notes10 - Risk and Return Holding Period Return Three month...

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Risk and Return
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Holding Period Return Three month ago, Peter Lynch purchased 100 shares of Iomega Corp. at $50 per share. Last month, he received dividends of $0.25 per share from Iomega. These shares are worth $56 each today. Compute Peter’s holding period return from his investment in Iomega common shares.
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Probability Concept Random variable Something whose value in the future is subject to uncertainty. Probability The relative likelihood of each possible outcome (or value) of a random variable Probabilities of individual outcomes cannot be negative nor greater than 1.0 Sum of the probabilities of all possible outcomes must equal 1.0 Moments Mean, Variance (or Standard deviation), covariance
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Computing the Basic Statistics A security analyst has prepared the following probability distribution of the possible returns on the common stock shares of two companies: Compu-Graphics Inc. (CGI) and Data Switch Corp. (DSC). Probability Return on CGI Return on DSC 0.30 0.50 0.20 10% 14% 20% 40% 16% 20%
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The Mean % 00 . 14 %) 20 ( 20 . 0 %) 14 ( 50 . 0 %) 10 ( 30 . 0 3 1 = + + = = = n n n x p CGI μ For CGI, the mean (or expected) return is: Similarly, the mean return for DSC is 24.00%
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The Variance and Standard Deviation ( 29 ( 29 00 12 14 20 20 0 14 14 50 0 14 10 30 0 2 2 2 1 2 2 . ) ( . . ) ( . x p N n x n n x = - + - + - = - = = μ σ % 46 . 3 00 . 12 2 = = = x x The variance of CGI’s returns is: The Standard Deviation of CGI’s return is:
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The Covariance ( 29 ( 29 00 24 24 20 14 20 20 0 24 16 14 14 50 0 24 40 14 10 30 0 1 . ) ( ) ( . ) ( ) ( . ) ( ) ( . y x p y n x n N n n CD - = - - + - - + - - = - - = = μ σ The covariance of the returns on CGI and DSC is:
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The Correlation Coefficient ( 29 ( 29 655 . 0 58 . 10 46 . 3 00 . 24 - = - = = y x xy xy σ ρ The correlation coefficient between CGI and DSC is:
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CGI DSC Mean Standard Deviation 14.00% 3.46% 24.00% 10.58% Correlation Coefficient -0.655 Summary of Results for CGI and DSC
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A portfolio is a combination of two or more securities. Combining securities into a portfolio reduces risk. An efficient portfolio is one that has the highest expected return for a given level of risk. We will look at two-asset portfolios in fair detail. Portfolio Securities
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Portfolio Expected Return and Risk Expected Return Risk The Expected Returns of the Securities The Portfolio Weights The Risk of the Securities The Portfolio Weights The Correlation Coefficients
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CGI DSC Expected Return Standard Deviation 1.00 0.75 0.67 0.50 0.25 0.00
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This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.

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notes10 - Risk and Return Holding Period Return Three month...

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