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Answer :
The expected return of the stock is 13.5%. The standard deviation of the stock's returns is approximately 6.73%.
Part 2a is that the expected return of the stock can be calculated by multiplying each potential return by its corresponding probability, and then summing the results.
To calculate the expected return, we need to consider the potential returns of the stock in each economic scenario (recession, normal economy, and boom) and their corresponding probabilities.
In a recession, the stock will have a loss of 10 percent. Since the probability of a recession is 10 percent, the contribution to the expected return from this scenario
is -10% * 10% = -1%.
In a normal economy, the stock will gain 15 percent. Since the probability of a normal economy is 70 percent, the contribution to the expected return from this scenario is
15% * 70% = 10.5%.
In a boom, the stock will gain 20 percent. Since the probability of a boom is 20 percent, the contribution to the expected return from this scenario is
20% * 20% = 4%.
To find the overall expected return, we sum up the contributions from each scenario:
-1% + 10.5% + 4% = 13.5%.
Therefore, the expected return of this stock is 13.5%.
Calculation:
Recession: -10% * 10% = -1%
Normal economy: 15% * 70% = 10.5%
Boom: 20% * 20% = 4%
Overall expected return = -1% + 10.5% + 4% = 13.5%
Part 2b is that the standard deviation of the stock's returns can be calculated using the formula for the weighted standard deviation.
The standard deviation measures the variability or dispersion of the stock's returns. In this case, we have different probabilities associated with each return.
To calculate the standard deviation, we first calculate the variance. The variance is the average of the squared deviations from the expected return, weighted by their respective probabilities.
In a recession, the deviation from the expected return is
-1% - 13.5% = -14.5%.
Squaring this value gives us 210.25. Multiplying this by the probability of a recession (10%) gives us a weighted contribution to the variance of 21.025.
In a normal economy, the deviation from the expected return is
10.5% - 13.5% = -3%.
Squaring this value gives us 9. Multiplying this by the probability of a normal economy (70%) gives us a weighted contribution to the variance of 6.3.
In a boom, the deviation from the expected return is
4% - 13.5% = -9.5%.
Squaring this value gives us 90.25. Multiplying this by the probability of a boom (20%) gives us a weighted contribution to the variance of 18.05.
To find the overall variance, we sum up the weighted contributions from each scenario:
21.025 + 6.3 + 18.05 = 45.375.
The standard deviation is the square root of the variance. Taking the square root of 45.375 gives us approximately 6.73.
Therefore, the standard deviation of the stock's returns is approximately 6.73%.
Learn more about standard deviation: https://brainly.com/question/13498201
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