Chapter 8 Lecture Notes - 8-07 - Chapter 8 The covariances...

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Chapter 8The covariances between securities are usually positive, because the same macroeconomic factors affect all firms. Unexpected changes in these factors affect the entire market.We can sum all these macro factors into one indicator and assume everything else that moves stocks is firm-specific and thus diversifiable.ri= E(ri) + mi+ eimi= impact of unanticipated macro eventsei= impact of unanticipated firm-specific eventsE(mi) = 0E(ei) = 0Different firms have different sensitivities to these macro events.F = level of unanticipated macro factorβi= sensitivity of firm i to that factormi= βiFSingle Factor Model – Only one macro factorri= E(ri) + βiF + ei-- the single factor modelUse return on S&P 500 as a proxy for this one factor and we can call it the single-index model because it uses the market index to proxy for the common factor.In single-factor models, the excess return is the sum of 3 components:ri– rf= αi+ βi(rm– rf) + eiαi= expected excess return if the market is neutralβi= responsiveness to the factor(rm– rf) = market movements. This is the one factor.Why use excess returns?If T-bill rate is 1% 8% is a result of good economic newsIf T-bill rate is 10% 8% is a result of bad economic news
A convenience of the index model is that it says that the covariance between two stocks is

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