Respuesta :
Answer:
For correlation 1 the standard deviation of portfolio is 0.433.
For correlation 0 the standard deviation of portfolio is 0.3191.
For correlation -1 the standard deviation of portfolio is 0.127.
Explanation:
The standard deviation of a portfolio is computed using the formula:
[tex]\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}[/tex]
(1)
For r = + 1 compute the standard deviation of portfolio as follows:
[tex]\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times1\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.187489}\\=0.433[/tex]
Thus, for correlation 1 the standard deviation of portfolio is 0.433.
(2)
For r = 0 compute the standard deviation of portfolio as follows:
[tex]\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times0\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.101809}\\=0.3191[/tex]
Thus, for correlation 0 the standard deviation of portfolio is 0.3191.
(3)
For r = -1 compute the standard deviation of portfolio as follows:
[tex]\sigma_{P}=\sqrt{w^{2}_{1}\sigma_{1}^{2}+w^{2}_{2}\sigma_{2}^{2}+2\times r\times w_{1}\sigma_{1}w_{2}\sigma_{2}}\\=\sqrt{(0.30^{2}\times 0.51^{2})+(0.70^{2}\times 0.40^{2})+(2\times-1\times0.30\times 0.51\times0.70\times 0.40)}\\=\sqrt{0.016129}\\=0.127[/tex]
Thus, for correlation -1 the standard deviation of portfolio is 0.127.
