Question

1) Consider the following information:

State Probability Stock A Stock B Stock C
Boom 0.65 0.23 0.20 0.14
Bust 0.35 0.01 0.05 0.27
What is the expected return on an equally weighted portfolio of these three stocks? (Hint: Equally means that each stock has the same weight. Given that there are only 3 stocks, each has a weight of 1/3) Enter the answer with 4 decimals (e.g. 0.1234).

Answer 1

To find the expected return on an equally weighted portfolio of three stocks, calculate the expected return for each state (Boom and Bust) using the returns of each stock and their equal weight, then combine these according to the probabilities of each state.

Step-by-step explanation:

To calculate the expected return on an equally weighted portfolio of three stocks (Stock A, Stock B, and Stock C), we need to consider the probability and return of each state (Boom and Bust), along with the weight of each stock in the portfolio. Since the portfolio is equally weighted and only contains three stocks, each stock contributes one third to the portfolio's return.

We can use the following formula to calculate the expected return for each state:

Expected Return (State) = (Return of Stock A × Weight) + (Return of Stock B × Weight) + (Return of Stock C × Weight)

For the 'Boom' state:

Expected Return (Boom) = (0.23 × 1/3) + (0.20 × 1/3) + (0.14 × 1/3)

For the 'Bust' state:

Expected Return (Bust) = (0.01 × 1/3) + (0.05 × 1/3) + (0.27 × 1/3)

Now, we compute the overall expected return of the portfolio by summing the product of the state probabilities and the expected returns of each state:

Total Expected Return = (Probability of Boom × Expected Return (Boom)) + (Probability of Bust × Expected Return (Bust))

After calculating the expected return for both states and factoring in the probabilities, we can determine the expected return for the portfolio to the fourth decimal point.