Question
In: Finance
***Please show your math work, thank you! Assume that stock market returns have the market index...
***Please show your math work, thank you!
Assume that stock market returns have the market index as a common factor, and that all stocks in the economy have a beta of 2.0 on the market index. Firm-specific returns all have a standard deviation of 32%.
Suppose that an analyst studies 20 stocks and finds that one-half of them have an alpha of +3.0%, and the other half have an alpha of −3.0%. Suppose the analyst invests $1.0 million in an equally weighted portfolio of the positive alpha stocks, and shorts $1 million of an equally weighted portfolio of the negative alpha stocks.
a. What is the expected profit (in dollars) and standard deviation of the analyst’s profit? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
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b. How does your answer change if the analyst examines 50 stocks instead of 20 stocks? 100 stocks? (Do not round intermediate calculations. Round your answers to the nearest whole dollar amount.)
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Solutions
jeff jeffy answered 9 months agoRelated Solutions
***Please show the math! Thank you! Assume that security returns are generated by the single-index model,...
***Please show the math! Thank you!
Assume that security returns are generated by the single-index
model,
Ri = αi +
βiRM + ei
where Ri is the excess return for security
i and RM is the market’s excess
return. The risk-free rate is 3%. Suppose also that there are three
securities A, B, and C, characterized by
the following data:
Security
βi
E(Ri)
σ(ei)
A
1.0
10
%
23
%
B
1.3
13
9
C
1.6
16
18
a. If...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock
market returns have the market index as a common factor, and that
all stocks in the economy have a beta of 1.3 on the market index.
Firm-specific returns all have a standard deviation of 35%.
Suppose that an
analyst studies 20 stocks, and finds that half have an alpha of
+1.8%, and the other half an alpha of –1.8%. Suppose the analyst
buys $2.0 million of an equally weighted portfolio of the positive
alpha stocks and shorts...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.6 on the market index. Firm-specific returns all have a standard
deviation of 20%. Suppose that an analyst studies 20 stocks and
finds that one-half of them have an alpha of +2.4%, and the other
half have an alpha of −2.4%. Suppose the analyst invests $1.0
million in an equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.9 on the market index. Firm-specific returns all have a standard
deviation of 40%.
Suppose that an analyst studies 20 stocks and finds that
one-half of them have an alpha of +2.8%, and the other half have an
alpha of −2.8%. Suppose the analyst invests $1.0 million in an
equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.8 on the market index. Firm-specific returns all have a standard
deviation of 40%.
Suppose that an analyst studies 20 stocks and finds that one-half
of them have an alpha of +2.8%, and the other half have an alpha of
−2.8%. Suppose the analyst invests $1.0 million in an equally
weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.2 on the market index. Firm-specific returns all have a standard
deviation of 25%.
Suppose that an analyst studies 20 stocks and finds that
one-half of them have an alpha of +1.6%, and the other half have an
alpha of −1.6%. Suppose the analyst invests $1.0 million in an
equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.9 on the market index. Firm-specific returns all have a standard
deviation of 40%. Suppose that an analyst studies 20 stocks and
finds that one-half of them have an alpha of +2.8%, and the other
half have an alpha of −2.8%. Suppose the analyst invests $1.0
million in an equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of 1
on the market index. Firm-specific returns all have a standard
deviation of 30%.
Suppose that an analyst studies 20 stocks, and finds that
one-half have an alpha of 2%, and the other half an alpha of −2%.
Suppose the analyst buys $1 million of an equally weighted
portfolio of the positive alpha stocks, and shorts...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.8 on the market index. Firm-specific returns all have a standard
deviation of 35%.
Suppose that an analyst studies 20 stocks and finds that
one-half of them have an alpha of +2.6%, and the other half have an
alpha of −2.6%. Suppose the analyst invests $1.0 million in an
equally weighted portfolio of the positive alpha...
Assume that stock market returns have the market index as a common factor, and that all...
Assume that stock market returns have the market index as a
common factor, and that all stocks in the economy have a beta of
1.7 on the market index. Firm-specific returns all have a standard
deviation of 35%.
Suppose that an analyst studies 20 stocks and finds that
one-half of them have an alpha of +2.6%, and the other half have an
alpha of −2.6%. Suppose the analyst invests $1.0 million in an
equally weighted portfolio of the positive alpha...
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