Final answer:
The expected rates of return for Stocks X and Y are 22% and 4.5% respectively. The standard deviations of returns on Stocks X and Y are 2.05% and 2.81% respectively. The expected return on the portfolio, which is weighted $9,000 in Stock X and $1,000 in Stock Y, is 20.25%.
Step-by-step explanation:
b. Expected Rates of Return:
To calculate the expected rate of return, we multiply the probability of each return by the corresponding return and sum them up. For Stock X:
Expected return = (0.20 * 0.15) + (0.30 * 0.20) + (0.40 * 0.25) + (0.10 * 0.30)
= 0.03 + 0.06 + 0.10 + 0.03
= 0.22 or 22%
For Stock Y:
Expected return = (0.10 * -0.05) + (0.25 * 0.00) + (0.30 * 0.05) + (0.35 * 0.10)
= -0.005 + 0 + 0.015 + 0.035
= 0.045 or 4.5%
c. Standard Deviations of Returns:
Standard deviation measures the volatility of returns. For Stock X:
Standard deviation = √(∑(Pi * (Ri - Expected return)^2))
= √((0.20 * (0.15 - 0.22)^2) + (0.30 * (0.20 - 0.22)^2) + (0.40 * (0.25 - 0.22)^2) + (0.10 * (0.30 - 0.22)^2))
= √(0.00034 + 0.00002 + 0.00002 + 0.00004)
= √0.00042
= 0.0205 or 2.05%
For Stock Y:
Standard deviation = √(∑(Pi * (Ri - Expected return)^2))
= √((0.10 * (-0.05 - 0.045)^2) + (0.25 * (0.00 - 0.045)^2) + (0.30 * (0.05 - 0.045)^2) + (0.35 * (0.10 - 0.045)^2))
= √(0.00036 + 0.00009 + 0.00009 + 0.00025)
= √0.00079
= 0.0281 or 2.81%
d. Expected Return on Portfolio:
Expected return on portfolio = (Weight of Stock X * Expected return of Stock X) + (Weight of Stock Y * Expected return of Stock Y)
= (0.90 * 0.22) + (0.10 * 0.045)
= 0.198 + 0.0045
= 0.2025 or 20.25%