Question

suppose the following information represents the return for General Motors (GM) and American Telephone & Telegraph (ATT) common stocks over a five-year period: Year Revenue GM ATT 1 10% 12% 2 4 6 3 -9 -10 4 20 22 5 5 5 a) what is the mean return for the GM common stock? what is it for ATT common stock? b) what is the variance of the return for GM common stock? what is it for the ATT common stock? c) what is the standard deviation of the return for GM common stock? what is it for the ATT common stock? d) suppose the returns for the GM and ATT have normally distributed returns with means and standard deviations (SDs) calculated in problems b) and c) respectively. for each stock, determine the range of returns within one SD of the mean and the range within two SDs of the mean. Interpret the results. e) Given the data from previous answers, what is the probability that, in any given year, the return for GM common stock will be negative? What is the probability that the ATT return will be negative? ASKING ABOUT D) AND E).

Answer 1

Answer (a) to (c):

Using excel formula, Mean, Variance and Standard deviation (SD) are calculated as below:

The excel with 'show formula" is as below:

Answer (d)

Mean +- one SD

GM Stock:

6% +/- 10.51%

GM stock: Range of returns within one SD of the mean for GM stock is -4.51% to 16.51% .

This implies that there is 68.26% probability that return on GM stock will vary between -4.51% to 16.51%.

ATT Stock:

7% +/- 11.66%

ATT stock: Range of returns within one SD of the mean for GM stock is - 4.66% to 18.66% .

This implies that there is 68.26% probability that return on GM stock will vary between - 4.66% to 18.66%.

Mean +- two SD

GM Stock:

6% +/- 2 * 10.51%

GM stock: Range of returns within two SD of the mean for GM stock is -15.02% to 27.02%.

This implies that there is 95.68% probability that return on GM stock will vary between -15.02% to 27.02%.

ATT Stock:

7% +/- 2 * 11.66%

ATT stock: Range of returns within two SD of the mean for GM stock is - 16.32% to 30.32%.

This implies that there is 95.68% probability that return on GM stock will vary between - 16.32% to 30.32%.

Answer (d)

Probability that, in any given year, the return for GM common stock will be negative:

GM Stock:

z value = (0% - 6%) / 10.51% = - 0.57

From z table we get:

Probability that, in any given year, the return for GM common stock will be negative (or Return < 0%) is = 28.43%

ATT Stock:

z value = (0% - 7%) / 11.66% = - 0.60

From z table we get:

Probability that, in any given year, the return for GM common stock will be negative (or Return < 0%) is = 27.43%