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Sagot :
Answer:
Variance of the portfolio = 1.96% for Correlation 1.0
Variance of the portfolio = 1.48% for Correlation 0.5
Variance of the portfolio = 1.00% for Correlation 0.0
Explanation:
Data Given:
Investment = 60% in stock I and the balance in ( 40% in stock J) = weights
Standard deviation on returns on I = 10%
Standard deviation on returns on J = 20%
Required:
Variance of portfolio returns.
Assumptions:
1) The correlation between returns is 1.0
2) The correlation is 0.5
3) The correlation is 0.0
Solution:σLet's suppose,
Weight of Stock I = w1
Weight of the Stock J = w2
so,
w1 = 60%
w2 = 40%
C = Correlation
SD = Standard deviation
SD1 = SD of stock I
SD2 = SD of stock J
So, the formula for the variance of the portfolio will be:
Variance of the portfolio = [tex]w1^{2}[/tex] . [tex]SD1^{2}[/tex] + [tex]w2^{2}[/tex] . [tex]SD2^{2}[/tex] + 2(w1.w2.C.SD1.SD2)
Plugging in the values for Assumption 1, where C = 1.0
Variance of the portfolio = [tex]0.60^{2}[/tex] . [tex]0.10^{2}[/tex] + [tex]0.40^{2}[/tex].[tex]0.20^{2}[/tex] + 2(0.60 x 0.40 x 1.0 x 0.10 x 0.20)
Hence,
Variance of the portfolio = 0.0196 x100 to get it in percentage
Variance of the portfolio = 1.96%
Similarly for the assumption 2, where C = 0.5
Variance of the Portfolio = [tex]w1^{2}[/tex] . [tex]SD1^{2}[/tex] + [tex]w2^{2}[/tex] . [tex]SD2^{2}[/tex] + 2(w1.w2.C.SD1.SD2)
Variance of the Portfolio = [tex]0.60^{2}[/tex] . [tex]0.10^{2}[/tex] + [tex]0.40^{2}[/tex].[tex]0.20^{2}[/tex] + 2(0.60 x 0.40 x 0.5 x 0.10 x 0.20)
Variance of the Portfolio = 0.0148 x 100
Variance of the Portfolio = 1.48%
Similarly, for assumption 3, where C = 0.0
Variance of the Portfolio = [tex]w1^{2}[/tex] . [tex]SD1^{2}[/tex] + [tex]w2^{2}[/tex] . [tex]SD2^{2}[/tex] + 2(w1.w2.C.SD1.SD2)
Variance of the Portfolio = [tex]0.60^{2}[/tex] . [tex]0.10^{2}[/tex] + [tex]0.40^{2}[/tex].[tex]0.20^{2}[/tex] + 2(0.60 x 0.40 x 0.0 x 0.10 x 0.20)
Variance of the Portfolio = 0.01 x 100
Variance of the Portfolio = 1%
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