Asked by shamimi samsudin on Jun 21, 2024
Verified
Stocks A and B each have an expected return of 15%,a standard deviation of 20%,and a beta of 1.2.The returns on the two stocks have a correlation coefficient of +0.6.You have a portfolio that consists of 50% A and 50% B.Which of the following statements is correct?
A) The portfolio's beta is less than 1.2.
B) The portfolio's expected return is 15%.
C) The portfolio's standard deviation is greater than 20%.
D) The portfolio's beta is greater than 1.2.
Correlation Coefficient
A statistical measure that calculates the strength and direction of a linear relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation).
Expected Return
The expected return is the anticipated profit or loss from an investment over a specified period, based on historical or projected rates.
Standard Deviation
A statistical measure of the dispersion or variability of a set of data points, often used in finance to quantify the risk of an investment.
- Ascertain and clarify the contribution of beta in assessing risk pertaining to single stock investments and diversified portfolio holdings.
- Analyze the impact of portfolio composition on expected return and risk.
Verified Answer
MS
Melissa SearsJun 27, 2024
Final Answer :
B
Explanation :
The expected return of the portfolio can be calculated as:
Expected return = (0.5 x 15%) + (0.5 x 15%) = 15%
Therefore, statement B is correct.
The portfolio's beta can be calculated as:
Portfolio beta = (0.5 x 1.2) + (0.5 x 1.2) = 1.2
Therefore, statement A and D are incorrect.
The portfolio's standard deviation can be calculated as:
Portfolio standard deviation = sqrt[(0.5^2 x 20%^2) + (0.5^2 x 20%^2) + 2 x 0.5 x 0.5 x 20% x 20% x 0.6] = 16.96%
Therefore, statement C is incorrect.
Expected return = (0.5 x 15%) + (0.5 x 15%) = 15%
Therefore, statement B is correct.
The portfolio's beta can be calculated as:
Portfolio beta = (0.5 x 1.2) + (0.5 x 1.2) = 1.2
Therefore, statement A and D are incorrect.
The portfolio's standard deviation can be calculated as:
Portfolio standard deviation = sqrt[(0.5^2 x 20%^2) + (0.5^2 x 20%^2) + 2 x 0.5 x 0.5 x 20% x 20% x 0.6] = 16.96%
Therefore, statement C is incorrect.
Learning Objectives
- Ascertain and clarify the contribution of beta in assessing risk pertaining to single stock investments and diversified portfolio holdings.
- Analyze the impact of portfolio composition on expected return and risk.