Question

10.1 A. Calculate the mean and standard deviation of the following securities’ returns: Year Computroids Inc. Blazers Inc. 1 10% 5% 2 5% 6% 3 –3% 7% 4 12% 8% 5 10% 9%

B. Assuming these observations are drawn from a normally distributed probability space, we know that about 68% of values drawn from a normal distribution are within one standard deviation away from the mean or expected return; about 95% of the values are within two standard deviations; and about 99.7% lie within three standard deviations. Using your calculations from part A, calculate the 68%, 95%, and 99% confidence intervals for the two stocks. To calculate the 68%, you would 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. Your answer should show three ranges from the bottom of the confidence interval to the top of the confidence interval.

C. For each security, would a return of 14% fall into the 68% confidence interval range? If not, what confidence interval range would it fall into, or would it be outside all three confidence intervals? (This is the same as asking whether a return of 14% has less than a 68% probability of occurring by chance for that security. If it’s not inside the 68% confidence interval, it’s unlikely to occur, since it will only occur by chance 32% of the time. Of course, the 99% confidence interval is much more likely to include the observed return, simply by chance. Only 1% of the time will it fall outside the 99% CI. Pretty rare.)

Answer 1

Sol:

A). Mean for Computroids Inc = 10+5+(-3)+12+10= 34 / 5 = 6.8
Mean for Blazers Inc. = 5+6+7+8+9 = 35 / 5 = 7
SD for Computroids Inc = 3.80789
SD for Blazers Inc = 1.58114

B). 2.07188 ? x ? 11.52812 for Computroids at 95%
-1.04050 ? x ? 14.64050 for Computroids at 99%
5.03676 ? x ? 8.96324 for Blazers at 95%
3.74441 ? x ? 10.25559 for Blazers at 99%

C). (This is the same as asking whether a return of 14% has less than a 68% probability of occuring by chance for that security. If it’s not inside the 68% confidence interval, it’s unlikely to occur, since it will only occur by chance 32% of the time. Of course, the 99% confidence interval is muchmore likely to include the observed return, simply by chance. Only 1% of the time will it fall outside the 99% CI. Pretty rare.) I think out of all three ranges it has better luck with the 99% range for computroids. As for Blazers I don’t think 14% return would fall into any of the three categories. Computroids has the best chance at the 14% return within the 99%.