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# Problem 11-10: Calculate expected return and standard deviation of portfolio

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Consider the information on the attached spreadsheet.

a. Your portfolio is invested 35% each in A and C, and 30% in B. What is the expected return of the portfolio?

b. What is the variance of this portfolio? The standard deviation?

Problem 11-10

Rate of Return, if State Occurs
Probability of
State of Economy State of Economy Stock A Stock B Stock C
Boom 0.3 0.3 0.45 0.33
Good 0.4 0.12 0.1 0.15
Poor 0.2 0.01 -0.15 -0.05
Bust 0.1 -0.2 -0.3 -0.09

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The solution shows the detailed calculations for the answers including formulas used in the computations.

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Probability of
State of Economy State of Economy Stock A Stock B Stock C
Boom 0.3 0.3 0.45 0.33
Good 0.4 0.12 0.1 0.15
Poor 0.2 0.01 -0.15 -0.05
Bust 0.1 -0.2 -0.3 -0.09

Given A - 35%, B - 30% and C - 35%

n
Expected Rate of Return = &#61523; Piki Where P = probability of state of economy
i = 1 k = rate of return

Step 1
Work out Expected Return for each stock, from Boom to Bust.

E(RA) = (0.3)*(0.3) + (0.4)*(0.12) + (0.2)*(0.01) + (0.1)*(-0.2)
= 0.09 + 0.048 + 0.002 -0.02
= 0.12

E(RB) = (0.3)*(0.45) + (0.4)*(0.1) + (0.2)*(-0.15) + (0.1)*(-0.3)
= 0.135 + 0.04 - 0.03 - 0.03
...

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