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Investment Analysis and Portfolio Management Frank K. Reilly & Keith C. Brown

Investment Analysis and Portfolio Management Frank K. Reilly & Keith C. Brown. C HAPTER 7. BADM 744: Portfolio Management and Security Analysis Ali Nejadmalayeri. A measure of the degree to which two variables “move together” relative to their individual mean values over time.

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Investment Analysis and Portfolio Management Frank K. Reilly & Keith C. Brown

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  1. Investment Analysis and Portfolio ManagementFrank K. Reilly & Keith C. Brown CHAPTER 7 BADM 744: Portfolio Management and Security AnalysisAli Nejadmalayeri

  2. A measure of the degree to which two variables “move together” relative to their individual mean values over time Covariance of Returns

  3. Covariance of Returns For two assets, i and j, the covariance of rates of return is defined as: Covij = E{[Ri - E(Ri)][Rj - E(Rj)]}

  4. The correlation coefficient is obtained by standardizing (dividing) the covariance by the product of the individual standard deviations Covariance and Correlation

  5. Covariance and Correlation Correlation coefficient varies from -1 to +1

  6. It can vary only in the range +1 to -1. A value of +1 would indicate perfect positive correlation. This means that returns for the two assets move together in a completely linear manner. A value of –1 would indicate perfect correlation. This means that the returns for two assets have the same percentage movement, but in opposite directions Correlation Coefficient

  7. Portfolio Standard Deviation Formula

  8. Portfolio Standard Deviation Calculation • Any asset of a portfolio may be described by two characteristics: • The expected rate of return • The expected standard deviations of returns • The correlation, measured by covariance, affects the portfolio standard deviation • Low correlation reduces portfolio risk while not affecting the expected return

  9. Combining Stocks with Different Returns and Risk Case Correlation Coefficient Covariance a +1.00 .0070 b +0.50 .0035 c 0.00 .0000 d -0.50 -.0035 e -1.00 -.0070 1 .10 .50 .0049 .07 2 .20 .50 .0100 .10

  10. Combining Stocks with Different Returns and Risk • Assets may differ in expected rates of return and individual standard deviations • Negative correlation reduces portfolio risk • Combining two assets with -1.0 correlation reduces the portfolio standard deviation to zero only when individual standard deviations are equal

  11. Constant Correlationwith Changing Weights 1 .10 rij = 0.00 2 .20

  12. Constant Correlationwith Changing Weights

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