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Catégorie :Category: nCreator TI-Nspire
Auteur Author: Nass23232
Type : Classeur 3.0.1
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Mis en ligne Uploaded: 20/12/2019 - 05:56:23
Mis à jour Updated: 20/12/2019 - 05:56:29
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Shortlink : http://ti-pla.net/a2528032
Type : Classeur 3.0.1
Page(s) : 1
Taille Size: 3.63 Ko KB
Mis en ligne Uploaded: 20/12/2019 - 05:56:23
Mis à jour Updated: 20/12/2019 - 05:56:29
Uploadeur Uploader: Nass23232 (Profil)
Téléchargements Downloads: 43
Visibilité Visibility: Archive publique
Shortlink : http://ti-pla.net/a2528032
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Fichier Nspire généré sur TI-Planet.org.
Compatible OS 3.0 et ultérieurs.
<<
2.2 Events and Probabilities of Single Assets Events are "mutually exclusive" when the possible future outcomes can only occur one at a time - Events are "exhaustive" when the set of outcomes includes every possible value the variable could take in the future. Sources of probabilities An empirical probability is one that is estimated from observed data, typically using the relative frequency at which an event or set of events has occurred in the past. A subjective probability is a personal assessment of the likelihood of an event or set of events occurring in the future and is so named because it relies on the subjective judgment of the person making the assessment. An a priori probability is one whose values are obtained from mathematical or logical analysis (6) Dependent and independent variables (a) Independent events A and B - When events are independent, the occurrence of one does not affect the probability of the other and vice versa: P ( A | B ) = P(A) and P ( B | A ) = P(B) - joint probability, use the multiplication rule: P(AB) = P(A) P(B) - generalization: P(ABC...) = P(A) P(B) (P(C) ... (b) Dependent events: total probability rule - example: Two events that are mutually exclusive and exhaustive " Recallthatwehavea60%(40%)chanceoftraderestrictionsbeing relaxed (maintained). P ( RR ) = 0.6, where RR is relaxed restrictions. P ( NR ) = 0.4, where NR is no relaxation. " Our analysts believe that the stock price will decrease if trade restrictions are relaxed with a probability of 30% and that they will decrease if trade restrictions are not relaxed with a probability of 15%: P ( DS | RR ) = 0.30 P ( DS | NR ) = 0.15 " What is the probability of a decrease in stock prices? 6) Random variables: measures of central tendency and dispersion (a) Expected value - probability-weighted average of the possible outcomes for that variable - example: We anticipate that there is a 15% chance that next years return on holding Cleveland Corp will be 4%, a 60% chance it will be 6%, and a 25% chance it will be 8%. What is the expected return on Cleveland Corp stock? e(x)= somme de 0.04 * O.15 + 0.06*0.6 + 0.08 * 0.25 (b) Variance - measure of the dispersion of possible values - expected value of squared deviations from the expected value: ýý 2 ýý =ýý ýý ýý(ýý) 2 - weighted sum of squared deviations from the expected value, where weights are given by the probabilities of the various outcomes: ýý 2 = Ã ýý ýý ýý(ýý) 2 ýý(ýý) ýý=1 ýý ýý - Example: Cleveland corporation from slide 18 Ã 2 (R) = 0.15 ( 0.04 0.062) 2 + 0.6 (0.06 0.062) 2 + 0.25(0.08 0.062) 2 = 0.000156 (a) Conditional expected value - ýý ýý ýý ýý : expected value of a random variable X, given a scenario S i - ýýýýýý=ýýýýýýýý+ýýýýýýýý+...+ýýýýýýýý ýý11ýý22ýý ýýýýýý - The total probability rule applies to expected values just as it does any mutually exclusive and exhaustive set of possible outcomes across a set of states: This equation allows us to calculate the expected value of a random variable ( X ) as a function of the probabilities of future possible states, P ( S ), and the conditional value of the expected value of X in those states, E ( X | S ). 2.3 Expected Return and Variance of Portfolios Portfolio expected return, variance, and standard deviation are functions of the weights invested in each asset, much like probabilities function as weights. (1) Expected return to a portfolio - sum of each of the individual assets expected returns (R i ) multiplied by its associated weight (w i ) (2) Variance of the portfolio return: survey The variance of a portfolio s return is the sum of the squared deviations from the mean multiplied by the associated weights. There are several ways to calculate a portfolio variance. (3) Covariance - Covariance and correlation are both measures of the extent to which two random variables move together - Covariance is the expected value of the product of each variable s deviation from its respective mean: (4) Correlation - Correlation is a scaled transformation of covariance wherein the extent of comovement is measured along a scale from exactly the same movement in the same direction to exactly the same movement in opposite directions. Made with nCreator - tiplanet.org
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Compatible OS 3.0 et ultérieurs.
<<
2.2 Events and Probabilities of Single Assets Events are "mutually exclusive" when the possible future outcomes can only occur one at a time - Events are "exhaustive" when the set of outcomes includes every possible value the variable could take in the future. Sources of probabilities An empirical probability is one that is estimated from observed data, typically using the relative frequency at which an event or set of events has occurred in the past. A subjective probability is a personal assessment of the likelihood of an event or set of events occurring in the future and is so named because it relies on the subjective judgment of the person making the assessment. An a priori probability is one whose values are obtained from mathematical or logical analysis (6) Dependent and independent variables (a) Independent events A and B - When events are independent, the occurrence of one does not affect the probability of the other and vice versa: P ( A | B ) = P(A) and P ( B | A ) = P(B) - joint probability, use the multiplication rule: P(AB) = P(A) P(B) - generalization: P(ABC...) = P(A) P(B) (P(C) ... (b) Dependent events: total probability rule - example: Two events that are mutually exclusive and exhaustive " Recallthatwehavea60%(40%)chanceoftraderestrictionsbeing relaxed (maintained). P ( RR ) = 0.6, where RR is relaxed restrictions. P ( NR ) = 0.4, where NR is no relaxation. " Our analysts believe that the stock price will decrease if trade restrictions are relaxed with a probability of 30% and that they will decrease if trade restrictions are not relaxed with a probability of 15%: P ( DS | RR ) = 0.30 P ( DS | NR ) = 0.15 " What is the probability of a decrease in stock prices? 6) Random variables: measures of central tendency and dispersion (a) Expected value - probability-weighted average of the possible outcomes for that variable - example: We anticipate that there is a 15% chance that next years return on holding Cleveland Corp will be 4%, a 60% chance it will be 6%, and a 25% chance it will be 8%. What is the expected return on Cleveland Corp stock? e(x)= somme de 0.04 * O.15 + 0.06*0.6 + 0.08 * 0.25 (b) Variance - measure of the dispersion of possible values - expected value of squared deviations from the expected value: ýý 2 ýý =ýý ýý ýý(ýý) 2 - weighted sum of squared deviations from the expected value, where weights are given by the probabilities of the various outcomes: ýý 2 = Ã ýý ýý ýý(ýý) 2 ýý(ýý) ýý=1 ýý ýý - Example: Cleveland corporation from slide 18 Ã 2 (R) = 0.15 ( 0.04 0.062) 2 + 0.6 (0.06 0.062) 2 + 0.25(0.08 0.062) 2 = 0.000156 (a) Conditional expected value - ýý ýý ýý ýý : expected value of a random variable X, given a scenario S i - ýýýýýý=ýýýýýýýý+ýýýýýýýý+...+ýýýýýýýý ýý11ýý22ýý ýýýýýý - The total probability rule applies to expected values just as it does any mutually exclusive and exhaustive set of possible outcomes across a set of states: This equation allows us to calculate the expected value of a random variable ( X ) as a function of the probabilities of future possible states, P ( S ), and the conditional value of the expected value of X in those states, E ( X | S ). 2.3 Expected Return and Variance of Portfolios Portfolio expected return, variance, and standard deviation are functions of the weights invested in each asset, much like probabilities function as weights. (1) Expected return to a portfolio - sum of each of the individual assets expected returns (R i ) multiplied by its associated weight (w i ) (2) Variance of the portfolio return: survey The variance of a portfolio s return is the sum of the squared deviations from the mean multiplied by the associated weights. There are several ways to calculate a portfolio variance. (3) Covariance - Covariance and correlation are both measures of the extent to which two random variables move together - Covariance is the expected value of the product of each variable s deviation from its respective mean: (4) Correlation - Correlation is a scaled transformation of covariance wherein the extent of comovement is measured along a scale from exactly the same movement in the same direction to exactly the same movement in opposite directions. Made with nCreator - tiplanet.org
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