Assume a market index represents the common factor and all stocks in the economy have a...

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Assume a market index represents the common factor and allstocks in the economy have a beta of 1. Firm-specific returns allhave a standard deviation of 41%. Suppose an analyst studies 20stocks and finds that one-half have an alpha of 4.3%, and one-halfhave an alpha of –4.3%. The analyst then buys $1.3 million of anequally weighted portfolio of the positive-alpha stocks and sellsshort $1.3 million of an equally weighted portfolio of thenegative-alpha stocks. a. What is the expected return (in dollars),and what is the standard deviation of the analyst’s profit? (Enteryour answers in dollars not in millions. Do not round intermediatecalculations. Round your answers to the nearest dollar amount.)Expected return $ Standard deviation $ b-1. How does your answerchange if the analyst examines 50 stocks instead of 20? (Enter youranswer in dollars not in millions. Do not round intermediatecalculations. Round your answer to the nearest dollar amount.)Standard deviation $ b-2. How does your answer change if theanalyst examines 100 stocks instead of 20? (Enter your answer indollars not in millions.) Standard deviation $

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a If alpha 43 then for the long portfolio return alpha betaRm 0043 1Rm 0043 Rm Similarly for alpha 43 then for the short portfolio return alpha betaRm 0043 Rm Total See Answer

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Transcribed Image Text

Assume a market index represents the common factor and allstocks in the economy have a beta of 1. Firm-specific returns allhave a standard deviation of 41%. Suppose an analyst studies 20stocks and finds that one-half have an alpha of 4.3%, and one-halfhave an alpha of –4.3%. The analyst then buys $1.3 million of anequally weighted portfolio of the positive-alpha stocks and sellsshort $1.3 million of an equally weighted portfolio of thenegative-alpha stocks. a. What is the expected return (in dollars),and what is the standard deviation of the analyst’s profit? (Enteryour answers in dollars not in millions. Do not round intermediatecalculations. Round your answers to the nearest dollar amount.)Expected return $ Standard deviation $ b-1. How does your answerchange if the analyst examines 50 stocks instead of 20? (Enter youranswer in dollars not in millions. Do not round intermediatecalculations. Round your answer to the nearest dollar amount.)Standard deviation $ b-2. How does your answer change if theanalyst examines 100 stocks instead of 20? (Enter your answer indollars not in millions.) Standard deviation $