Consider the following information: State ofEconomy Probability of State of Economy Rate of Return if State OccursStock A Stock B Stock CBoom 0.60 0.08 0.16 0.34 Bust 0.40 0.18 0.09 −0.06 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)
Question
Consider the following information: State ofEconomy Probability of State of Economy Rate of Return if State OccursStock A Stock B Stock CBoom 0.60 0.08 0.16 0.34 Bust 0.40 0.18 0.09 −0.06 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)
Solution
To calculate the expected return on an equally weighted portfolio of these three stocks, we first need to calculate the expected return for each stock individually. The expected return for a stock is calculated by multiplying the probability of each state of the economy by the rate of return if that state occurs, and then summing these products.
For Stock A: Expected return = (0.60 * 0.08) + (0.40 * 0.18) = 0.048 + 0.072 = 0.12 or 12%
For Stock B: Expected return = (0.60 * 0.16) + (0.40 * 0.09) = 0.096 + 0.036 = 0.132 or 13.2%
For Stock C: Expected return = (0.60 * 0.34) + (0.40 * -0.06) = 0.204 - 0.024 = 0.18 or 18%
Since the portfolio is equally weighted, we assume that one-third of the portfolio is invested in each stock. Therefore, the expected return on the portfolio is the average of the expected returns of the three stocks.
Expected return on portfolio = (0.12 + 0.132 + 0.18) / 3 = 0.144 or 14.4%
So, the expected return on an equally weighted portfolio of these three stocks is 14.4%.
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