Question

Given the following price and dividend information, calculate the arithmetic average return, the geometric average return, the sample variance and the sample standard deviation for the returns, holding period return, the $1 invested equivalent, the probability of losing money, the upper bound to the 95th confidence interval, the lower bound to the 99th confidence interval, the lower bound to the 68th confidence interval. (Enter percentages as decimals and round to 4 decimals)

Year	Price	Dividend
0	50.72
1	43.54	1.75
2	49.22	2.10
3	51.30	2.20
4	52.45	2.50
5	56.35	2.75

Answer 1

We need to construct the following table

Year	Price A = Pt in year T	Dividend (B)	Annual Returns Excld Dividend C = (P(t+1) - P(t)	Annual Returns Including Dividend D = C + B	Returns in % Terms E = (D / Previous Year Price)	Deviation from Mean F = ( E - Mean)	Square of Deviations G = F^2
0	50.72
1	43.54	1.75	(7.18)	(5.43)	-10.71%	-17.84%	0.031813
2	49.22	2.10	5.68	7.78	17.87%	10.74%	0.011531
3	51.30	2.20	2.08	4.28	8.70%	1.57%	0.000245
4	52.45	2.50	1.15	3.65	7.12%	-0.02%	0.000000
5	56.35	2.75	3.90	6.65	12.68%	5.55%	0.003078
	Total				35.65%	0.00%	0.04667

Arithmetic mean = Sum of All Returns in % / Total number of counts =( -10.71 + 17.87 + 8.70 + 7.12 + 12.68) / 5 = 35.65 /5 = 7.13%

Formula for Geometric Mean = ((1+ R1) x (1+R2) x (1+R3) X..... (1+Rn)) ^ (1/n) -1,

where R1 , R2,.... Rn are returns in yr 1, 2,....n

Geometric Mean =( ((1-10.71%) X (1+17.87%) X (1+8.70%) x (1+7.12%) x (1+12.68%)) ^ (1/5)) -1 = ((138.05%)^(1/5)) -1

= 106.67% -1 = 6.67%

Sample Variance = Sum of the Squares of Deviation / (n-1), where n is total values

Here N =5 (5 values of mean)

Sample variance from above = (0.0318 + 0.0115 + 0.0002 + 0.0000+ 0.0031)/ (5-1)

= 0.04667 / 4 = 0.0117

Standard Deviation = (Variance) ^ (1/2) = (0.0117) ^ (1/2) = 0.108 = 10.80%