A. This is the variance of the security, but it is not its standard deviation. The standard deviation is the square root of the variance.
B. This answer results from summing the squared deviations and taking the square root of the sum of the squared deviations. However, it does not take into account the probabilities of each occurring.
C. The first step in calculating the standard deviation of an individual security is to determine the expected return. The expected return is a weighted average of all of the possible returns, weighted according to each one's probability of occurring.
The expected return is: (.04 * .05) + (.07 * .25) + (.09 * .45) + (.15 * .20) + (.20 * .05) = .10 or 10%.
The standard deviation of an individual security is calculated with the following formula:
s=([(x1-x)^2+(x2-x)^2+......(xn-x)^2]/n)^(1/2) x=10%
D. This answer results from taking each of the deviations from the expected return and, using the absolute values of the results, weighting them according to their probabilities, summing them, and taking the square root of the sum. However, this is not the way to eliminate negative numbers from the deviations. The deviations (negative and positive) should each be squared to eliminate the negative amounts. The squared values are then weighted according to their probabilities, summed, and the square root of the sum is the standard deviation.