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Calculating the Variance –Covariance matrix . MGT 4850 Spring 2008 University of Lethbridge. Efficient Portfolios. Efficient frontier Black (1972) – convex combination of any two efficient portfolios, e.g. if we have two efficient portfolios we can find the whole efficient frontier.

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Calculating the Variance –Covariance matrix

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Calculating the variance covariance matrix l.jpg

Calculating the Variance –Covariance matrix

MGT 4850

Spring 2008

University of Lethbridge


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Efficient Portfolios

  • Efficient frontier

  • Black (1972) – convex combination of any two efficient portfolios, e.g. if we have two efficient portfolios we can find the whole efficient frontier.

  • Minimize portfolio variance, subject to defined return and sum of weights equal 1.


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Transpose and Multiplication

  • Weights - column vector Γ (row vector ΓT)

  • Returns - column vector E (row vector ET)

  • Portfolio return ET Γ

  • 25 stocks portfolio varianceΓTSΓ

    ΓT(1x25)*S(25x25)* Γ(25x1)

  • To calculate portfolio variance we need the variance/covariance matrix S.


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variance/covariance matrix

  • Using Excess Returns

  • Return data for variance-covariance p. 151

  • Excess return matrix R and its transpose RT for the calculation of S matrix

  • RT R/10 → S (p. 153-154).


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VBA (skip for now)

Function VarCovar(rng As Range) As Variant

Dim i As Integer

Dim j As Integer

Dim numCols As Integer

numCols = rng.Columns.Count

Dim matrix() As Double

ReDim matrix(numCols - 1, numCols - 1)

For i = 1 To numCols

For j = 1 To numCols

matrix(i - 1, j - 1) = Application.WorksheetFunction.Covar(rng.Columns(i), rng.Columns(j))

Next j

Next i

VarCovar = matrix

End Function


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variance/covariance matrix

  • Offset Function → returns a reference to a range that is a given number of rows and columns for a given reference


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Single Index Model


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