Chapter 10 Capital Market Theory

Chapter 10 Capital Market Theory - Chapter 10 Return and...

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Chapter 10 Return and Risk: The Capital-Asset-Pricing Model (CAPM) 10.1 Individual Securities Characteristics of securities Expected return - return that an individual expects a stock to earn over the next period Variance and Standard Deviation Covariance and Correlation -Returns on individual securities are related to one another o Covariance is a statistic measuring the interrelationship between two securities →can be restated in terms of correlation 10.2 Expected Return, Variance, and Covariance Expected Return and Variance Variance can be calculated in four steps: Calculate the expected return of two securities: Expected Return Security A = (R At + R At+1 + R At+2 + R At+3 )/ t Expected Return Security B = (R Bt + R Bt+1 + R Bt+2 + R Bt+3 )/ t Calculate the deviation of each possible return from each of the securities expected return calculated previously Calculate the squared deviations from the deviations calculated before Calculate the variance , which is the average of all squared deviations for a security After having calculated the variance , we can calculate the standard deviation by taking the square root of the variance →Because variance is still expressed in squared terms, it is difficult to interpret → Standard deviation has a much simpler interpretation Covariance and Correlation Variance and standard deviation measure the variability of individual stocks →to measure the relationship between the return on one stock and the return of another, we make use of covariance and correlation Covariance and correlation measure how two random variables are related . Using the standard deviations for the two securities that we calculated in the section above and the deviation of each possible return from the expected return, we can calculate covariance in two steps o First calculate the deviations from their expected return for both securities and than multiply the outcomes: ( R At – R A ) * (R Bt – R B ) Calculate average value of product deviations σ AB = Cov (R A , R B ) = Cov (R B, R A ) = (R At – R A ) * (R Bt – R B ) N Note that is the above expression will be positive in any state where both returns are above their averages , and will be still positive in any state where both terms are below their averages 1
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Chapter 10 Return and Risk: The Capital-Asset-Pricing Model (CAPM) On the other hand, if one return is generally above its average when the other one is below its average, or vice versa, this is indicative of a negative dependency or negative relationship between the two returns Further, if there is no relation between the two returns →the one return tells us nothing about the other one o there will be no tendency for the deviations to be positive or negative together → On average they will tend to offset each other and cancel out, making the covariance close to zero The covariance formula seems to capture what we are looking for
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This note was uploaded on 11/16/2009 for the course F 3033 taught by Professor Hh during the Spring '09 term at Maastricht.

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Chapter 10 Capital Market Theory - Chapter 10 Return and...

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