Capm Cours PCTTT
DownloadTélécharger
Actions
Vote :
ScreenshotAperçu
Informations
Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 7.63 Ko KB
Mis en ligne Uploaded: 22/11/2024 - 05:49:14
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4334771
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 7.63 Ko KB
Mis en ligne Uploaded: 22/11/2024 - 05:49:14
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4334771
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
The Capital Asset Pricing Model (CAPM) was developed by Sharpe (1964), Lintner (1965) and Mossin (1966) and is a theory of how asset prices form in the market. ¶ It is predicated on two key assumptions: ¶ Rationality: investors pick optimal portfolios. ¶ Market equilibrium: supply equals demand for all assets. ¶ The CAPM builds on the mean-variance portfolio selection model with a risk-free asset. ¶ Its central prediction is that the expected return on any asset depends on its risk, measured as the exposure (beta) to market movements, rather than the volatility. Assumptions: 1. Markets are frictionless (no taxes, no transaction costs, divisible assets). 2. Short sales are permitted with no restriction. 3. Unlimited borrowing and lending at the same risk-free rate is permitted. 4. All investors face the same investment universe. 5. Investors invest for one period, the same for all, and they have buy-and-hold portfolios. 6. Investors have mean-variance preferences. 7. Investors have identical beliefs about expected returns and covariances. 8. Market is in equilibrium: demand equals supply for every security. ¶ Under these conditions, investors differ only through their risk tolerance and their current wealth. ¶ The CAPM derives the asset pricing implications of these stylizing assumptions. If investors have the same beliefs, they all see the same efficient frontier and hold the same tangency portfolio. The mix between the tangency portfolio and the risk-free asset depends on risk tolerance. ¶ What is the common tangency portfolio? The Market Portfolio Definition The market portfolio consists of all risky assets available for investment, weighted by their market capitalization. ¶ This includes at least all financial assets available for public trading (stocks, bonds, real estate...). ¶ The status of non-financial and/or non-tradable assets is less clear (see e.g. Mayers (1973) and Fama and French (2004)): ¶ Human capital, i.e. claims to future labor income? ¶ Claims to government transfers like Social Security? ¶ These claims do not have observable market prices, so they are difficult to consider in empirical work. ¶ The market portfolio is most often proxied as a broad cap-weighted portfolio of stocks. Prediction 1: The Market Portfolio is Efficient CAPM Prediction 1 (Efficiency of Market Portfolio) Under the CAPMs assumptions, the market portfolio is the common tangency portfolio for all investors. ¶ By the two-fund separation theorem, it follows that all investors hold a mixture of the market portfolio and the risk-free asset. Under the CAPMs assumptions, the efficient frontier with a risk-free asset is the Capital Market Line (CML), whose intercept is the risk-free rate (5E5S ) and whose slope is the Sharpe ratio of the market portfolio (55Z). ¶ The CML is tangent to the the efficient frontier with risky assets only. Investor 1 holds long positions in the market portfolio and the risk-free asset, while Investor 2 has a leveraged position in the market portfolio. (illustration ou les deux sont sur la CML l'investiseur 1 est plus proche de l'axe des ordonnés que l'investisseur deux . Prediction 2: Expected Excess Returns are Proportional to Market Betas CAPM Prediction 2 (Expected Return - Covariance Relationship) Under the CAPMs assumptions, the expected excess return over the risk-free rate of any asset is proportional to the covariance of its excess return with the excess return on the market portfolio: 55V 5E5S = 55V5Z × (55Z 5E5S) /525Z 55Z 5E5S = expected excess return on market portfolio; 525Z = variance of excess returns on the market portfolio; 55V5Z = covariance between excess returns of asset 5V and market portfolio The market factor, defined as the excess return on the market portfolio, is said to be a pricing factor. ¶ More generally, a pricing factor is any factor 59 such that all expected excess returns have the form 55V 5E5S = 55V59 ×( / 5259) for some constant factor premium , where 55V59 is the covariance between asset 5V and the factor. ¶ In fact, finding a pricing factor is equivalent to searching for the tangency portfolio because: ¶ The excess return on the tangency portfolio is always a pricing factor; ¶ If the excess return on a portfolio of risky assets acts a pricing factor, this portfolio is the tangency portfolio. ¶ Therefore, Predictions 1 and 2 are equivalent propositions. Market Beta : Definition: : The market beta of asset 5V is defined as 5ý5V = ov [5_5V 5E5S , 5_5Z 5E5S ] / 5M [5_5Z 5E5S ] 5_5V = return on asset 5V; 5_5Z = return on market portfolio; 5E5S = risk-free rate ¶ The beta is a measure of exposure to market risk. ¶ The expected return - covariance relationship can be rewritten as 55V 5E5S = 5ý5V × [55Z 5E5S ] Beta As a Regression Slope ¶ The market beta is also the slope in a regression of the excess returns on asset 5V on the excess returns on the market portfolio : 5_5V 5E5S = 5ü5V + 5ý5V[5_5Z 5E5S ] + 5 5V 5ü5V = interc
[...]
>>
Compatible OS 3.0 et ultérieurs.
<<
The Capital Asset Pricing Model (CAPM) was developed by Sharpe (1964), Lintner (1965) and Mossin (1966) and is a theory of how asset prices form in the market. ¶ It is predicated on two key assumptions: ¶ Rationality: investors pick optimal portfolios. ¶ Market equilibrium: supply equals demand for all assets. ¶ The CAPM builds on the mean-variance portfolio selection model with a risk-free asset. ¶ Its central prediction is that the expected return on any asset depends on its risk, measured as the exposure (beta) to market movements, rather than the volatility. Assumptions: 1. Markets are frictionless (no taxes, no transaction costs, divisible assets). 2. Short sales are permitted with no restriction. 3. Unlimited borrowing and lending at the same risk-free rate is permitted. 4. All investors face the same investment universe. 5. Investors invest for one period, the same for all, and they have buy-and-hold portfolios. 6. Investors have mean-variance preferences. 7. Investors have identical beliefs about expected returns and covariances. 8. Market is in equilibrium: demand equals supply for every security. ¶ Under these conditions, investors differ only through their risk tolerance and their current wealth. ¶ The CAPM derives the asset pricing implications of these stylizing assumptions. If investors have the same beliefs, they all see the same efficient frontier and hold the same tangency portfolio. The mix between the tangency portfolio and the risk-free asset depends on risk tolerance. ¶ What is the common tangency portfolio? The Market Portfolio Definition The market portfolio consists of all risky assets available for investment, weighted by their market capitalization. ¶ This includes at least all financial assets available for public trading (stocks, bonds, real estate...). ¶ The status of non-financial and/or non-tradable assets is less clear (see e.g. Mayers (1973) and Fama and French (2004)): ¶ Human capital, i.e. claims to future labor income? ¶ Claims to government transfers like Social Security? ¶ These claims do not have observable market prices, so they are difficult to consider in empirical work. ¶ The market portfolio is most often proxied as a broad cap-weighted portfolio of stocks. Prediction 1: The Market Portfolio is Efficient CAPM Prediction 1 (Efficiency of Market Portfolio) Under the CAPMs assumptions, the market portfolio is the common tangency portfolio for all investors. ¶ By the two-fund separation theorem, it follows that all investors hold a mixture of the market portfolio and the risk-free asset. Under the CAPMs assumptions, the efficient frontier with a risk-free asset is the Capital Market Line (CML), whose intercept is the risk-free rate (5E5S ) and whose slope is the Sharpe ratio of the market portfolio (55Z). ¶ The CML is tangent to the the efficient frontier with risky assets only. Investor 1 holds long positions in the market portfolio and the risk-free asset, while Investor 2 has a leveraged position in the market portfolio. (illustration ou les deux sont sur la CML l'investiseur 1 est plus proche de l'axe des ordonnés que l'investisseur deux . Prediction 2: Expected Excess Returns are Proportional to Market Betas CAPM Prediction 2 (Expected Return - Covariance Relationship) Under the CAPMs assumptions, the expected excess return over the risk-free rate of any asset is proportional to the covariance of its excess return with the excess return on the market portfolio: 55V 5E5S = 55V5Z × (55Z 5E5S) /525Z 55Z 5E5S = expected excess return on market portfolio; 525Z = variance of excess returns on the market portfolio; 55V5Z = covariance between excess returns of asset 5V and market portfolio The market factor, defined as the excess return on the market portfolio, is said to be a pricing factor. ¶ More generally, a pricing factor is any factor 59 such that all expected excess returns have the form 55V 5E5S = 55V59 ×( / 5259) for some constant factor premium , where 55V59 is the covariance between asset 5V and the factor. ¶ In fact, finding a pricing factor is equivalent to searching for the tangency portfolio because: ¶ The excess return on the tangency portfolio is always a pricing factor; ¶ If the excess return on a portfolio of risky assets acts a pricing factor, this portfolio is the tangency portfolio. ¶ Therefore, Predictions 1 and 2 are equivalent propositions. Market Beta : Definition: : The market beta of asset 5V is defined as 5ý5V = ov [5_5V 5E5S , 5_5Z 5E5S ] / 5M [5_5Z 5E5S ] 5_5V = return on asset 5V; 5_5Z = return on market portfolio; 5E5S = risk-free rate ¶ The beta is a measure of exposure to market risk. ¶ The expected return - covariance relationship can be rewritten as 55V 5E5S = 5ý5V × [55Z 5E5S ] Beta As a Regression Slope ¶ The market beta is also the slope in a regression of the excess returns on asset 5V on the excess returns on the market portfolio : 5_5V 5E5S = 5ü5V + 5ý5V[5_5Z 5E5S ] + 5 5V 5ü5V = interc
[...]
>>
