Distributions. What are distributions? First, you should know they could be called by a handful of different names. You may hear the phrase probability distribution. You may hear frequency distribution. You may even hear continuous or non-continuous distribution. They could also be seen and depicted in a handful of ways. You may see a table, you may see a chart or even an equation. But in the end, what a distribution does for us is it allows us to analyze and summarize large amounts of data around a random variable. And in nearly all investment decisions, we work with random variables. It could be stock returns, it could be a company's earnings per share. It could be a number of things. Before we can meaningfully forecast any of these variables, we need to first understand how it's been distributed historically. Here's an example of a tabular distribution. The column on the left labeled stock monthly returns shows ranges or bands of stock returns for a specific security.

And on the right in the column labeled frequency, we have a count in the number of times that the security returned in each range or band.

Here's an example of a graphical distribution. Here we see S&P 500 returns versus an option strategy returns. It may look familiar. It's often known as a histogram. It's very attractive to analysts because it allows us to analyze vast amounts of data and get a sense of where the concentration is and where the outliers are, if there are any. Some other key takeaways about distributions. First, many investment models assume that returns on securities are normally distributed even though that's not always the case. Not only can distributions be used to model specific securities, but it can also be used to model vast portfolios of multiple assets. In fact, modern portfolio theory and its mean variance framework assumes that all securities have a normal distribution of returns.

And also from a risk management point of view, distributions are used to calculate the probabilities and the levels of potential losses for portfolios and managers use this to determine if they have more exposure than they wanna have. A typical risk management analysis that's built from distributions is called value at risk analysis.