Question

Gas Co. for 2013. Using these data, estimate the average monthly return and the volatility for each stock 6.00% January February 9.60% -1.40% 5.30% March -0.80% - 2.50% -2.90% 14.30% April May -3.40% - 1.20% -4.00% June 6.80% 1.17% July August September 12.30% 4.40% 3.20% -3.80% -4.20% October -3.30% 4.80% 0.70% 1.40% November December 1.40% 8.60% The average monthly return for Cola Co. is %. (Round to two decimal places.)

Answer 1

The average monthly return of Stock 1 is the average return of the 12 months

= (6% -1.4% - 0.8% - 2.9% -3.4% -4% + 1.17% +3.20% -3.80%- 3.30% +0.70% +1.4%) /12

= -0.59%

Volatility = (sum of deviations/ n) ^0.5

Stock 1	Xi - Mean	(Xi - Mean)^2
6.00%	6.59%	0.00434281
-1.40%	-0.81%	0.00006561
-0.80%	-0.21%	0.00000441
-2.90%	-2.31%	0.00053361
-3.40%	-2.81%	0.00078961
-4.00%	-3.41%	0.00116281
1.17%	1.76%	0.00030976
3.20%	3.79%	0.00143641
-3.80%	-3.21%	0.00103041
-3.30%	-2.71%	0.00073441
0.70%	1.29%	0.00016641
1.40%	1.99%	0.00039601
Sum of deviations		0.01097227

Volatility = (0.01097227 /12)^0.5

= 3.02%

The average monthly return of Stock 2 is the average return of the 12 months

= (9.6% + 5.3% -2.5% + 14.3% -1.2% + 6.8% +12.3% + 4.4% -4.2% + 4.8% + 1.4% + 8.6%) /12

= 4.97%

Stock 2	Xi - Mean	(Xi - Mean)^2
9.60%	4.63%	0.00214369
5.30%	0.33%	0.00001089
-2.50%	-7.47%	0.00558009
14.30%	9.33%	0.00870489
-1.20%	-6.17%	0.00380689
6.80%	1.83%	0.00033489
12.30%	7.33%	0.00537289
4.40%	-0.57%	0.00003249
-4.20%	-9.17%	0.00840889
4.80%	-0.17%	2.89E-06
1.40%	-3.57%	0.00127449
8.60%	3.63%	0.00131769
Sum of deviations		0.03699068

Volatility = (Sum of deviations / n ) ^ 0.5

= (0.03699068 /12)^0.5

= 5.55%