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 σ₁
The standard deviation of the second stock is σ₂
The weight of the first stock W₁
The weight of the second stock W₂
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
