10.1 (14 marks)

a. Calculate the mean and standard deviation of the following securities returns and enter them in the table below: (4 marks)

Year	Computroids Inc.	Blazers Inc.
1	10%	5%
2	5%	6%
3	3%	7%
4	12%	8%
5	10%	9%
Mean
Standard deviation

b. Assuming these observations are drawn from a normally distributed probability distribution, we know that about 68.27% of values are within one standard deviation above and below the mean or expected return; about 95.45% of the values are within two standard deviations, and about 99.73% lie within three standard deviations. For simplicity, these are commonly called the 68%, 95%, and 99% confidence intervals.

Using your calculations from part a, calculate the 68%, 95% and 99% confidence intervals for the two stocks. To calculate the 68%, calculate the top of the confidence interval range by adding one standard deviation to the expected return, and calculate the bottom of the confidence interval by subtracting one standard deviation from the expected return. For 95%, use two standard deviations, and for 99%, use three. (6 marks)

c. Finally, determine whether a return of 14% would fall within each of the six confidence intervals. (4 marks)

Complete the table below with your calculated ranges/confidence intervals.

Computroids:

Confidence interval	Bottom of range	Top of range	Includes a 14% return*
68%			Yes/No
95%			Yes/No
99%			Yes/No

Blazers:

Confidence interval	Bottom of range	Top of range	Includes a 14% return*
68%			Yes/No
95%			Yes/No
99%			Yes/No

*This is the same as asking whether a return of 14% has less than the stated probability to occur by chance for that security. If a 14% return is not inside the 68% CI, its somewhat unlikely to occur, since it will only occur by chance 32% of the time. Of course, the 99% CI is much more likely to include the observed return simply by chance. A 14% return will fall outside the 99% CI only 1% of the time (quite rare compared to the 32% for the 68% CI.)