Respuesta :
Answer: a. 16% b. 53.30%
Step-by-step explanation:
For Security F
Expected return [tex]r_1= 0.12[/tex]
Standard deviation [tex]SD_1= 0.45[/tex]
Weight [tex]w_1= 0.2[/tex]
For security G
Expected return [tex]r_2= 0.17[/tex]
Standard deviation [tex]SD_2= 0.64[/tex]
Weight [tex]w_2= 0.8[/tex]
a. Expected return = [tex]r_1w_1+r_2w_2=0.12\times0.2+0.17\times0.8=0.16[/tex]
Hence, the expected return on a portfolio composed of 20 percent of Security F and 80 percent of Security G = 16%.
b. Standard deviation of the portfolio [tex]=\sqrt{w_1^2\cdot SD_1^2+w_2^2\cdot SD_2^2+2\cdot w_1\cdot\ w_2\cdot\ SD_1\cdot\ SD_2\cdot\text{correlation}}[/tex]
[tex]=\sqrt{0.2^2\cdot0.45^2+0.8^2\cdot0.64^2+2\cdot0.2\cdot0.8\cdot0.45\cdot0.64\cdot0.15}\\\\=\sqrt{0.0081+0.262144+0.013824}\\\\=\sqrt{0.284068}=0.53298\approx53.30\%[/tex]
Hence, the standard deviation of the portfolio =53.30%
The expected return on a portfolio composed of 20 percent of Security F and 80 percent of Security G is 0.16 and the standard deviation of the portfolio described is 53.30%.
What are statistics?
Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Security F has an expected return of 12.0 percent and a standard deviation of 45.0 percent per year.
Security G has an expected return of 17.0 percent and a standard deviation of 64.0 percent per year.
For security F,
Expected return (r₁) = 0.12
Standard deviation (SD₁) = 0.45
Weight (w₁) = 0.2
For security G,
Expected return (r₂) = 0.17
STandard deviation (SD₂) = 0.64
Weight (w₂) = 0.8
a. Then the expected return on a portfolio composed of 20 percent of Security F and 80 percent of Security G will be
Expected return = r₁w₁ + r₂w₂
Expected return = 0.12 × 0.2 + 0.17 × 0.8
Expected return = 0.16
b. If the correlation between the returns of Security F and Security G is 0.15, then the standard deviation of the portfolio described will be
[tex]\rm \rightarrow \sqrt{w_1^2 * SD_1^2 + w_2^2*SD_2^2 + 2\ w_1 \ w_2 \ SD_1 \ SD_2 \ correlation}\\\\\\\rightarrow \sqrt{0.2^2*0.45^2+0.8^2*0.64^2+2*0.2*0.8*0.45*0.64*0.15}\\\\\\\rightarrow \sqrt{0.284068}\\\\\\\rightarrow 0.53298 \ or \ 53.30\%[/tex]
More about the statistics link is given below.
https://brainly.com/question/10951564
