Asked by Shauntae Davis on May 12, 2024
Verified
Given the following historical returns, what is the variance? Year 1 = 8%; year 2 = -12%; year 3 = 6%; year 4 = 1%; year 5 = -19%.
A) 0.0063
B) 0.0089
C) 0.0139
D) 0.0394
E) 0.1178
Variance
A statistical measurement of the dispersion of a set of data points, reflecting how much each number in the set differs from the mean.
- Compute and comprehend the differences in returns on investments.
Verified Answer
KJ
Katelund JonesMay 19, 2024
Final Answer :
C
Explanation :
To calculate the variance of these returns, first, find the mean (average) return: 8−12+6+1−195=−3.2% \frac{8 - 12 + 6 + 1 - 19}{5} = -3.2\% 58−12+6+1−19=−3.2% . Then, calculate the squared deviations from the mean for each year, sum them, and divide by the number of observations minus one (for sample variance): (8−(−3.2))2+(−12−(−3.2))2+(6−(−3.2))2+(1−(−3.2))2+(−19−(−3.2))25−1=0.0139 \frac{(8 - (-3.2))^2 + (-12 - (-3.2))^2 + (6 - (-3.2))^2 + (1 - (-3.2))^2 + (-19 - (-3.2))^2}{5 - 1} = 0.0139 5−1(8−(−3.2))2+(−12−(−3.2))2+(6−(−3.2))2+(1−(−3.2))2+(−19−(−3.2))2=0.0139 or 1.39%.
Learning Objectives
- Compute and comprehend the differences in returns on investments.