Respuesta :
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Based on the following information calculate the expected return and standard deviation for two stocks:
State of Economy Recession Normal Boom
Probability of State of Economy .15 .55 0.30
Rate of Return if State Occurs
Stock A .04 .09 .17
Stock B -.17 .12 .27
Answer:
The expected return of stock A is 10.65%
The expected return of stock B is 12.15%
The standard deviation of stock A is 4.5%
The standard deviation of stock B is 13.92%
Explanation:
The expected return of stock A is given by
[tex]E(A) = \sum ROR_{A} \cdot P \\\\E(A) = 0.04\cdot 0.15 + 0.09 \cdot 0.55 + 0.17 \cdot 0.30 \\\\E(A) = 0.006 + 0.0495 + 0.051 \\\\E(A) = 0.1065 \\\\[/tex]
Therefore, the expected return of stock A is 10.65%
The expected return of stock B is given by
[tex]E(B) = \sum ROR_{B} \cdot P \\\\E(B) = -0.17\cdot 0.15 + 0.12 \cdot 0.55 + 0.27 \cdot 0.30 \\\\E(B) = -0.0255 + 0.066 + 0.081 \\\\E(B) = 0.1215 \\\\[/tex]
Therefore, the expected return of stock B is 12.15%
The standard deviation of stock A is given by[tex]\sigma_A = \sqrt{\sum (ROR_{A} -E(A))^2 \cdot P} \\\\\sigma_A = \sqrt{(0.04 -0.1065)^2 \cdot 0.15 + (0.09 -0.1065)^2 \cdot 0.55 + (0.17 -0.1065)^2 \cdot 0.30} \\\\\sigma_A = \sqrt{0.000663337 + 0.000149737 + 0.00120967} \\\\\sigma_A = 0.045[/tex]Therefore, the standard deviation of stock A is 4.5%
The standard deviation of stock B is given by[tex]\sigma_B = \sqrt{\sum (ROR_{B} -E(B))^2 \cdot P} \\\\\sigma_B = \sqrt{(-0.17 -0.1215)^2 \cdot 0.15 + (0.12 -0.1215)^2 \cdot 0.55 + (0.27 -0.1215)^2 \cdot 0.30} \\\\\sigma_B = \sqrt{0.012745 + 0.0000012375 + 0.00661567} \\\\\sigma_B = 0.1392[/tex]Therefore, the standard deviation of stock B is 13.92%
