[PDF] [PDF] Efficient Portfolios in Excel Using the Solver and Matrix Algebra

24 nov 2009 · In this note we show how it can be used to find portfolios that minimize risk subject to certain constraints The solver add-in must be activated 



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insbyclickingontheoffice menu.

MatrixAlgebrainExcel

functionsarelistedintablebelow

ArrayFunctionDescription

MINVERSEComputeinverseofmatrix

MMULTMatrixmultiplication

TRANSPOSEComputetransposeofmatrix

ExampleData

shotbelow. highlighted rangesinarrayformulas.

TheGlobalMinimumVariancePortfolio

2 min s.t. 1 pm 6 m mm m1 portfolio.Asimpleguessfor thisvectorwhoseweightssumtooneis

0.3, 0.3, 0.4.

msft nord sbux mmm 2 ,pm mm.Noticethat needacelltocontainaformulathatwillbe 1. msft nord sbux mmmm1

ThisformulaisspecifiedincellE10as

=SUM(mvec) wemustspecifythecells byclickingtheAddbutton,whichopenstheAdd

Constraintdialogueboxshowbelow.

1. msft nord sbux oneshownbelow. seethefollowingdialoguebox theKeepSolverSolutionoption formula ,pm m.TheExcelarrayformulais {=MMULT(TRANSPOSE(mvec),muvec)} F10. 0 solvestheoptimizationproblem 2 ,0 min s.t. and 1 pyy

6 yy y y1

Asimpleguessforthisvector

whoseweightssumtooneis

0.3, 0.3, 0.4.

msft nord sbux yyyThecellcontainingtheformulafor portfoliovariance, 2 ,py ,0py c y,andthattheportfolio weightssumtoone, 1. msft nord sbux msft nord sbux yyyy1, andthesecondoneimposes ,0

0.0475

py msft y.Torunthesolver,clicktheSolve below.

Theefficientportfoliohasweights

0.83, 0.09, 0.26.

msft nord sbux yy y NoticethatNordstromis (seecellC3).

1. Efficientportfolio1:globalminimumvariance

portfolio

2. Efficientportfolio2:efficientportfoliowithtargetexpectedreturnequaltothehighestaverage

returnamongtheassetsunderconsideration. equaltotheaveragereturn onMicrosoft. (1 ) quotesdbs_dbs19.pdfusesText_25