Answer:
a. The expected return on the equally weighted portfolio of the three stocks is 16.23%.
b. The variance of the portfolio is 0.020353.
Explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf file for the complete question.
a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
This can be calculated using the following 2 steps:
Step 1: Calculation of expected returns under each state of the economy
Expected return under a state of the economy is the sum of the multiplication of the percentage invested in each stock and the rate of return of each stock under the state of the economy.
This can be calculated using the following formula:
Expected return under a state of the economy = (Percentage invested in Stock A * Return of Stock A under the state of the economy) + (Percentage invested in Stock B * Return of Stock B under the state of the economy) + (Percentage invested in Stock C * Return of Stock C under the state of the economy) …………… (1)
Since we have an equally weighted portfolio, this implies that percentage invested on each stock can be calculated as follows:
Percentage invested on each stock = 100% / 3 = 33.3333333333333%, or 0.333333333333333
Substituting the relevant values into equation (1), we have:
Expected return under Boom = (0.333333333333333 * 0.09) + (0.333333333333333 * 0.03) + (0.333333333333333 * 0.39) = 0.17
Expected return under Bust = (0.333333333333333 * 0.28) + (0.333333333333333 * 0.34) + (0.333333333333333 * (-0.19)) = 0.143333333333333
Step 2: Calculation of expected return of the portfolio
This can be calculated using the following formula:
Portfolio expected return = (Probability of Boom Occurring * Expected Return under Boom) + (Probability of Bust Occurring * Expected Return under Bust) …………………. (2)
Substituting the relevant values into equation (2), we have::
Portfolio expected return = (0.71 * 0.17) + (0.29 * 0.143333333333333) = 0.162266666666667, or 16.2266666666667%
Rounding to 2 decimal places as required by the question, we have:
Portfolio expected return = 16.23%
Therefore, the expected return on the equally weighted portfolio of the three stocks is 16.23%.
b. What is the variance of a portfolio invested 16 percent each in A and B and 68 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., .161616.)
This can be calculated using the following 3 steps:
Step 1: Calculation of expected returns under each state of the economy
Using equation (1) in part a above, we have:
Expected return under Boom = (16% * 0.09) + (16% * 0.03) + (68% * 0.39) = 0.2844
Expected return under Boom = (16% * 0.28) + (16% * 0.34) + (68% * (-0.19)) = -0.03
Step 2: Calculation of expected return of the portfolio
Using equation (2) in part a above, we have:
Portfolio expected return = (0.71 * 0.2844) + (0.29 *(-0.03)) = 0.193224
Step 3: Calculation of the variance of the portfolio
Variance of the portfolio = (Probability of Boom Occurring * (Expected Return under Boom - Portfolio expected return)^2) + (Probability of Bust Occurring * (Expected Return under Bust - Portfolio expected return)^2) …………………….. (3)
Substituting the relevant values into equation (3), we have:
Variance of the portfolio = (0.71 * (0.2844 - 0.193224)^2) + (0.29 * (-0.03- 0.193224)^2) = 0.020352671424
Rounding to 6 decimal places as required by the question, we have:
Variance of the portfolio = 0.020353
Therefore, the variance of the portfolio is 0.020353.
