R Tutorial : Risk-factor returns

Want to learn more? Take the full course at https://learn.datacamp.com/courses/quantitative-risk-management-in-r at your own pace. More than a video, you'll learn hands-on coding & quickly apply skills to your daily work. --- In QRM the aim is to model the fluctuations in key risk factors which affect the value of a portfolio. These fluctuations are called the risk-factor changes or risk-factor returns, or simply returns. However, there are a few different ways of defining returns. Let (Z_t) be a time series containing the values of a risk factor at time at a set of regularly-spaced times which could represent days, weeks, months, etc. For illustration let's suppose it is a daily series. Here are 3 different ways of defining risk-factor returns (X_t): In the first definition, the returns are the differences of the risk-factor values, known as simple returns. This is the simplest definition but not the most common. It tends to be used when the risk factors have very small values close to zero (like certain interest-rate series). The second definition is the easiest to interpret. The relative returns are the differences divided by the initial values. If you multiply the relative returns by one hundred you get percentage changes. So if a stock has a relative return of 0.02 it gains 2% in value; if it has a relative return of -0.03 it falls 3% in value. In the third definition, the return is the differences of the log-values of the risk factors; these are log-returns. This definition is, in fact, the most widely used. Here are a few of the reasons why log-returns are popular. If you build a model for the log-returns of a risk factor you know that the risk-factor can never become negative. This is generally a desirable feature for risk factors that are prices and rates. However, some risk factors can become negative under unusual market conditions, an example being short-term interest rates. Log returns are in fact very close to log returns for typical values.