bonds)=

E_mv =­­­

σ_mv =

2. Calculate the weights of the optimal risky portfolio and compute its expected return and standard deviation. You can use Solver to compute the optimal weights. To receive full credit, show the formulas with plugged-in numbers only for the expected return and standard deviation. (12 points)

ω_op(stocks)=

ω_op(bonds)=

E_op =

σ_op =

3. Using the obtained valued from previous two steps, show on the graph in the space provided: (a) efficient frontier, (b) optimal risky portfolio, (c) risk-free asset, (d) capital allocation line, (e) minimum variance portfolio. Don’t worry about scaling properly. Make sure to label the axes, as well as corresponding values for expected returns and standard deviations. (7 points)

Answer 1

1. Give 50% weight to both stock fund and bond fund

2. Open solver and set the conditions

Optimal Portfolio

Wmv(stocks) = 73.12%

Wmv(bonds) = 26.88%

Expected return = 17.70%

Standard deviation = 43.19%