Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 14 percent, –9 percent, 16 percent, 21 percent, and 3 percent. For this stock, please calculate the:
a.Arithmetic average return (as a percentage, to 2 decimal places)
b.Historical variance (to 5 decimal places)
c.Standard deviation. (as a percentage, to 2 decimal places)

Answer 1

Answer:

a. 9%

b. 0.01445

c. 12.02%

Step-by-step explanation:

n = 5 years

Return rates = 14%, –9%, 16%, 21%, and 3%

a. Arithmetic average return

$A= \frac{14-9+16+21+3}{5} \\A=9.00$

b. Historical variance (to 5 decimal places)

$V= \frac{\sum (X_i-A)^2}{n-1} \\V= \frac{(0.14-0.09)^2+(-0.09-0.09)^2+(0.16-0.09)^2(0.21-0.09)^2(0.03-0.09)^2}{5-1}\\ V=0.01445$

c. Standard deviation.

$s = \sqrt{V} \\s= \sqrt{0.01445}\\s=0.1202 = 12.02\%$