Section I.A. Statistics and Methods Flashcards
1
Q
Arithmetic average (mean)
A
- Simple average of the sum of all values measured, divided by the number of those values
- Excludes the impact of compounding
2
Q
Geometric average (mean)
A
- A measure of the central tendency of a set of numbers
- Calculated as the n’th root of the product of values
- Commonly used to determine investment performance
- The return based solely on the investment performance of assets held for the time period being measured and eliminates the impact of cash flows
- Reflects the impact of compounding
3
Q
Dispersion
A
How far a set of numbers is spread out
4
Q
Variance
A
- A measure of dispersion, defined as the average squared difference between the mean and each item in the population or in the sample
- Variance is always non-negative
- A high variance means that data points are very spread out
- Variance value of zero means that all values within the set are identical
- Standard deviation, squared
5
Q
Standard deviation
A
- A measure of dispersion expressed as the square root of the variance
- It measures the amount of variability around the average or mean
- An advantage of using standard deviation (as compared to variance) is that it expresses dispersion in the same units as the original values in the sample or population
- A low standard deviation indicates that data points gather close to the mean, while a high standard deviation indicates that data points are spread far apart from the mean
6
Q
Semi-variance
A
- A measurement of dispersion
- Measures data that is below the mean or target value of a data set
- Considered a better measurement of downside risk
- Semi-variance is the average of the squares deviations of all values less than the average or mean
7
Q
Coefficient of variation (CV)
A
- A relative, not absolute, measure of dispersion
- It is the ratio of standard deviation divided by the mean
- Also known as unitized risk, variation coefficient, relative standard deviation
- Shows the extent of variability in relation to the mean of the population
- Assumes a normal distribution
- Used (instead of standard deviation) to compare data sets with different units or widely different means
8
Q
Skewness
A
- Describes asymmetry of data points from a normal distribution
- If data points are skewed to the left it is described as negative skew and if data points are skewed to the right it is described as positive skew
- For distributions that are non-normal (e.g., exhibit skewness, which is a measure of the distribution’s asymmetry around the mean), the standard mean-variance analysis is limited, which means standard deviation is simply less meaningful
- With a negative skew, we have fewer, but more extreme outcomes to the left of the mean. Those outcomes pull the distribution and mean to the left. For a negative skew, the standard deviation may be underestimating the risk because the possibility of that extreme left tail event is not captured by the stat.
- With a positive skew, we have fewer, but more extreme outcomes to the right of the mean. Those outcomes pull the distribution and mean to the right. For a positive skew, the standard deviation may be overestimating the risk.
9
Q
Kurtosis
A
- Measures the peakedness / fatness of the tails (i.e., the tendency for extreme returns) of a probability distribution or normal distribution curve
- If kurtosis is high (leptokurtic), the chart will show fatter tails (i.e., more extreme outcomes), creating a tendency for the observations around the mean to seem great (relative to those between the mean and tails) and appearing to have a higher peak
- If kurtosis is low (platykurtic), a chart will show thinner tails (i.e., fewer extreme outliers) with a tendency for a distribution that appears to have a flatter top (less peakedness) because those observations that would otherwise be concentrated around the mean are elsewhere in the distribution
- Higher kurtosis suggests greater risk than reflected in the normal distribution relied upon in the traditional mean-variance framework
10
Q
Normal distribution
A
- A probability density, commonly described as a “bell shaped curve”
- The mean, median, and mode together lie at the center of the distribution, while the two “tails” extend indefinitely and never touch the x-axis
- Has two parameters, the mean and the standard deviation
- Standard deviation is a good measure of risk when returns are symmetric
- If security returns are symmetric, portfolio returns will be, too
- Future returns can be estimated using only the mean and the standard deviation
- Considered foundational in the development of Modern Portfolio Theory
- Assumptions: no black swan events; the data used is good; the data is applicable going forward
11
Q
Monte Carlo simulation
A
- Statistical modeling method used to approximate the probability of future outcomes through multiple trials (simulations) using random variables
- Can help one visualize and understand variability of future growth (and returns)
- Offers a way to analyze risk
- Powerful tool for illustrating a variety of possible outcomes that could be useful in planning
- Generates a normal distribution where the most likely scenario is found in the middle of the events - this is not always realistic and can create overconfidence which may lead to developing overly aggressive, risky portfolios
- These models are not built to allow for a wide range of inputs: factors, expectations, etc.
- Model assumes efficient markets
12
Q
Covariance
A
- Indicates how two variables are related
- A measure of the degree to which the returns of two assets move together
- A positive covariance indicates that assets move together while a negative covariance indicates that assets move inversely
- Assets possessing a high covariance with each other do not offer much diversification
13
Q
Correlation coefficient
A
- Indicates the degree of relationship between two variables
- Always lies between -1 and +1
- -1 indicates perfect negative relationship, +1 indicates perfect positive relationship, 0 indicates lack of any linear relationship
14
Q
Seasonality
A
- Predictable changes in a time series that recur every year
- As opposed to cyclical effects which may occur in time spans of more or less than one year
- Adjusting past performance or forecasts for demonstrated or expected impact of factors such as seasonality may be beneficial when analyzing data including specific company and industry stock returns and volatility
15
Q
Mean reversion
A
- Theory that asserts data points or events (e.g., stock prices or returns) eventually move toward their long-term average
