DERNIER ACTIVIT2 EXCEL CAPM EXPECTED RETURN
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.75 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:09:47
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333641
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.75 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:09:47
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 1
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333641
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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CAPM expect return activity : (semblable a la question donné dans les samples questions) : Risk analysis : Market factor volatility : =RACINE(SOMMEPROD(weights;PRODUITMAT(covariance matrix; weights))) Systematic variance A : =Betas A ^2 * Market factor volatility ^2 Idiosyncratic volatilities : =RACINE(VolatitéA ^2- Systematic variance A) Systematic covariance matrix : =Market factor volatility ^2*PRODUITMAT(Betas (A,B,C);TRANSPOSE(Betas (A,B,C))) Idiosyncratic covariance matrix : DANS CHAQUE CELLULE : = Sample covariance matrix (already given by the exercice, the classical covariance matrix) - Systematic covariance matrix Idiosyncratic variance of market portfolio : =SOMMEPROD (weights column ;PRODUITMAT(Idiosyncratic covariance matrix; weights column)) Idiosyncratic volatility matrix : Dans les diagonnales valeur de Idiosyncratic volatilities A puis B puis C Correlation matrix of residuals : =PRODUITMAT(INVERSEMAT(Idiosyncratic volatility matrix);PRODUITMAT(Idiosyncratic covariance matrix ;INVERSEMAT(Idiosyncratic volatility matrix))) Alpha A : epected excess return A Beta A * Market risk premium Efficient frontier : slope : Market Factor volatilité / Market risk prenium Maximum expected excess return = Target volatility(volatilité already given dans lexo) * slope of efficient frontier (ligne avant) Commentaire du prof : The market portfolio has zero idiosyncratic variance by definition, so we can verify that we have the correct idiosyncratic covariance matrix by checking that the idiosyncratic variance of the market portfolio, w_m^' £_µ w_m is zero. The residuals of different assets have non-zero correlations because the variance of the residual of the market portfolio is equal to 0. To see this, note that the residual of the market portfolio is the weighted sum of the individual residuals (N=3 here), _(i=1)^N( n en haut)w_(m,i) µ_i, so that the variance of the portfolio residual is _(i,j=1)^N( n en haut)w_(m,i) w_(m,j) Cov[µ_i,µ_j ], which we can decompose as _(i=1)^N( n en haut) w_(m,i)^2 V[µ_i ]+_(i,j=1, i`j)^N( n en haut) w_(m,i) w_(m,j) Cov[µ_i,µ_j ]. But as we have seen previously, the market portfolio has zero idiosyncratic variance, so this sum must be zero. The first sum in the above expression is clearly positive, so the second sum must be negative. Because the market portfolio weights are positive, it follows that the covariances between the residuals of different assets must be negative on average. Overall, the reason why the residuals cannot be uncorrelated across assets is that the common risk factor is "endogenous" to the investment universe, i.e., it is the excess return on a portfolio made of the investable assets. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
CAPM expect return activity : (semblable a la question donné dans les samples questions) : Risk analysis : Market factor volatility : =RACINE(SOMMEPROD(weights;PRODUITMAT(covariance matrix; weights))) Systematic variance A : =Betas A ^2 * Market factor volatility ^2 Idiosyncratic volatilities : =RACINE(VolatitéA ^2- Systematic variance A) Systematic covariance matrix : =Market factor volatility ^2*PRODUITMAT(Betas (A,B,C);TRANSPOSE(Betas (A,B,C))) Idiosyncratic covariance matrix : DANS CHAQUE CELLULE : = Sample covariance matrix (already given by the exercice, the classical covariance matrix) - Systematic covariance matrix Idiosyncratic variance of market portfolio : =SOMMEPROD (weights column ;PRODUITMAT(Idiosyncratic covariance matrix; weights column)) Idiosyncratic volatility matrix : Dans les diagonnales valeur de Idiosyncratic volatilities A puis B puis C Correlation matrix of residuals : =PRODUITMAT(INVERSEMAT(Idiosyncratic volatility matrix);PRODUITMAT(Idiosyncratic covariance matrix ;INVERSEMAT(Idiosyncratic volatility matrix))) Alpha A : epected excess return A Beta A * Market risk premium Efficient frontier : slope : Market Factor volatilité / Market risk prenium Maximum expected excess return = Target volatility(volatilité already given dans lexo) * slope of efficient frontier (ligne avant) Commentaire du prof : The market portfolio has zero idiosyncratic variance by definition, so we can verify that we have the correct idiosyncratic covariance matrix by checking that the idiosyncratic variance of the market portfolio, w_m^' £_µ w_m is zero. The residuals of different assets have non-zero correlations because the variance of the residual of the market portfolio is equal to 0. To see this, note that the residual of the market portfolio is the weighted sum of the individual residuals (N=3 here), _(i=1)^N( n en haut)w_(m,i) µ_i, so that the variance of the portfolio residual is _(i,j=1)^N( n en haut)w_(m,i) w_(m,j) Cov[µ_i,µ_j ], which we can decompose as _(i=1)^N( n en haut) w_(m,i)^2 V[µ_i ]+_(i,j=1, i`j)^N( n en haut) w_(m,i) w_(m,j) Cov[µ_i,µ_j ]. But as we have seen previously, the market portfolio has zero idiosyncratic variance, so this sum must be zero. The first sum in the above expression is clearly positive, so the second sum must be negative. Because the market portfolio weights are positive, it follows that the covariances between the residuals of different assets must be negative on average. Overall, the reason why the residuals cannot be uncorrelated across assets is that the common risk factor is "endogenous" to the investment universe, i.e., it is the excess return on a portfolio made of the investable assets. Made with nCreator - tiplanet.org
>>
