1. Statistics Flashcards
What are the main measures of dispersion?
The range, variance and standard deviation
What are the main measures of central tendency?
Mean, median and mode
What is dispersion?
The extent to which values within the distribution are spread around, or deviate from, a single number (found through the mean, median or mode)
What is the mean?
The average value of all the date
What is the median?
The middle item that has exactly half the data above it and half below it
What is the mode?
The most common number that occurs
what is the most commonly used measure of central tendency and what is its main drawback?
The mean
It takes into account extremes of data which influence the result
What measure of central tendency would be used for data which had extreme outliers?
The median
When would it be useful to use the geometric mean?
When looking at compound changes such as portfolio returns
What is the range?
The simplest measure of dispersion - the difference between the highest and the lowest values in a set of data
What is the main drawback of using range as a measure of dispersion?
It is distorted by extreme values and ignores the numbers in between
What is the variance?
The variance measures the spread of data to determine the dispersion of data around the arithmetic mean
What is the main advantage and the main disadvantage of variance?
It provides a measure of dispersion and is used to calculate the beta of a stock
It results in a value in different units than the original
How do you work out the standard deviation from the variance?
Standard deviation is the square root of the variance
It is the most commonly used measure of dispersion
Using standard deviation, what does the resultant frequency curve look like on a graph?
A bell shaped curve
What is it called when data does not conform to a normal pattern?
Skewed data
If the peak of the data is tot he left of centre how’s is the data viewed?
Positively skewed
If the peak of the data is to the right of centre how is the data viewed?
Negatively skewed
What is kurtosis?
When equity markets produce more extreme positive and negative returns than should statistically be the case.
What is the inter-quartile range?
The inter-quartile range ranks data such as comparable performance returns from funds against each other, presents the data as a series of quartiles, and then measures the difference between the lowest rank quartile to the highest.
What is diversification?
The reduction in risk for a given level of expected return
What are the two ways of quantifying the diversification potential of combining securities when constructing a portfolio?
Correlation
Covariance
Each asset class is differentiated by three factors that characterise its investment performance. What are these?
- The historic level of return that the asset class has delivered
- The historic level of risk that the asset class has experienced
- The level of correlation between the investment performance of each asset class
What is correlation?
Correlation measures how the returns from two different assets move together over time and is scaled between +1 and -1
How do assets with a high level of correlation (close to +1) tend to move?
In the same direction as each other
How do assets with a low of correlation (close to 0) tend to move?
These would move independently of each other
How do assets with a negative correlation (less and 0) tend to move?
An increase in one share price is associated with a decrease in another.
Assets with strong negative correlations (close to -1) tend to move in opposite directions
What is a perfect correlation?
Where the change in the price of one share is exactly matched by an equal change in another.
What is covariance?
A statistical measure of the relationship between two variables such as share prices.
How is the covariance calculated?
By multiplying the standard deviation of the first share by the standard deviation of the second share and then by the correlation coefficient.
A positive covariance between the returns of the two shares shows they have moved in the same direction, while a negative covariance means they have moved inversely. The larger the covariance, the greater the historic joint movements of the two securities in the same direction.
