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Given the following: Stock A Expected return= 0.28, standard deviation = 0.40 Stock B Expected return=...

Given the following:

  • Stock A Expected return= 0.28, standard deviation = 0.40
  • Stock B Expected return= 0.16, standard deviation = 0.25

If stock A and stock B have a positive correlation of 0.48, which portfolio represent the minimum variance portfolio?

  1. Weight of Stock A in the minimum variance portfolio: _____
  2. Weight of Stock B in the minimum variance portfolio: _____
  3. The expected return and standard deviation of this minimum variance portfolio: ______ and ________

show all formulas and calculations please

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Answer #1

SOLUTION:

WA + WB = 1
WB = 1 - WA

Variance of a Portfolio = WA2.σA2 + WB2.σB2 + 2.WA.WB.σA.σB.Cor(A,B)
σ2 = WA2.(0.4)2. + (1 - WA)2.(0.25)2 + 2.WA.(1 - WA).(0.4).(0.25).(0.48)
σ2 = 0.16WA2 + (1 + WA2 - 2WA)*0.0625 + 0.096WA - 0.096WA2
σ2 = 0.16WA2 + 0.0625 + 0.0625WA2 - 0.125WA + 0.096WA - 0.096WA2
σ2 = 0.1275WA2 - 0.029WA + 0.0625
Differentiate w.r.t. WA
dσ2/dWA = 0.1275WA - 0.029
0 + 0.029 = 0.1275WA
WA = 0.029/0.1275 = 0.2275

1. Weight of Stock A in Minimum Variance Portfolio = 0.2275 or 22.75%

2. Weight of Stock B in Minimum Variance Portfolio = 1 - 0.2275 = 0.7725 or 77.25%

3. Expected Return = (28*0.2275) + (16*0.7725) = 18.73%
Standard Deviation = (0.1275WA2 - 0.029WA + 0.0625)1/2 = ((0.1275*0.22752 - 0.029*0.2275 + 0.0625)1/2 =0.25 or 25%

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