CAIA Level 1 - Chapter 4 - Statistical Foundations Questions and Answers Already Passed

CAIA Level 1 - Chapter 4 - Statistical Foundations Questions and Answers Already Passed Ex Post Returns - Answers Realized outcomes rather than anticipated outcomes Ex Ante Returns - Answers Future possible returns and their probabilities Normal Distribution - Answers Bell-shaped distribution, symmetric with mirror image sides, peaks near center with decreasing probabilities of extreme events Lognormal Distribution - Answers Distribution where the logarithm of the variable is normally distributed, usually exhibits some right-skew Variance - Answers Measurement of spread between numbers in a data set, key parameter in asset allocation, helps optimize return-volatility trade-off in portfolios Standard Deviation - Answers Statistic measuring dispersion of a dataset relative to its mean, calculated as square root of variance Volatility - Answers Statistical measure of dispersion of returns for a security or market index, higher volatility indicates higher risk, can be measured using standard deviation or variance Skewness - Answers Degree of distortion from symmetrical bell curve in a set of data, can be negative, positive, zero, or undefined, used with kurtosis to assess tail probabilities Kurtosis - Answers Statistical measure describing distribution, measures extreme values in tails Excess Kurtosis - Answers Probability or return distribution with kurtosis coefficient larger than normal distribution, indicates higher probability of extreme outcomes Mesokurtosis - Answers A return distribution with no excess kurtosis, similar to the normal distribution, is called mesokurtic or normal tailed. Platykurtosis - Answers A return distribution with negative excess kurtosis, indicating less kurtosis than the normal distribution, is considered thin tailed. Lepokurtosis - Answers A return distribution with positive excess kurtosis, meaning more kurtosis than the normal distribution, is termed fat tailed. Covariance - Answers Measures the directional relationship between returns on two risky assets. Positive covariance indicates returns move together, while negative covariance means returns move inversely. Correlation Coefficient - Answers Calculates the strength of the relationship between the relative movements of two variables. Values range from -1.0 to 1.0. Perfect Linear Negative Correlation - Answers A correlation coefficient of -1 indicates assets move in opposite directions and in the same proportion. Perfect Linear Positive Correlation - Answers A correlation coefficient of +1 indicates assets move in the same direction and in the same proportion. Spearman Rank Correlation - Answers Adjusts for outliers by measuring the relationship between variable ranks rather than values.