Modules for Traders
Introducing the statistics of risk
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Glossary: 20 terms that will introduce you to risk and the statistics involved
In finance and investing, risk is the probability that the actual returns experienced by the investor will differ from the expected returns. It signifies the chance of losing some portion of the investment, or in some cases, even all of it.
2. Expected returns
Simply put, they are the returns that you expect from an investment or a portfolio of investments.
3. Systematic risk
Systematic risk is the probability of a loss that is associated with the entire market or market segment. It is a risk that is linked with a market, as a whole. For example, investing in the stock market - as a broad category - carries its own risk. Similarly, the bond market also has its own set of risks. This is what’s referred to as systematic risk, and it is generally external to the asset that you’re investing in. So, it is also not within your control, and therefore, cannot be avoided as such.
4. Unsystematic risk
Unsystematic risk is the probability of loss that is associated with a specific industry or security. For example, if stock A is considered to be more risky than stock B, this is a difference in the unsystematic risks of those stocks. Similarly, if investing in a cyclical industry like aviation is considered riskier than investing in a defensive industry like utilities, this is a difference in the unsystematic risks of those industries. They are specific to the asset or the industry in question.
5. Portfolio risk
Portfolio risk is the probability that the mix of assets in a portfolio will fail to deliver the returns expected from them. Each asset in the portfolio carries its own level and nature of risk, and these elements of risk together make up the risk of the portfolio, as a whole. The risk posed by the overall portfolio can theoretically be altered by modifying the constituents of the portfolio.
Covariance is a measure of how two variables are related to one another. It tells you how two random variables change together. Covariance can be a positive number or a negative number. A positive covariance means that the two variables move in the same direction. And a negative covariance means that they move in opposite directions.
The correlation shows the strength of the relationship between the variables. The correlation coefficient is a measure of the correlation between two variables. It ranges from -1 to +1. The symbol tells you the direction of movement. A positive symbol means that the two variables tend to move in the same direction, while a negative symbol means they typically move in opposite directions. The number following the symbol tells you the strength of the correlation.
A matrix is a rectangular array of numbers or expressions. These numbers or expressions are arranged in rows and columns. And they are contained within boxed/square brackets. The numbers or expressions in a matrix are called elements. The horizontal line entries in a matrix are called rows and the vertical line entries are called columns. The size of a matrix is represented using its rows and columns. So, a matrix with p rows and q columns is called a ‘p x q matrix.’ This is read as a ‘p by q matrix.’ 0
9. Transpose of a matrix
The transpose of a matrix is formed by turning its rows into its columns, and its columns into its rows. So, if you originally have a 3 x 4 matrix, its transpose will be a 4 x 3 matrix. The transpose of a matrix M is represented as MT. Similarly, the transpose of a matrix A is represented as AT.
10. Variance-covariance matrix
In the context of investment-related risk calculations, a variance-covariance matrix is a rectangular matrix that contains the variances and covariances of the stocks in a portfolio. The diagonal elements of the variance-covariance matrix represent the variances of the individual stocks. The other elements represent the covariances between the different pairs of stocks in the portfolio.
11. Correlation matrix
In the context of investment-related risk calculations, a correlation matrix is an array that shows the correlation between the different stocks in an investment portfolio. The diagonal elements of the correlation matrix represent the correlation of a stock with itself. This is why the elements in the diagonal are all equal to 1. The other elements represent the correlation between the different pairs of stocks in the portfolio.
12. Portfolio range
Every portfolio of assets has a range over which it may likely move over the course of the year. As an investor, you need to be able to assess this to a certain degree, so you can plan your investments accordingly.
13. Minimum variance portfolio
An investment portfolio where the weights of the stocks are adjusted so that the overall portfolio variance is at its minimum is called a minimum variance portfolio. The risk in this portfolio is assumed to be at the lowest level possible, for the given combination of stocks.
14. Maximum return portfolio
It is also possible to maximize the returns by modifying the weights. In this case, the risk may go up significantly. That is because the higher the potential returns, the higher the risk too. The portfolio that optimizes returns for you is the maximum return portfolio.
15. Value at Risk
Value at Risk or VAR is a statistical measure of the level of financial risk within a portfolio, over a given period. It helps measure the amount of potential loss that your portfolio could incur over a specified investment tenure. So, you can estimate the probability of losing more than a given amount in a given portfolio.
16. The historical method
The historical method is the simplest way to determine the VAR. It relies on the assumption that in the market, history tends to repeat itself. You first need to list out the returns from the stock over the given period. Then, sort the data so it is arranged in an ascending order. Lastly, choose the percentage of certainty with which you want to know the value at risk and determine the VAR.
17. The variance-covariance method
The variance-covariance method, also known as the parametric method relies on two points of data to determine the VAR: The expected or average returns and the standard deviation of a stock or a portfolio, as the case may be. Once you have these two bits of information, you can make use of the empirical rule to identify the VAR with varying levels of certainty.
18. Risk avoidance
Risk avoidance is all about eliminating any exposure to risk that could pose a potential loss. One of the strategies that traders and investors use to manage risk is to avoid investing in any asset with risks altogether.
19. Risk reduction
Risk reduction entails the adoption of different methods to reduce the overall risk of an investment option or an investment portfolio. Reducing risk is a strategy that many traders and investors use to manage risk.
Portfolio diversification is one of the most popular methods used by investors to reduce risk. By possessing a good mix of assets from different classes, you can effectively bring the overall investment risk down.
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