Answer:
Explanation:
The formula to compute the volatility of a portfolio
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
Here,
The standard deviation of the first stock is Οβ
The standard deviation of the second stock is Οβ
The weight of the first stock Wβ
The weight of the second stock Wβ
The correlation between the stock c
a) If the correlation between the stock is +1
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
[tex]=\sqrt{(0.5\times0.33)^2+(0.5\times0.33)^2+(2\times(0.5\times 0.33)\times(0.5\times0.33)\times1} \\\\=0.33[/tex]
Hence, the volatility of the portfolio is 0.33 0r 33%
b) If the correlation between the stock is 0.50
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
[tex]=\sqrt{(0.5\times0.33)^2+(0.5\times0.33)^2+(2\times(0.5\times 0.33)\times(0.5\times0.33)\times0.5} \\\\=0.29[/tex]
Hence, the volatility of the portfolio is 0.29 0r 29%
c) If the correlation between the stock is 0.00
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
[tex]=\sqrt{(0.5\times0.33)^2+(0.5\times0.33)^2+(2\times(0.5\times 0.33)\times(0.5\times0.33)\times0.0} \\\\=0.23[/tex]
Hence, the volatility of the portfolio is 0.23 0r 23%
d) If the correlation between the stock is -0.50
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
[tex]=\sqrt{(0.5\times0.33)^2+(0.5\times0.33)^2+(2\times(0.5\times 0.33)\times(0.5\times0.33)\times-0.5} \\\\=0.17[/tex]
Hence, the volatility of the portfolio is 0.17 or 17%
e) If the correlation between the stock is -1
[tex]=\sqrt{W_1^2\sigma_1^2+W_2^2\sigma_2^2+2W_1W_2\sigma_1\sigma_2*c}[/tex]
[tex]=\sqrt{(0.5\times0.33)^2+(0.5\times0.33)^2+(2\times(0.5\times 0.33)\times(0.5\times0.33)\times-1} \\\\=0[/tex]
Hence, the volatility of the portfolio is 0
