Download presentation
Presentation is loading. Please wait.
Published byJack McDaniel Modified over 9 years ago
1
Portfolio Statistics Portfolio Expected Return: E(r p ) = w T r Portfolio Variance: 2 p = w T w Sum of portfolio weights: = w T 1 –where w is a 1xn vector (column) of weights, –r is a 1xn vector of expected return on the n assets, – is a nxn matrix containing the variances and covariances –1 is a 1xn vector of ones w T is the transpose of w Note that the resulting portfolio expected return E(r p ), portfolio variance ( 2 p ) and sum of portfolio weights are all scalars.
2
Matrix Functions in Excel
3
Scalar versus Matrix Scalar is a single cell –As long as the end result is a scalar, the formula will be treated as a scalar even if the intermediate calculations involve matrices. Matrix is an array (range) –Both vectors and matrices are considered Matrix by Excel –Entering formulas for an array Select the range with the proper dimension Type formula Press Ctrl+Shift+Enter
4
Excel Matrix Functions SUMPRODUCT(array1,array2..array30) –Arrays must be of the same dimension but can be row or column vectors –This function is useful whenever you need to computed a weighted average –You can get the same result using SUM(array1*array2) entered as an array, i.e. Ctrl+Shift+Enter. MMULT(x,y) –X and Y must be conforming in dimensions (consistent) MINVERSE(x) –Returns the inverse of a matrix MDETERM(x) –Returns the determinant of a matrix
5
Other Related Excel Functions SUMSQ(array1,array2..)
6
Review Materials for Matrix Algebra http://www.mathphysics.com/spingarn/lane/ http://www.mathphysics.com/spingarn/lane/ http://planetmath.org/encyclopedia/MatrixOperations.html http://planetmath.org/encyclopedia/MatrixOperations.html
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.