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# BerkDEkap11 - Forventet afkast af en porteflje I vrdi af...

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Forventet afkast af en porteflLje I PorteflLjev&gt= v&rdi af investering i totaLe v&rdi af investeringen R p = n i = 1 x i & R i E [ R p ] = E [ n i = 1 x i & R i ] = n i = 1 E [ x i & R i ] = n i = 1 x i & E [ R i ] Hans SommerfeLdt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 1 / 24

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Volatilitet af en to-aktie portefLlje I Hvilken risiko har de to aktier til f&lles og hvordan kan den statistisk beskrives? Kombinationer af risici: Hans Sommerfeldt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 2 / 24
Volatilitet af en to-aktie portefLlje II Bestemmelse af kovarians og korrelation: Hans Sommerfeldt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 3 / 24

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Volatilitet af en to-aktie portefLlje III Kovarians og korrelation m&ler samvariationen i afkastene. Cov ( R i , R j ) = E [( R i & E [ R i ]) ± ( R j & E [ R j ])] Estimation ud fra historiske data: Cov ( R i , R j ) = 1 T & 1 n t = 1 & R i , t & R i ± ± & R j , t & R j ± vanskeligt at fortolke stLrrelsen, derfor i stedet: Corr( R i , R j ) = Cov ( R i , R j ) SD ( R i ) ± SD ( R j ) Hans Sommerfeldt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 4 / 24
Volatilitet af en to-aktie portefLlje IV Beregning af portefLljens varians og volatilitet: To-aktie portefLlje: R P = x 1 & R 1 + x 2 & R 2 Hans Sommerfeldt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 5 / 24

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Volatilitet af en to-aktie portefLlje V Var [ R P ] = Cov [ R P , R P ] [ R P ] = Cov [ x 1 & R 1 + x 2 & R 2 , x 1 & R 1 + x 2 & R 2 ] ved brug af fodnote 2 p. 330 f&r vi [ R P ] = x 1 & x 1 & cov ( R 1 , R 1 ) + x 1 & x 2 & cov ( R 1 , R 2 ) + x 2 & x 1 & cov ( R 2 , R 1 ) + x 2 & x 2 & cov ( R 2 , R 2 ) [ R P ] = x 2 1 & ( R 1 ) + 2 & x 1 & x 2 & cov ( R 1 , R 2 ) + x 2 2 & ( R 2 ) SD [ R P ] = p [ R P ] [ R P ] = x 2 1 & SD ( R 1 ) 2 + 2 & x 1 & x 2 & corr ( R 1 , R 2 ) & SD ( R 1 ) & SD ( R 2 ) + x 2 2 & SD ( R 2 ) 2 Max. varians hvis perfekt positiv korrelation lig +1 Hans Sommerfeldt Department of Business Studies Kap.11 Berk DeMarzo: Optimalt portefLljevalg 6 / 24
Volatilitet af en stLrre portefLlje I R P = n i = 1 x i & R i Var [ R P ] = Cov ( R P , R P ) = Cov ( n i = 1 x i & R i , R P ) = n i = 1 x i & Cov ( R i , R P ) Dvs. PortefLljevariansen er et vejet gns. af kovariansen af hver aktie med portefLljen [ R P ] = n i = 1 x i & Cov ( R i , n i = 1 x i & R i ) [ R P ] = i j x i & x j & Cov ( R

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BerkDEkap11 - Forventet afkast af en porteflje I vrdi af...

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