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

Question

Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of 40%. Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.3%. and one-half have an alpha of -2.3%. The analyst then buys $1.2 million of an equally weighted portfolio of the positive-alpha stocks and sells short $1.2 million of an equally weighted portfolio of the negative-alpha stocks. a. What is the expected return (in dollars), and what is the standard deviation of the analyst?s profit? (Enter your answers in dollars not n millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount.) Expected Return Standard Deviation b-1. How does your answer change if the analyst examines 50 stocks instead of 20? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) Standard Deviation $ b-2. How does your answer change if the analyst examines 100 stocks instead of 20? (Enter your answer in dollars not in millions.) Standard Deviation $

Explanation / Answer

Answer:-

one-half have an alpha = 2.3%

one-half have an alpha = -2.3%

Buys = $1200000 positive alpha

Sells = $1200000 negative alpha

a.) Total stocks = 20 stocks

Equally weighted = 1

=(276000-552000)2 * 1

=76176000000

=(276000-552000)2 * 1

=76176000000

Expected Return = $552000

Standered Deviation = (Return - Expected Return)2 * Weight

= 152352000000

= $390322.94

b-1) Total stocks = 50 stocks

Equally weighted = 1

=(690000 - 1380000)2 * 1

=476100000000

=(690000 - 1380000)2 * 1

=476100000000

Expected Return = $1380000

Standered Deviation = (Return - Expected Return)2 * Weight

=  952200000000

= $975807.36

b-2) Total stocks = 100 stocks

Equally weighted = 1

=(1380000 - 2760000)2 * 1

= 1904400000000

=(1380000 - 2760000)2 * 1

= 1904400000000

Expected Return = $2760000

Standered Deviation = (Return - Expected Return)2 * Weight

=  3808800000000

= $1951614.72

Particulars Expected Return (Return - Expected Return)2 * Weight positive alpha =[1200000 * (20/2) * 2.3% * 1] = 276000

=(276000-552000)2 * 1

=76176000000

negative alpha =[-1200000 * (20/2) * -2.3% * 1] = 276000

=(276000-552000)2 * 1

=76176000000

TOTAL 552000 152352000000

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