cfaquantreview-investmenttoolsprobability(ppt47)-it(编辑修改稿)

cfaquantreview-investmenttoolsprobability(ppt47)-it(编辑修改稿)内容摘要：

t h .30 B o o m .20 20 Calculating ER and Risk Can use the previous table to calculate ER and variance (risk) for each asset. Show calculations for Asset A below. Ec onom ic C onditi ons P(R i ) R i for A P()R i for A R i ER (R i ER )2 P(R i ) (R i ER )2 Rec es si on .10 .3 1 1 Stabl e .40 .28 4 Mode rate .30 .30 .81 .243 B oom .20 .30 1 2 E R = 2 = A = % ERA = % ERA/A = 21 Covariance Covariance between two random variables X and Y is defined as A negative covariance between X and Y means that when X is above its mean its is likely that Y is below its mean value. If the covariance of the two random variables is zero then on average the values of the two variables are unrelated. A positive covariance between X and Y means that when X is above its mean its is likely that Y is above its mean value. Covariance of a random variable with itself, its own covariance, is equal to its variance.           YEYXEXEYXYXC o v XY   ,22 Correlation Correlation between two random variables X and Y measured as: Correlation takes on values between –1 and +1. Correlation is a standardized measure of how two random variables move together, . correlation has no units associated with it. A correlation of 0 means there is no straightline (linear) relationship between the two variables. Increasingly positive (negative) correlations indicate an increasingly strong positive (negative) linear relationship between the variables. When the correlation equals 1 (1) there is a perfect positive (negative) linear relationship between the two variables.    YXYXXYXY YXCo vYXCo r r  , 23 Portfolio Probability Calculations Portfolio consisting of two assets A and B, wA invested in A. Asset A has expected return rA and variance 2A. Asset B has expected return rB and variance 2B. The correlation between the two returns is AB. Portfolio Expected Return: E(rp) = wA rA + (1wA )rB Portfolio Variance: or      BAAABAAAr rrC o vwp ,121 22222      BAABAABAAAr wp   121 2222224 Exam Questions on Probability 28. The probability that two or more events will happen concurrently is: A. joint probability. B. multiple probability. C. concurrent probability. D. conditional probability. 25 Exam Question on Expected Values 24. An analyst developed the following probability distribution of the rate of return for a mon stock: Scenario Probability Rate of return 1 2 3 The standard deviation of the rate of return is closest to: A. . B. . C. . D. . To calculate standard deviation must first calculate expected value, mean, of the rate of return. = [.25 x .08 + .5 x .12 + .25 x .16] = Calculate variance as probabilityweighted squared deviations of values from expected value. 2 = .25[.08 .12]2 + .5[.12 .12]2 + .25[.16 .12]2 = Finally calculate standard deviation as square root of variance.   = SQRT() = Common Probability Distributions 27 Probability Distributions Probability distribution specifies the probabilities of the possible outes of a random variable. Discrete random variable can take on at most a countable number of possible values, such as coin flip or rolling dice. Continuous random variable can take on an uncountable (infinite) number of possible values, such as asset returns or temperatures. Probability function specifies the probability that the random varia。