Question

You’ve observed the following returns on Crash-n-Burn Computer’s stock over the past five years: 8 percent, −15 percent, 19 percent, 31 percent, and 21 percent. a. What was the arithmetic average return on the company's stock over this five-year period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b-1. What was the variance of the company's returns over this period? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.) b-2. What was the standard deviation of the company's returns over this period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

a). Arithmetic average return=12.80%

b). The variance of the company's returns=116.2

c). Standard deviation=10.78

Explanation:

a). The arithmetic average return can be expressed as;

Arithmetic average return=Sum of returns/Number of returns

where;

Sum of returns=8%+(-15%)+19%+31%+21%=64

Number of returns=5

replacing;

Arithmetic average return=64/5=12.80%

b). Variance of the company's returns

Step 1: Write down formula for variance

Variance=∑(Xi-X)²/n-1

where;

Xi=term in data set

X=sample mean

∑=sum

n=sample size

Step 2: write down each data set

X1=8%, X2=-15%, X3=19%, X4=31%, X5=21%

Step 3: Subtract the mean from each data set

Take the absolute value of each data

X1-X=8-12.8=-4.8

X2-X=15-12.8=2.2

X3-X=19-12.8=6.2

X4-X=31-12.8=18.2

X5-X=21-12.8=8.2

Step 4: Square each result and sum

∑(Xi-X)²=4.8²+2.2²+6.2²+18.2²+8.2²=464.8

Step 5: Divide by n-1

n=number of data points=5

n-1=5-1=4

∑(Xi-X)²/n-1=464.8/4=116.2

The variance of the company's returns=116.2

c). Standard deviation=√variance=√116.2

Standard deviation=10.78