Question

Consider the following information: 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.) b. What is the variance of a portfolio invested 24 percent each in A and B and 52 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., .161616.) a. Expected return ___ % b. Variance ____

Answer 1

The expected return on an equally weighted portfolio of three stocks is $400,000.

Step-by-step explanation:

To find the expected return of an equally weighted portfolio of three stocks, we need to calculate the expected return of each stock first. In this case, we are given the probabilities and returns for each investment. We can calculate the expected return by multiplying each possible return by its corresponding probability and summing them up. The expected return for a stock can be calculated using the formula: Expected Return = (Probability of Return 1 * Return 1) + (Probability of Return 2 * Return 2) + ... + (Probability of Return n * Return n).

Let's calculate the expected return for each stock:

Stock A: (0.10 * $5,000,000) + (0.30 * $1,000,000) + (0.60 * -$1,000,000) = $400,000

Stock B: (0.20 * $3,000,000) + (0.40 * $1,000,000) + (0.40 * -$1,000,000) = $200,000

Stock C: (0.10 * $6,000,000) + (0.70 * $0) + (0.20 * -$1,000,000) = $400,000

To calculate the expected return on an equally weighted portfolio, we simply take the average of the expected returns of the three stocks. In this case, since all three stocks have the same expected return of $400,000, the expected return on the equally weighted portfolio would also be $400,000.

Answer 2

a. Expected return = 16.17%

b. Variance = 0.000391

Step-by-step explanation:

a. To find the expected return on an equally weighted portfolio, we first calculate the expected return for each stock by multiplying the probability of each scenario by its respective return, and then adding up the results.

Expected return for stock A = (0.3 × 0.15) + (0.5 × 0.1) + (0.2 × 0.05) = 0.105 or 10.5%

Expected return for stock B = (0.2 × 0.12) + (0.4 × 0.09) + (0.4 × 0.06) = 0.084 or 8.4%

Expected return for stock C = (0.25 × 0.25) + (0.5 × 0.1) + (0.25 × 0.05) = 0.125 or 12.5%

The expected return on an equally weighted portfolio is the average of the expected returns for each stock, which is (10.5% + 8.4% + 12.5%) / 3 = 16.17%.

b. To find the variance of a portfolio invested in A, B, and C, we use the formula:

Variance = wA^2σA^2 + wB^2σB^2 + wC^2σC^2 + 2wAwBCov(A,B) + 2wAwCCov(A,C) + 2wBwCCov(B,C)

where w is the weight of each stock in the portfolio, σ^2 is the variance of each stock, and Cov is the covariance between each pair of stocks.

Substituting the given values, we get:

Variance = (0.24^2 × 0.04^2) + (0.24^2 × 0.09^2) + (0.52^2 × 0.05^2) + 2(0.24 × 0.24 × 0.04 × 0.09 × 0.6) + 2(0.24 × 0.52 × 0.04 × 0.05 × (-0.1)) + 2(0.52 × 0.24 × 0.09 × 0.05 × (-0.1))

= 0.000391 or 0.0391% (rounded to 6 decimal places)