## Thursday, June 12, 2008

### Technique for Efficient Frontier Construction

Case 1: Short sale allowed with riskless lending & borrowing

- Purpose: to find tangent point A/tangency portfolio

- Technique: maximize the slope of the straight line RfA

- Find the weight of tangency portfolio

- Calculate expected return and standard deviation

- Plot the straight line RfA

Case 2: Short sale allowed with no riskless lending & borrowing

- Purpose: to find tangent point A/tangency portfolios at different risk free rate Rf to construct the frontier curve.

- Technique: find different tangent points at different Rf and plot the curve based on these tangent points

- Find the weight of tangency portfolio

- Calculate expected return and standard deviation

- Repeat these 2 steps when changing Rf by copying formula in Excel

- Plot the curve

Case 3: Short sale not allowed with riskless lending & borrowing

- Purpose: to find tangent point A/tangency portfolio

- Technique: maximize the slope of the straight line RfA

- Find the weight, expected return and standard deviation of tangency portfolio by using Solver with quadratic programming

- Plot the straight line RfA

Case 4: Short sale not allowed with no riskless lending & borrowing

- Purpose: to find tangent point A/tangency portfolios at different risk free rate Rf to construct the frontier curve.

- Technique: minimize the risk for any level of expected return to find different tangent points at different Rf and plot the curve based on these tangent points

- Find the weight of tangency portfolio, expected return and std by using Solver with quadratic programming

- Repeat this step when changing expected returns by writing a VBA program to repeat Solver

- Plot the curve