Question

Using the following returns, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.

  

	Returns
Year	X	Y
1	10 %	23 %
2	28	44
3	17	-11
4	-18	-25
5	19	52

   

Requirement 1:
(a)	Calculate the arithmetic average return for X.
	(Click to select)13.66%14.00%11.20%12.66%9.07%

   

(b)	Calculate the arithmetic average return for Y.
	(Click to select)16.60%13.45%18.76%20.25%20.75%

  

Requirement 2:
(a)	Calculate the variance for X. (Do not round intermediate calculations.)
	(Click to select)0.0307700.0384620.0305450.0381810.024924

   

(b)	Calculate the variance for Y. (Do not round intermediate calculations.)
	(Click to select)0.0918780.1037690.1297110.1417870.113430

  

Requirement 3:
(a)	Calculate the standard deviation for X. (Do not round intermediate calculations.)
	(Click to select)17.38%21.93%17.54%19.54%14.21%

   

(b)	Calculate the standard deviation for Y. (Do not round intermediate calculations.)

Suppose a stock had an initial price of $72 per share, paid a dividend of $1.20 per share during the year, and had an ending share price of $79.

Compute the percentage total return.

A stock had returns of 11 percent, 16 percent, 14 percent, 8 percent, 13 percent, and -1 percent over the last six years.

  

Required:
(a)	What is the arithmetic return for the stock?
	(Click to select)10.17%12.20%10.68%10.27%10.37%

  

(b)	What is the geometric return for the stock?

Answer 1

Requirement 1

Arithmetic average return = X1 +X2 + . . . .Xn / n

a) Arithmetic average return for X = [ 10 + 28 + 17 + (-18) + 19 ]/ 5 = 11.20 %
ANSWER = C) 11.20 %

b) Arithmetic average return for Y = [ 23 + 44 + (-11) + (-25) + 52 ]/ 5 = 16.60 %
ANSWER = A) 16.60%

Requirement 2

Variance = [ (X1 - x)2 + (x2 - x)2 + . . . .. (Xn - x)/ (n-1)]
a) Variance X = [( 10 - 11.20)2 + (28 - 11.20)2 + (17- 11.20)2 + (-18 - 11.20)2 + (19 - 11.20)2] / (5 - 1)
= 1.44 + 282.24 + 33.64 + 852.64 + 60.84 / 4
= 307.70 or 0.0307700
ANSWER = A) 0.0307700

b) Variance Y = [(23 - 16.6)2 + (44 - 16.60) 2 + (-11 - 16.60)2 + (-25-16.60)2 + (52 - 16.60)2 ] / 4

= 1134.30 or 0.113430
ANSWER = D) 0.113430

Requirement 3

Standard deviation = (Variance)^1/2

a) Standard deviation for X = (307.70)^1/2 = 17.54 %
ANSWER = c) 17.54%

b) Standard deviation for Y = (1134.30)^1/2 = 33.68%

Initial price (P₀)= $72 per share,

Dividend (d)= $1.20 per share

Ending share price (P₁) = $79

percentage total return = (P1 + D - P0) / P0 * 100

= (79 + 1.2 - 72 )/ 72 * 100

= 11.39 %

stock had returns = 11 percent, 16 percent, 14 percent, 8 percent, 13 percent, and -1 percent over the last six years.

a) arithmetic return for the stock = X1 +X2 + . . . .Xn / n

= ( 11 + 16 + 14 + 8 + 13 + (-1) ) / 6

= 10.17 %

ANSWER =A) 10.17%