Mean-Variance Optimization with Risky Assets
DownloadTélécharger
Actions
Vote :
ScreenshotAperçu
Informations
Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.97 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:23:15
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333681
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 1.97 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 21:23:15
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333681
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
Consider the optimization program max 50 55] subject to 5025Ï = 1 and 525] d 52 Then, for every target volatility 5, the optimal portfolio is a weighted average of two portfolios (a.k.a. mutual funds) that are independent of the target: 50 = 5e(5)501 + [1 5e(5)] 502 Only the relative allocation 5e(5) depends on the target volatility. ¶ This result is one of the many mutual fund theorems in finance. ¶ First references: Cass and Stiglitz (1970); Merton (1972). ¶ If we know the compositions 501 and 502, we can calculate the optimal portfolio for any target volatility without re-doing optimization. Consider the optimization program max 50 55] subject to 5025Ï = 1 and 52 5] d 52 Let 5N = 5Ï25º15Ï, 5O = 5Ï25º15Í, 5P = 5Í25º15Í and make the following technical assumptions: 1. The covariance matrix 5º is non singular; 2. The target variance satisfies 52 e 1/5N; 3. The expected returns in 5Í are not equal across constituents. Then, the unique solution to the program is given by 50 = 5O5 5º15Í /5Ï25º15Í + [1 5O5] 5º15Ï /5Ï25º15Ï where 5 is the risk tolerance parameter, given by 5 = 5N52 1 /5N5P 5O2 If the covariance matrix 5º is non-singular, the GMV portfolio is given by 50gmv = 5º15Ï / 5Ï25º15Ï Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
Consider the optimization program max 50 55] subject to 5025Ï = 1 and 525] d 52 Then, for every target volatility 5, the optimal portfolio is a weighted average of two portfolios (a.k.a. mutual funds) that are independent of the target: 50 = 5e(5)501 + [1 5e(5)] 502 Only the relative allocation 5e(5) depends on the target volatility. ¶ This result is one of the many mutual fund theorems in finance. ¶ First references: Cass and Stiglitz (1970); Merton (1972). ¶ If we know the compositions 501 and 502, we can calculate the optimal portfolio for any target volatility without re-doing optimization. Consider the optimization program max 50 55] subject to 5025Ï = 1 and 52 5] d 52 Let 5N = 5Ï25º15Ï, 5O = 5Ï25º15Í, 5P = 5Í25º15Í and make the following technical assumptions: 1. The covariance matrix 5º is non singular; 2. The target variance satisfies 52 e 1/5N; 3. The expected returns in 5Í are not equal across constituents. Then, the unique solution to the program is given by 50 = 5O5 5º15Í /5Ï25º15Í + [1 5O5] 5º15Ï /5Ï25º15Ï where 5 is the risk tolerance parameter, given by 5 = 5N52 1 /5N5P 5O2 If the covariance matrix 5º is non-singular, the GMV portfolio is given by 50gmv = 5º15Ï / 5Ï25º15Ï Made with nCreator - tiplanet.org
>>
