Question

Please show all the calculations

year	Computroids Inc	Blazers Inc
1	10%	5%
2	5%	6%
3	-3%	7%
4	12%	8%
5	10%	9%
Mean	6.8	7
Standard Deviation	5.42	1.41

a) Assuming these observations are drawn from a normally distributed probability distribution, 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.

b) determine whether a return of 14% would fall within each of the six confidence intervals and complete the table below with your calculated ranges/confidence intervals.

Computroids:

Confidence interval	Bottom of range	Top of range	Includes 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, it’s 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.)

Answer 1

	a)	As per 68-95-99 emperical rule,68% values lie within
		one Sigma(Standard Deviation) around the Mean
		95% values lie within TWO Sigma around the Mean
		99% values lie within TWO Sigma around the Mean
		of a normal distribution
		COMPUTROIDS
		68% Confidence Interval:Lower Range 6.8%-5.42%=	1.38%
		68% Confidence Interval:Upper Range 6.8%+5.42%=	12.22%
		95% Confidence Interval:Lower Range 6.8%-(2*5.42%)=	-4.04%
		95% Confidence Interval:Upper Range 6.8%+(2*5.42%)=	17.64%
		99% Confidence Interval:Lower Range 6.8%-(3*5.42%)=	-9.46%
		99% Confidence Interval:Upper Range 6.8%+(3*5.42%)=	23.06%
		BLAZERS INC
		68% Confidence Interval:Lower Range 7%-1.41%=	5.59%
		68% Confidence Interval:Upper Range 7%+1.41%=	8.41%
		95% Confidence Interval:Lower Range 7%-(2*1.41%)=	4.18%
		95% Confidence Interval:Upper Range 7%+(2*1.41%)=	9.82%
		99% Confidence Interval:Lower Range 7%-(3*1.41%)=	2.77%
		99% Confidence Interval:Upper Range 7%+(3*1.41%)=	11.23%

b)

Computroids:

Confidence interval	Bottom of range	Top of range	Includes 14% return*
68%	1.38	12.22	No
95%	-4.04	17.64	Yes
99%	-9.46	23.06	Yes

Blazers:

Confidence interval	Bottom of range	Top of range	Includes a 14% return*
68%	5.59	8.41	No
95%	4.18	9.82	No
99%	2.77	11.23	No