1. Portfolio theory

2. DESCRIPTIVE STATISTICS
From prices to returns
Mean => =AVERAGE(X)
Variance => =VARP(X)
Standard deviation => =STDEVP(X)

3. Covariance and correlation
Degree to which the returns on the two assets move together:
Covariance => =COVAR(X;Y)
Degree of linear relation between reurns:
Correlation => =CORREL(X;Y) (unit-free)

4. Add Trendline

5. Portfolios: 2 assets
Mean:
Variance:

6. Portfolios: n assets
Mean:
Variance:
Covariance:

7. Portfolios of 4 assets

8. Variance-Covariance matrix
Additional returns Matrix:
n=number of assets
m=number observations
Variance covariance matrix:

9. Minimun variance portfolios
Every portfolio on the minimum variance frontier:
R – c = S * z
R = vector of E(Ri)
c = constant
S = variance-covariance matrix
z = portfolio components

10. Minimum variance portfolios
x = normalized portfolio components:
Select two values for c (correspond to two portfolios):
z = S-1 * ( R – c )
compute xi

11. WHEN c = rf, THE ENVELOPE PORTFOLIO IS THE MARKET PORTFOLIO M