Stock A: ER = 5%, SD = 5%; Stock B: ER = 10%, SD = 10%;
The correlation coefficient is 0.5.
a) Show how you can create a portfolio with these two stocks which would have an ER of 8%. What is the SD of this portfolio?
Formula : ?(Wa2 x oa2 + Wb2 x ob2 + 2 x Wa x Wb x oa x ob x pab)
Standard Deviation of the Portfolio = (Wa2 x 0.052 + Wb2 x 0.12 + 2 x Wa x Wb x 0.05 x 0.01 x 0.5)
Expected Return : ER = Wa x Ra + Wb + Rb
8% = 5% X + (1 X) x 10%
5% x X + 10% - 8% - 10% x X = 0
- 5% x X = 2%
X = - 2/5 = - 40%
Wa = 40% and Wb = 60% (100 40)
We have to invest 40% of our money in Stock A and 60% of Stock B.
Standard Deviation of the Portfolio = ?(Wa2 x 0.052 + Wb2 x 0.12 + 2 x Wa x Wb x 0.05 x 0.01 x 0.5) = ?(0.42 x 0.052 + 0.62 x 0.12 + 2 x 0.4 x 0.6 x 0.05 x 0.01 x 0.5) = 7.21%
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