Question

Consider the following returns and states of the economy for TZ.Com.: Economy Probability Return Weak 25% 2% Normal 50% 8% Strong 25% 15% What is the standard deviation of TZ's returns?

Answer 1

To calculate the standard deviation of TZ's returns, one must determine the expected return, find the squared differences from the mean, sum these values weighted by their probabilities, and take the square root of this sum. The standard deviation is approximately 14.507%.

Step-by-step explanation:

The question involves calculating the standard deviation of the returns of a company called TZ.Com given different states of the economy with their respective probabilities and returns. Standard deviation is a measure of the amount of variance or dispersion of a set of values.

Here are the steps to calculate the standard deviation:

1. Calculate the expected return (mean). This is done by multiplying each possible return by its probability and adding the results together.
2. Find the squared differences from the mean for each state. Multiply each squared difference by the corresponding probability.
3. Sum the values obtained in step 2.
4. The variance is the sum from step 3. To get the standard deviation, take the square root of the variance.

Let's go through the steps using the provided data:

1. Expected return (mean) = (0.25×2%) + (0.50×8%) + (0.25×15%) = 0.005 + 0.04 + 0.0375 = 0.0825 or 8.25%
2. The squared differences from the mean for each state are:
   
3. Sum of squared differences times their probabilities: (0.25×0.03890625) + (0.50×0.0000625) + (0.25×0.04515625) = 0.0097265625 + 0.00003125 + 0.0112890625 = 0.021046875
4. The variance is 0.021046875. Taking the square root gives us the standard deviation: √0.021046875 ≈ 0.14507 or 14.507%.

Answer 2

Answer: To calculate the standard deviation of TZ's returns, we first need to calculate the expected return and variance. The expected return is calculated by multiplying each return by its probability and summing the results:

Expected return = (0.25 x 2%) + (0.5 x 8%) + (0.25 x 15%) = 6.25%

Next, we calculate the variance, which measures the average squared deviation from the expected return:

Variance = (0.25 x (2% - 6.25%)^2) + (0.5 x (8% - 6.25%)^2) + (0.25 x (15% - 6.25%)^2) = 20.89%

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation = sqrt(20.89%) = 0.457 or 45.7% (rounded to one decimal place)

Therefore, the standard deviation of TZ's returns is approximately 45.7%.

Step-by-step explanation: