Probability is a measure of the likelihood that something will happen. We usually express probabilities as percentages, from 0% (impossible to happen) to 100% (guaranteed). We can express almost any event as a probability. For instance, we can gauge the…

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…

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…

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…

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…

When trying to estimate downside risk (i.e., returns below the mean), we can use the following measures: Semi-variance: The average squared deviation below the mean. Semi-deviation (also known as semi-standard deviation): The positive square root of semi-variance. Target semi-variance: The…

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…