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Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.62 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 20:55:29
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333589
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.62 Ko KB
Mis en ligne Uploaded: 21/11/2024 - 20:55:29
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 3
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4333589
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
CAPM : CAPM Regression Excess returns times 100 =100*(value time 1 / (value time 0 ) -1)- Rf Regression capm (time series regression) : = DROITEREG(Excess returns; Market factor;;VRAI) T-statistics for nullity test = Estimates / Standard errors T-statistics for test of beta = 1: Estimates 1 /Std error Correlation between excess returns : =COEFFICIENT.CORRELATION(Portfolio 1 excess return; stock excess return ) Comment written by the prof : The R2 is higher for the fund than for the individual stock, which is an example of the idiosyncratic risk reduction through diversification.Both alphas are insignificant at the 5% level, but the betas are significantly different from 0.The fact that both assets have significant exposure (beta) to the market factor and that the market factor has substantial explanatory power (though higher for the fund than for the stock) implies that the market is a "common risk factor" for the stock and the fund. The presence of this common factor, to which both assets are positively exposed, explains why the correlation between excess returns is positive (53.0%).The standard errors are also lower for the portfolio than for the stock, implying that the parameters are more precisely estimated at the portfolio level than at the individual stock level.The tests do not reject the assumption that the beta is 1, neither for the fund nor for the stock. Regression residuals : Excess return Alpha Beta * Mkt RF ( market risk premium) Correlation between residuals =COEFFICIENT.CORRELATION(Regression residual of potfolio ; Regression residual of stock ) Eliminating the influence of the market factor leaves us with a negative correlation between residuals. Alpha of a portfolio : = ORDONNEE.ORIGINE(portfolio excess return; Market factor (Mkt - RF) Beta of a portfolio : =PENTE(portfolio excess return ;Market factor (Mkt - RF)) Mean excess return : = Moyenne(EXCESS RETURN) 1. The ex-post betas (i.e., the betas estimated over the entire sample) increase as we move from low ex-ante betas to high ex-ante betas, meaning that securities with low betas over the estimation period tend to keep having low betas over the holding period. In other words, betas are rather stable out of sample.2. Within quintile portfolios, the mean excess return turns out to be increasing in the ex-post beta, which is consistent with the CAPM's prediction, but within decile portfolios, the relation between the two quantities is not as monotonic. In particular, the top 10% portfolio earns 0.83% per month, while the 9th decile group has a much higher excess return of 1.17%.Moreover, the second chart reveals that the alpha is decreasing in the beta. In other words, high beta portfolios earn less than predicted by the CAPM, while low beta portfolios earn more. This effect is known as the "beta effect" in stock returns and was analyzed in depth by Frazzini and Pedersen in 2014 ("Betting Against Beta", Journal of Financial Economics). 3.The third chart displays the t-stats for the alphas. None of them is significant at the 5% level, as evidenced by the t-stats less than 1.96 in absolute value. Betas w.r.t. tangency portfolio returns : =PENTE('Returns and Excess returns'!K4:K265;'Tangency portfolio returns'!$Y4:$Y265) When we calculate the betas of stock returns with respect to the returns of the tangency portfolio, we obtain a perfect linear relationship between the average excess returns and the betas. The R-squared is 1, the intercept is 0 and the slope equals the average excess return on the tangency portfolio. This result is always true: it can be shown that the expected excess return on a risky asset equals the beta of this asset with respect to the tangency portfolio, multiplied by the expected excess return on the tangency portfolio. This equality holds both ex-ante (in terms of expected returns) and ex-post (in terms of average returns). The CAPM predicts that the market portfolio is the tangency portfolio, hence that expected excess returns are proportional to market betas. The lack of empirical support for this prediction implies that the market portfolio (or strictly speaking, our proxy for the market portfolio) is not efficient in the mean-variance sense. Made with nCreator - tiplanet.org
>>
Compatible OS 3.0 et ultérieurs.
<<
CAPM : CAPM Regression Excess returns times 100 =100*(value time 1 / (value time 0 ) -1)- Rf Regression capm (time series regression) : = DROITEREG(Excess returns; Market factor;;VRAI) T-statistics for nullity test = Estimates / Standard errors T-statistics for test of beta = 1: Estimates 1 /Std error Correlation between excess returns : =COEFFICIENT.CORRELATION(Portfolio 1 excess return; stock excess return ) Comment written by the prof : The R2 is higher for the fund than for the individual stock, which is an example of the idiosyncratic risk reduction through diversification.Both alphas are insignificant at the 5% level, but the betas are significantly different from 0.The fact that both assets have significant exposure (beta) to the market factor and that the market factor has substantial explanatory power (though higher for the fund than for the stock) implies that the market is a "common risk factor" for the stock and the fund. The presence of this common factor, to which both assets are positively exposed, explains why the correlation between excess returns is positive (53.0%).The standard errors are also lower for the portfolio than for the stock, implying that the parameters are more precisely estimated at the portfolio level than at the individual stock level.The tests do not reject the assumption that the beta is 1, neither for the fund nor for the stock. Regression residuals : Excess return Alpha Beta * Mkt RF ( market risk premium) Correlation between residuals =COEFFICIENT.CORRELATION(Regression residual of potfolio ; Regression residual of stock ) Eliminating the influence of the market factor leaves us with a negative correlation between residuals. Alpha of a portfolio : = ORDONNEE.ORIGINE(portfolio excess return; Market factor (Mkt - RF) Beta of a portfolio : =PENTE(portfolio excess return ;Market factor (Mkt - RF)) Mean excess return : = Moyenne(EXCESS RETURN) 1. The ex-post betas (i.e., the betas estimated over the entire sample) increase as we move from low ex-ante betas to high ex-ante betas, meaning that securities with low betas over the estimation period tend to keep having low betas over the holding period. In other words, betas are rather stable out of sample.2. Within quintile portfolios, the mean excess return turns out to be increasing in the ex-post beta, which is consistent with the CAPM's prediction, but within decile portfolios, the relation between the two quantities is not as monotonic. In particular, the top 10% portfolio earns 0.83% per month, while the 9th decile group has a much higher excess return of 1.17%.Moreover, the second chart reveals that the alpha is decreasing in the beta. In other words, high beta portfolios earn less than predicted by the CAPM, while low beta portfolios earn more. This effect is known as the "beta effect" in stock returns and was analyzed in depth by Frazzini and Pedersen in 2014 ("Betting Against Beta", Journal of Financial Economics). 3.The third chart displays the t-stats for the alphas. None of them is significant at the 5% level, as evidenced by the t-stats less than 1.96 in absolute value. Betas w.r.t. tangency portfolio returns : =PENTE('Returns and Excess returns'!K4:K265;'Tangency portfolio returns'!$Y4:$Y265) When we calculate the betas of stock returns with respect to the returns of the tangency portfolio, we obtain a perfect linear relationship between the average excess returns and the betas. The R-squared is 1, the intercept is 0 and the slope equals the average excess return on the tangency portfolio. This result is always true: it can be shown that the expected excess return on a risky asset equals the beta of this asset with respect to the tangency portfolio, multiplied by the expected excess return on the tangency portfolio. This equality holds both ex-ante (in terms of expected returns) and ex-post (in terms of average returns). The CAPM predicts that the market portfolio is the tangency portfolio, hence that expected excess returns are proportional to market betas. The lack of empirical support for this prediction implies that the market portfolio (or strictly speaking, our proxy for the market portfolio) is not efficient in the mean-variance sense. Made with nCreator - tiplanet.org
>>
