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Consider the following information:

| State of Economy | Probability of State | Stock A | Stock B | Stock C |
|------------------|----------------------|---------|---------|---------|
| Boom | 0.60 | 0.09 | 0.18 | 0.36 |
| Bust | 0.40 | 0.15 | 0.07 | -0.05 |

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 15 percent each in A and B and 70 percent in C?
(Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 0.161616.)

Expected return: 15.68%
Variance: 0.218810

Answer :

a. The expected return on an equally weighted portfolio of the three stocks is 15.68%. b. The variance of a portfolio invested 15% each in Stock A and Stock B and 70% in Stock C is 0.218810.

To calculate the expected return on an equally weighted portfolio, we multiply the rate of return of each stock by its corresponding probability and sum them up. In this case, we have two possible states of the economy (Boom and Bust) with their respective probabilities and rates of return for three stocks (A, B, and C). We calculate the expected return by multiplying the probability of each state by the rate of return for that state, and then summing these values.

To calculate the variance of a portfolio, we consider the weights of each stock, the variances of each stock, and the covariances between the stocks. In this case, we are given the weights and variances. We calculate the variance by multiplying the square of the weight of each stock by its variance, and then summing these values. Additionally, we consider the covariances between the stocks by multiplying the weights of each pair of stocks by their respective covariance values, and summing these as well.

By performing the necessary calculations, we find that the expected return on the equally weighted portfolio is 15.68%, and the variance of the portfolio is 0.218810. These values provide insights into the potential returns and risks associated with the portfolio.

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