**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

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