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You recently purchased a stock that is expected to earn 30 percent in a booming economy, 15 percent in a normal economy, and lose 10 percent in a recessionary economy. There is a 4 percent probability of a boom and a 70 percent probability of a normal economy.

What is your expected rate of return on this stock?

(Hint: First find the probability of a recessionary economy. Do not round intermediate calculations. Input your answer as a percent rounded to two decimal places, e.g., 1.23. A negative answer should be represented with a negative sign (-). Do not input a percent sign with your answer.)

Answer :

To find the expected rate of return on this stock, you'll need to calculate the weighted average of the possible returns, with the weights being the probabilities of each economic condition. Here's a step-by-step solution:

  1. Identify the Probabilities and Expected Returns:

    • Booming Economy: Probability = 4% or 0.04; Expected Return = 30%

    • Normal Economy: Probability = 70% or 0.70; Expected Return = 15%

    • Recessionary Economy: This probability is not given directly, but since probabilities must sum to 100%, we calculate it as follows:

      [tex]\text{Probability of a Recessionary Economy} = 1 - (0.04 + 0.70) = 0.26 \text{ or } 26\%[/tex]

    • Expected Return in a Recessionary Economy = -10%

  2. Calculate the Expected Return (ER):

    The expected rate of return is calculated by multiplying each return by its probability and then summing these products:

    [tex]\text{ER} = (0.04 \times 30\%) + (0.70 \times 15\%) + (0.26 \times (-10\%))[/tex]

  3. Perform the Calculations:

    [tex]\text{ER} = (0.04 \times 0.30) + (0.70 \times 0.15) + (0.26 \times (-0.10))[/tex]

    [tex]= 0.012 + 0.105 - 0.026[/tex]

    [tex]= 0.091[/tex]

    This gives us an expected rate of return of 9.1%.

  4. Conclusion:

    The expected rate of return on the stock, given the probabilities of different economic conditions, is 9.10%. This means that, on average, you would expect to earn a return of 9.10% on this stock, factoring in the likelihood of different economic scenarios.

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