Question

1. Suppose a stock had an initial price of $67 per share, paid a dividend of $1.55 per share during the year, and had an ending share price of $82. Compute the percentage total return.

2. A stock had returns of 13 percent, 13 percent, 14 percent, -10 percent, 19 percent, and 8 percent over the last six years.

a) What is the arithmetic return for the stock?

b) What is the geometric return for the stock?

3.  

	Returns
Year	X			Y
1		16	%		22	%
2		30			31
3		11			12
4	–	23		–	28
5		10			22

  

Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y. (Do not round intermediate calculations. Enter your average return and standard deviation as a percent rounded to 2 decimal places, e.g., 32.16, and round the variance to 5 decimal places, e.g., 32.16161.)
	X	Y
Average return	%	%
Variance
Standard deviation	%	%

4. You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 3 percent, -12 percent, 29 percent, 16 percent, and 15 percent.

a) What was the arithmetic average return on Crash-n-Burn’s stock over this five year period?

b) What was the variance of Crash-n-Burn’s returns over this period? (Do not round intermediate calculations.)

c) What was the standard deviation of Crash-n-Burn’s returns over this period? (Do not round intermediate calculations.)

Answer 1

1)

Total percentage return = ( ending value + dividends - beginning value) / beginning value

Total percentage return = ( 82 + 1.55 - 67 ) / 67

Total percentage return = 16.55 / 67

Total percentage return = 0.247015 or 24.7%

2)

a)

Arithmetic return = sum of returns / number of returns

Arithmetic return = [ 0.13 + 0.13 + 0.14 + (- 0.1) + 0.19 + 0.08) / 6

Arithmetic return = 0.57 / 6

Arithmetic return = 0.095 or 9.5%

b)

Add 1 to all the returns:

1 + 0.13 = 1.13, 1 + 0.13 = 1.13, 1 + 0.14 = 1.14, 1 + (-0.1) = 0.9, 1 + 0.19 = 1.19, 1 + 0.08 = 1.08

Multiply all: 1.13 * 1.13 * 1.14 * 0.9 * 1.19 * 1.08 = 1.68374

Since there are 6 periods, take the 6th root of 1.68374

6th root of 1.168374 = 1.090718

Deduct 1 = 1.090718 - 1 = 0.090718

Geometric return = 9.0718%

3)

Arithmetic return of X = [ 0.16 + 0.3 + 0.11 + (-0.23) + 0.1 ] / 5

Arithmetic return of X = 0.088 or 8.8%

To calculate variance, first calculate the difference between each observed return and the average return and square the difference:

(0.16 - 0.088)² = 0.005184, ( 0.3 - 0.088)² = 0.044944, ( 0.11 - 0.088)² = 0.000484, [(-0.23) - 0.088]² = 0.101124, ( 0.1 - 0.088)² = 0.000144

Sum the results and divide by N(number of observations) - 1 = (0.005184 + 0.044944 + 0.000484 + 0.101124 + 0.000144) / 5 - 1 = 0.15188 / 4

Variance of X= 0.15188 / 4 = 0.03797

To find standard deviation, we take the square root of variance:

Square root of 0.03797 = 0.194859

Standard deviation of X = 19.49%

Arithmetic return of Y = [ 0.22 + 0.31 + 0.12 + (-0.28) + 0.22 ] / 5

Arithmetic return of Y = 0.118 or 11.8%

To calculate variance, first calculate the difference between each observed return and the average return and square the difference:

(0.22 - 0.118)² = 0.010404, ( 0.31 - 0.118)² = 0.036864, ( 0.12 - 0.118)² = 0.000004, [(-0.28) - 0.118]² = 0.158404, ( 0.22 - 0.118)² = 0.010404

Sum the results and divide by N(number of observations) - 1 = (0.010404 + 0.036864 + 0.000004 + 0.158404 + 0.010404) / 5 - 1 = 0.21608 / 4

Variance of Y = 0.21608 / 4 = 0.05402

To find standard deviation, we take the square root of variance:

Square root of 0.05402 = 0.232422

Standard deviation of Y = 23.24%

4)

Arithmetic return of Crash-n-Burn = [ 0.03 + (-0.12) + 0.29 + 0.16 + 0.15 ] / 5

Arithmetic return of Crash-n-Burn = 0.102 or 10.2%

To calculate variance, first calculate the difference between each observed return and the average return and square the difference:

(0.03 - 0.102)² = 0.005184, [(-0.12) - 0.102]² = 0.049284, ( 0.29 - 0.102)² = 0.035344, (0.16 - 0.102]² = 0.003364, ( 0.15 - 0.102)² = 0.002304

Sum the results and divide by N(number of observations) - 1 = (0.005184 + 0.049284+ 0.035344+ 0.003364+ 0.002304) / 5 - 1 = 0.09548 / 4

Variance of Crash-n-burn= 0.15188 / 4 = 0.02387

To find standard deviation, we take the square root of variance:

Square root of 0.02387 = 0.154499

Standard deviation of Crash-n-burn = 15.45%