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What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

A)
6.20%.
B)
0.38%.
C)
6.83%.

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What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

A)
6.20%.
B)
0.38%.
C)
6.83%.



The standard deviation of the portfolio is found by:

[W12 σ12 + W22 σ22 + 2W1W2σ1σ2r1,2]0.5, or [(0.30)2(0.046)2 + (0.70)2(0.078)2 + (2)(0.30)(0.70)(0.046)(0.078)(0.45)]0.5 = 0.0620, or 6.20%.

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An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

  • σR = 34%
  • σS = 16%
  • rR,S = 0.67
  • WR = 80%
  • WS = 20%

A)
29.4%.
B)
7.8%.
C)
8.7%.

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An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

  • σR = 34%
  • σS = 16%
  • rR,S = 0.67
  • WR = 80%
  • WS = 20%

A)
29.4%.
B)
7.8%.
C)
8.7%.



The formula for the standard deviation of a 2-stock portfolio is:

s = [WA2sA2 + WB2sB2 + 2WAWBsAsBrA,B]1/2

s = [(0.82 × 0.342) + (0.22 × 0.162) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]1/2 = [0.073984 + 0.001024 + 0.0116634]1/2 = 0.08667141/2 = 0.2944, or approximately 29.4%.

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c

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