Unimodal Distribution – Locations of the Mean, Mode and the Median
A unimodal distribution is a distribution that has one clear peak. The values increase first, rising to a single highest point where they then start to decrease. A unimodal distribution can either be symmetrical or nonsymmetrical. A symmetrical distribution is…
The Short-run and Long-run Aggregate Supply Curve
Aggregate supply refers to the total amount of goods and services that firms in an economy are both willing and able to sell at a given price level. We must differentiate between the short- and long-run aggregate supply curves. Master…
Correlation in CFA Level 1 (With Examples)
Covariance Covariance is a measure of how two variables move together. The sample covariance of X and Y is calculated as follows: $$\mathrm{S}_{\mathrm{XY}}=\frac{\sum_{\mathrm{i}=1}^{\mathrm{N}}\left(\mathrm{X}_{\mathrm{i}}-\overline{\mathrm{X}}\right)\left(\mathrm{Y}_{\mathrm{i}}-\overline{\mathrm{Y}}\right)}{\mathrm{n}-1}$$ A major drawback of covariance is that it is difficult to interpret since its value can vary…
StickyKurtosis
Kurtosis refers to the measurement of the degree to which a given distribution is more or less ‘peaked’ relative to the normal distribution. The concept of kurtosis is very useful in decision-making. In this regard, we have 3 categories of…
Interpreting Skewness
Skewness refers to the degree of deviation from a symmetrical distribution, such as the normal distribution. A symmetrical distribution has identical shapes on either side of the mean. Distributions that are nonsymmetrical have unequal shapes on either side of the…
Downside Deviation
When trying to estimate downside risk (i.e., returns below the mean), we can use the following measures:
Calculating and Interpreting Measures of Dispersion
Measures of dispersion are used to describe the variability or spread in a sample or population. They are usually used in conjunction with measures of central tendency, such as the mean and the median. Specifically, measures of dispersion are the…
Quantiles and Related Visualizations
Quantiles Quartiles, quintiles, deciles, and percentiles are values or cut points that partition a finite number of observations into nearly equal-sized subsets. The number of partitions depends on the type of cut point involved.
Alternative Mean Definitions for Different Investment Problems
Suitability of Alternative Mean Definitions for Different Investment Problems $$ \begin{array}{l|l} \textbf { Type of Data } & \textbf { Mean to Use } \\ \hline \text { Single period data } & \text { Arithmetic mean } \\ \hline…
Summarizing Data Using Frequency Distributions
Frequency Distribution A frequency distribution refers to the presentation of statistical data in a tabular format to simplify data analysis. In a frequency distribution, data is subdivided into groups or intervals. The standard procedure for constructing a frequency distribution involves…
