# Variance - Portfolio Probability

Sorry for the terrible paste job below but can anyone explain why you don’t divide by n when calculating variance in this problem (Schweser Qbank problem)? ------------------- Tully Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Tully’s economist has estimated the probability of each scenario, as shown in the table below. Given this information, what is the standard deviation of expected returns on portfolio B? Scenario Probability Return on Portfolio A Return on Portfolio B A 15% 18% 19% B 20% 17% 18% C 25% 11% 10% D 40% 7% 9% A) 9.51%. B) 4.34%. C) 12.55%. D) 8.35%. Your answer: B was correct! Scenario Probability Return on Portfolio B P * [RB – E(RB)]2 A 15% 19% 0.000624 B 20% 18% 0.000594 C 25% 10% 0.000163 D 40% 9% 0.000504 E(RB) = 12.55% ó2 = 0.001885 ó = 0.0434166

These are weighted averages. Think about it conceptually. What does variance measure? It measures the average variability in the data set. More specifically, it measures the average squared deviations from the mean. If you are just given a set of numbers (no probabilities of occurrence), you have to divide by n to get the average. If you are given the percentage weights of each of your set of numbers, then you are factoring in the average by multiplying the squared deviation by the weight. Get it?

Here is how to get it right on the test. Think: What does N mean? N is the numbe of observations. You are not calculating variance using the observations, you are calculating variance using the probability distribution.

That makes absolute sense!

Perfect - thanks.