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.
• Minimize portfolio variance, subject to
defined return and sum of weights equal 1.
Transpose and Multiplication
• Weights - column vector Γ (row vector ΓT)
• Returns - column vector E (row vector ET)
• Portfolio return ET Γ
• 25 stocks portfolio variance ΓTS Γ
ΓT(1x25)*S(25x25)* Γ(25x1)
• To calculate portfolio variance we need
the variance/covariance matrix S.
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).
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
variance/covariance matrix
• Offset Function → returns a reference to a range that is a
given number of rows and columns for a given reference
Single Index Model