Stocks A and B have the following returns: What are the expected returns of the
ID: 2764106 • Letter: S
Question
Stocks A and B have the following returns: What are the expected returns of the two stocks? What are the standard deviations of the returns of the two stocks? If their correlation is 0.46, what is the expected return and standard deviation of a portfolio of 70% stock A and 30% stock B? What are the expected return of the two stock? The expected return for stock A is.070. (Round to three decimal places.) The expected return for stock B is.024. (Round to three decimal places.) What are the standard deviations of the returns of the two stocks? The standard deviation of the return for stock A is. (Round to four decimal places.) The standard deviation of the return for stock B is. (Round to four decimal places.) If their correlation is 0.46, what is the expected return and standard deviation of a portfolio of 70% stock A and 30% stock B? The expected return for the portfolio is. (Round to four decimal places.) The standard deviation of the return for the portfolio is. (Round to four decimal places.)Explanation / Answer
Part b)
To determine the standard deviation, we need to calculate the variance of each stock. The variance can be calculated with the use of following formula:
Variance = 1/(n-1)*[(Return in Year 1 - Expected Return)^2 + (Return in Year 2 - Expected Return)^2 + (Return in Year 3 - Expected Return)^2 + (Return in Year 4 - Expected Return)^2 + (Return in Year 5 - Expected Return)^2] where n = Years
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Using the information provided in the question, we get,
Variance (Stock A) = 1/(5-1)[(.10 - .070)^2 + (.07 - .070)^2 + + (.15 - .070)^2 + (-.05 - .070)^2 + (.08 - .070)^2] = .00545
Variance (Stock B) = 1/(5-1)[(.06 - .024)^2 + (.02 - .024)^2 + (.05 - .024)^2 + (.01 - .024)^2 + (-.02 - .024)^2] = .00103
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The standard deviation can be calculated with the use of following formula:
Standard Deviation = (Variance)^(1/2)
Standard Deviation (Stock A) = (.00545)^(1/2) = .0738
Standard Deviation (Stock B) = (.00103)^(1/2) = .0321
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Part c)
The expected return of the portfolio is calculated as follows:
Expected Return of the Portfolio = Weight of Stock A*Expected Return on Stock A + Weight of Stock B*Expected Return of Stock B = 70%*.070 + 30%*.024 = .0562
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The standard deviation of the return of the portfolio is calculated as follows:
Standard Deviation = [(Weight of Stock A)^2*(Standard Deviation of Stock A)^2 + (Weight of Stock B)^2*(Standard Deviation of Stock B)^2 + 2*Weight of Stock A*Weight of Stock B*Correlation Coefficient*Standard Deviation of Stock A*Standard Deviation of Stock B)]^(1/2)
Standard Deviation = [(70%)^2*(.0738)^2 + (30%)^2*(.0321)^2 + (2*70%*30%*.46*.0738*.0321)]^(1/2) =.0567 or .0568