Final answer:
The variance of a portfolio's returns with a standard deviation of 30% is found by squaring the standard deviation, resulting in 900%, which is correctly expressed as 900.00% squared.
Step-by-step explanation:
If the standard deviation of a portfolio's returns is 30%, then the variance is calculated by squaring the standard deviation. The formula for variance (σ²) given the standard deviation (σ) is σ² = σ x σ.
Therefore, the variance in this case is:
σ² = 30% x 30% = 900%
But when we express this in terms of percentage points squared, it becomes:
σ² = (30%)^2 = (0.30)^2 = 0.09 or 9%
However, to leave it as purely a numerical value without converting it into a percentage, we use:
σ² = 900.00%, or more accurately, 900.00% squared when expressing variance as a percent.
Hence, the correct option would be b. 900.00% squared.
The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.
Here,
Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).