Consider the following information: Calculate the expected return for each stock

Question

Consider the following information:

  

  

Calculate the expected return for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

  

Calculate the standard deviation for each stock. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

Rate of Return If State Occurs   State of Probability of   Economy State of Economy Stock A Stock B   Recession .15 .06 .19   Normal .60 .09 .10   Boom .25 .14 .27

Explanation / Answer

Part A)

The expected return on the stock can be calculated with the use of following formula:

Expected Return = Probability of Recessionary Economy*Return under Recession Economy + Probability of Normal Economy*Return under Normal Economy + Probability of Boom Economy*Return under Boom Economy

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Using the values provided in the question, we get,

Stock A = .15*.06 + .60*.09 + .25*.14 = 9.80%

Stock B = .15*-.19 + .60*.10 + .25*.27 = 9.90%

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Part B)

To determine the standard deviation, we first need to calculate the variance for both the stocks. The formula for variance is given below:

Variance = Probability of Recession*(Return under Recessionary Economy - Expected Return)^2 + Probability of Normal Economy*(Return under Normal Economy - Expected Return)^2 + Probability of Boom Economy*(Return under Boom Economy - Expected Return)^2

The formula for standard deviation is:

Standard Deviation = (Variance)^(1/2)

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Variance (Stock A) = .15*(.06 - .098)^2 + .60*(.09 - .098)^2 + .25*(.14 - .098)^2 = .000696

Variance (Stock B) = .15*(-.19 - .099)^2 + .60*(.10 - .099)^2 + .25*(.27 - .099)^2 = .019839

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Standard Deviation (Stock A) = (.000696)^(1/2) = 2.64%

Standard Deviation (Stock B) = (.019839)^(1/2) = 14.09%

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