Assume a market index represents he common actor and all stocks n he economy hav
ID: 2780707 • Letter: A
Question
Assume a market index represents he common actor and all stocks n he economy have a beta of 1 Fin -specific returns al have a standard de ton of 4 % Suppose an analyst studies 20 stocks and finds that one-half have an alpha of 2.3%, and one-half have an alpha of-2.396. 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 analysfs profit? (Enter your answers in dollars not in millions. Do not round intermediate calculations. Round your answers to the nearest dollar amount.) Expected return Standard deviation S 55200 S 214662.5 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 deviationExplanation / Answer
a.
RM,the expected dollar return is:
$1,200,000x [.023 + 1.0xRM] – $1,200,000x[–.023 + 1.0xRM] = $1,200,000 x 0,046 = $55,200
Sensitivity to market is zero as the positive alpha stocks cancel out the negaive alpha stock. Thus, the systematic component risk is zero.However, The variance of the profit is not zero, since the portfolio is not diversified.
Investment in Each Stock = 1,200,000/10 = 120,000
The variance of dollar returns from the positions in the 20 firms is 20x[(120,000x0.40)2] = 46,080,000,000
Standard Deviation = 214,663
b-1. Investment in Each Stock = 1,200,000/25 = 48,000
The variance of dollar returns from the positions in the firms is 50x[(48,000x0.40)2] = 18,432,000,000
Standard Deviation = 135,764
b-2. Investment in Each Stock = 1,200,000/50 = 24,000
The variance of dollar returns from the positions in the firms is 100x[(24,000x0.40)2] = 9,216,000,000
Standard Deviation = 96,000
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