The Skinny On Options Math

# Correlation, Beta and R-Squared

| Oct 9, 2014
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The Skinny On Options Math

# Correlation, Beta and R-Squared

Oct 9, 2014

When trading a portfolio of numerous underlyings, it can be very beneficial to know how one underlying moves in relation to another. Knowing this information can help us not only avoid adding positions that will move similarly to positions we already have, but it also allows us to choose a hedge to offset the risk of existing positions, or even find an interesting pairs trade.

Metrics that explain how two or more assets move in relation to each other are called measures of dependence. There are three primary measures of dependence that we can use to our benefit in trading, or when analyzing any two sets of data. These measures are known as correlation, beta, and r^2.

1. Correlation represents how two underlyings deviate from their averages. It is expressed as a number between -1 and +1. A correlation coefficient of +1 means that both of the underlyings deviate from their averages in the same direction perfectly. A correlation coefficient of -1 means that both of the underlyings deviate from their averages in opposite directions perfectly. A correlation coefficient that is close to 0 means that the two underlyings are not correlated at all, or in other words, they move independently.

2. Beta represents how one underlying moves with every \$1 move in a benchmark. For example, if \$IWM (Russell 2000 ETF) had a beta of 1.25 against \$SPY (S&P 500 ETF), then we would expect \$IWM to move 25% more than \$SPY. In other words, if \$SPY increased by \$1, then we would expect \$IWM to increase by \$1.25. Jacob notes that beta has limitations on its own because of volatility scaling between the benchmark and the underlying in which beta is being calculated. For example, you can have two assets that aren’t correlated at all, but show a high beta due to the assets being very volatile. Therefore, using beta alone isn’t sufficient when interpreting whether or not two assets move independently.

3. r^2 is the final measure of dependence and is simply the square of the correlation coefficient. The purpose of r^2 is to tell us the strength of the correlation between two underlyings, but not if the correlation between the two assets is positive or negative. Since r^2 is the square of the correlation coefficient, this number will always be positive, ranging between 0 and +1. The closer r^2 is to +1, the stronger the correlation between the two underlyings. Conversely, the closer the r^2 value is to 0, the weaker the correlation between the assets. So, with the correlation coefficient, we can tell whether two assets are positively or negatively correlated. By squaring the correlation coefficient, we arrive at r^2, which tells us the strength of the negative or positive correlation.

In conclusion, all three of these measures of dependence are very useful when investigating the relationship between two underlyings. However, Jacob warns against using just one of these measures alone when interpreting the relationship between two underlyings, as vital information will be missing. Instead, Jacob suggests using any two of the three measures together.

This video and its content are provided solely by tastylive, Inc. (“tastylive”) and are for informational and educational purposes only. tastylive was previously known as tastytrade, Inc. (“tastytrade”). This video and its content were created prior to the legal name change of tastylive. As a result, this video may reference tastytrade, its prior legal name.