CAIA Level 1 - Chapter 4: Statistical Foundations with Correct Solutions

Ex post returns - ANSWER-- are realized outcomes rather than anticipated outcomes ex ante returns - ANSWER-- future possible returns and their probabilities normal distribution - ANSWER-- is the familiar bell shaped distribution, also known as the Gaussian distribution - is symmetric, meaning the left and the right sides are mirror images of each other. - also, it peaks (or clusters) near the center, with decreasing probabilities of extreme events lognormal distribution - ANSWER-- a variable has this if the distribution the logarithm of the variable is normally distributed. - Usually exhibits some degree of a right-skew Variance - ANSWER-- measurement of the spread between numbers in a data set. - It measures how far each number in the set is from the mean and is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. - one of the key parameters in asset allocation. Along with correlation, helps investors to develop optimal portfolios by optimizing the return-volatility trade-off in investment portfolios. Standard Deviation - ANSWER-- a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance Volatility - ANSWER-- a statistical measure of the dispersion of returns for a given security or market index. In most cases, the higher the volatility, the riskier the security. - can either be measured by using the standard deviation or variance between returns from that same security or market index. - In the securities markets, it is often associated with big swings in either direction. Skewness - ANSWER-- in statistics, is the degree of distortion from the symmetrical bell c