Portfolio theory

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

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)

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Portfolios: 2 assets Mean: Variance:

Portfolios: n assets Mean: Variance: Covariance:

Portfolios of 4 assets

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

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

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

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