Portfolio moments COUR 2 PCT
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Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.95 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:19:24
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333670
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.95 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:19:24
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333670
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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DEFINITION : The expectation (mean) of a random variable is the mean of outcomes weighted by probabilities. 5<[5_] The variance of a random variable 5_ is the expected squared difference between 5_ and its mean: 5M[5_] = 5< [[5_ 5<[5_]]2] The covariance between two random variables 5_1 and 5_2 is ov [5_1, 5_2] = 5< [[5_1 5<[5_1]] [5_2 5<[5_2]]] ¶ Covariance is a measure of the intensity of the comovement between two random variables. ¶ Covariance is symmetric with respect to the inputs: ov [5_1, 5_2] = ov [5_2, 5_1] ¶ The covariance of a random variable with itself equals its variance: ov[5_, 5_] = 5M[5_] ¶ In mean-variance optimization, we consider a single investment period ranging from time 0 to time 1 with buy-and-hold portfolios. ¶ The return on a portfolio 5] is given by 5_0,1,5] = 5d0,15_0,1,1 + 5d0,25_0,1,2 + ï + 5d0,5A5_0,1,5A ¶ We drop the time subscripts 0 and 1 for notational simplicity. Therefore, 5_5] = 5d15_1 + 5d25_2 + ï + 5d5A5_5A If a portfolio is buy-and-hold over the investment period, its expected return is the inner product of the vector of weights and the vector of constituents expected returns: 55] = 5025Í The variance of a 2-asset portfolio / ¶A negative covariance reduces the portfolio variance. ¶ A positive covariance increases the portfolio variance. The variance of a portfolio invested in assets with covariance matrix 5º with the percentage weights 50 is 525] = 5025º50 Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
DEFINITION : The expectation (mean) of a random variable is the mean of outcomes weighted by probabilities. 5<[5_] The variance of a random variable 5_ is the expected squared difference between 5_ and its mean: 5M[5_] = 5< [[5_ 5<[5_]]2] The covariance between two random variables 5_1 and 5_2 is ov [5_1, 5_2] = 5< [[5_1 5<[5_1]] [5_2 5<[5_2]]] ¶ Covariance is a measure of the intensity of the comovement between two random variables. ¶ Covariance is symmetric with respect to the inputs: ov [5_1, 5_2] = ov [5_2, 5_1] ¶ The covariance of a random variable with itself equals its variance: ov[5_, 5_] = 5M[5_] ¶ In mean-variance optimization, we consider a single investment period ranging from time 0 to time 1 with buy-and-hold portfolios. ¶ The return on a portfolio 5] is given by 5_0,1,5] = 5d0,15_0,1,1 + 5d0,25_0,1,2 + ï + 5d0,5A5_0,1,5A ¶ We drop the time subscripts 0 and 1 for notational simplicity. Therefore, 5_5] = 5d15_1 + 5d25_2 + ï + 5d5A5_5A If a portfolio is buy-and-hold over the investment period, its expected return is the inner product of the vector of weights and the vector of constituents expected returns: 55] = 5025Í The variance of a 2-asset portfolio / ¶A negative covariance reduces the portfolio variance. ¶ A positive covariance increases the portfolio variance. The variance of a portfolio invested in assets with covariance matrix 5º with the percentage weights 50 is 525] = 5025º50 Made with nCreator - tiplanet.org
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