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Catégorie :Category: nCreator TI-Nspire
Auteur Author: SPITZER2001
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.99 Ko KB
Mis en ligne Uploaded: 22/11/2024 - 08:34:15
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4335099
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 2.99 Ko KB
Mis en ligne Uploaded: 22/11/2024 - 08:34:15
Uploadeur Uploader: SPITZER2001 (Profil)
Téléchargements Downloads: 2
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a4335099
Description
Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
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Question 1 Write the mathematical formula for the return on a buy-and-hold and equally weighted portfolio invested in N constituents, in terms of the constituents' returns. The portfolio return is the weighted average of constituents returns, which is an equally weighted average here because constituents are equally weighted: 5_5] = 5_1 + 5_2 + ï + 5_5A /N Question 2 Write the mathematical formula for the variance of a portfolio invested in 3 assets, in terms of the asset variances and covariances. Then, rewrite the formula in the special case where the covariances are zero and the variances are equal. 525] = 5d12 52 + 5d22 52 + 5d32 52, which we can rewrite in a more compact form as 525] = [5d12 + 5d22 + 5d32 ] 52 Question 3 A portfolio of risky assets has an expected excess return (over the risk-free rate) of 7%, a volatility of 11% and a market beta of 1.05. If you take a leveraged position of 120% in this portfolio by borrowing 20% of your current assets in the risk-free asset, what are the expected excess return and the volatility of your portfolio? f51 is the expected excess return on the portfolio of risky assets, then the expected excess return on the leveraged portfolio with a percentage allocation 5e to the risky portfolio is 52 = 5e51 522 = [5e501]25º[5e501] = 5e250215º501 = 5e2512 Question 4 The tangency portfolio has a volatility of 18%. If you have a target volatility at 20%, what percentages of your assets should you optimally allocate to the tangency portfolio and the risk-free asset? By the two-fund separation theorem with a risk-free asset, the optimal percentage allocation to the tangency portfolio is 5/5tan, where 5 is the target volatility and 5tan is the volatility of the tangency portfolio. Therefore, the optimal allocation to the tangency portfolio is 20/18 H 111.1%, and the optimal allocation to the risk-free asset is 1 20/18 H 11.1% Question 5 What is the CAPM-implied expected excess return of an asset with a volatility of 14% and a market beta of 0.98, if the market risk premium (i.e., the expected excess return on the market portfolio) is 7%?55V = 5ý5V × 55Z, Question 6 If the market alpha of a portfolio is estimated to be -0.05 with a standard error of 0.021, is the alpha statistically significant (at the usual confidence level)? Does this result support or invalidate the CAPM? 5a [5ü] = 5ü /SE [5ü] The absolute value of the t-statistic is greater than 1.96, so the alpha is statistically significant at the usual 95% confidence level, i.e., we reject the null hypothesis that the true alpha is zero. But the CAPM implies that the true alpha should be zero. Therefore, this result provides evidence against the CAPM. We assume that the investment universe contains a risk-free asset. The risk aversion parameter gamma for an investor is defined in such a way that the optimal vector of weights in the risky assets is given by w = 1 / gama (y) le tout foit matrice de covariance invers fois mutilda (expected execs return) where capital sigma denotes the covariance matrix and mu with tilde on top is the vector of expected excess returns. Give an expression of the risk aversion parameter in terms of the investor's target volatility and capital sigma and mu with tilde on top Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
Question 1 Write the mathematical formula for the return on a buy-and-hold and equally weighted portfolio invested in N constituents, in terms of the constituents' returns. The portfolio return is the weighted average of constituents returns, which is an equally weighted average here because constituents are equally weighted: 5_5] = 5_1 + 5_2 + ï + 5_5A /N Question 2 Write the mathematical formula for the variance of a portfolio invested in 3 assets, in terms of the asset variances and covariances. Then, rewrite the formula in the special case where the covariances are zero and the variances are equal. 525] = 5d12 52 + 5d22 52 + 5d32 52, which we can rewrite in a more compact form as 525] = [5d12 + 5d22 + 5d32 ] 52 Question 3 A portfolio of risky assets has an expected excess return (over the risk-free rate) of 7%, a volatility of 11% and a market beta of 1.05. If you take a leveraged position of 120% in this portfolio by borrowing 20% of your current assets in the risk-free asset, what are the expected excess return and the volatility of your portfolio? f51 is the expected excess return on the portfolio of risky assets, then the expected excess return on the leveraged portfolio with a percentage allocation 5e to the risky portfolio is 52 = 5e51 522 = [5e501]25º[5e501] = 5e250215º501 = 5e2512 Question 4 The tangency portfolio has a volatility of 18%. If you have a target volatility at 20%, what percentages of your assets should you optimally allocate to the tangency portfolio and the risk-free asset? By the two-fund separation theorem with a risk-free asset, the optimal percentage allocation to the tangency portfolio is 5/5tan, where 5 is the target volatility and 5tan is the volatility of the tangency portfolio. Therefore, the optimal allocation to the tangency portfolio is 20/18 H 111.1%, and the optimal allocation to the risk-free asset is 1 20/18 H 11.1% Question 5 What is the CAPM-implied expected excess return of an asset with a volatility of 14% and a market beta of 0.98, if the market risk premium (i.e., the expected excess return on the market portfolio) is 7%?55V = 5ý5V × 55Z, Question 6 If the market alpha of a portfolio is estimated to be -0.05 with a standard error of 0.021, is the alpha statistically significant (at the usual confidence level)? Does this result support or invalidate the CAPM? 5a [5ü] = 5ü /SE [5ü] The absolute value of the t-statistic is greater than 1.96, so the alpha is statistically significant at the usual 95% confidence level, i.e., we reject the null hypothesis that the true alpha is zero. But the CAPM implies that the true alpha should be zero. Therefore, this result provides evidence against the CAPM. We assume that the investment universe contains a risk-free asset. The risk aversion parameter gamma for an investor is defined in such a way that the optimal vector of weights in the risky assets is given by w = 1 / gama (y) le tout foit matrice de covariance invers fois mutilda (expected execs return) where capital sigma denotes the covariance matrix and mu with tilde on top is the vector of expected excess returns. Give an expression of the risk aversion parameter in terms of the investor's target volatility and capital sigma and mu with tilde on top Made with nCreator - tiplanet.org
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