What is Correlation?
Correlation is a measure of how one security moves in relation to another. A correlation value of 1 means that Stock A is exactly Correlated with Stock B. Take a look at the following charts of Amazon (AMZN) and Facebook (FB) for example:
A Correlation value of -1 means that Stock A and Stock B are exactly inversely correlated to each other over the measured period.
Take a look at the following chart of TZA over the same time period as the above charts:
TZA has a Correlation value of -0.95 vs FB and -0.97 vs AMZN over the last 10 bars of the chart. It is inversely correlated, meaning that when FB and AMZN moved up TZA moved down and vice-versa.
What are Alpha and Beta?
Alpha and Beta are statistical measures of a stock’s performance vs another instrument (usually an index such as the S&P 500, but could be vs another stock).
Beta is a measure of how much a stock moved up or down compared to the up or down move of the other instrument. It can be thought of as the volatility or risk of one stock vs another. A stock with a Beta value of 1 has exactly the same magnitude of move as the compared stock. A beta value of 2 means the magnitude is twice that of the compared stock. A negative beta value of -2 means that the stock had twice the magnitude of move in the opposite direction.
The following image shows the Correlation (ρ), Alpha (α) and Beta (β) values over different time periods of several stocks and ETFs vs the SPY ETF.
You can see that the SPY vs itself has perfect correlation (ρ=1) , Equal Magnitude moves (β=1) and same returns (α=0).
You can also see that Ultra S&P500 Proshares (UPRO) has perfect correlation to SPY (ρ=1), nearly 3x the magnitude of move (β=3) and similar excess returns. This makes sense because UPRO is an ETF which is designed to be a 3x leveraged ETF.
In the following image you can see the negatively correlated instruments:
For instance you can see that SPXS Direxion Daily S&P 500 Bear 3x ETF has nearly perfect negative correlation, -3x Beta (over longer time periods) and similar excess returns.
Alpha is the difference between the returns of a stock vs the expected returns based on its Beta. If a stock has a high Beta value then it has more risk and so the expected returns are higher. If Alpha is zero then it is returning as expected. If Alpha is negative it is underperforming for its risk level. If Alpha is positive then it is overperforming based for its risk level.
How to find Correlated Stocks
If you have a list of stocks, one thing that you can do is compare the correlation of each stock in your list to every other stock in your list for a chosen time period. The result is a ‘Correlation Matrix’.
Here’s an example of a Correlation Matrix:
In EdgeRater you will find the Correlation Matrix in the ‘Pro Tools’ category of templates. The template has one setting which is the number of bars to run the correlation over.
The resulting report (.xlsx file) contains N x N values where N is the number of symbols in your list. If you run the report on 1000 symbols you will end up with 1 million values reported. If you run the report on 8000 US securites you will get 64 million values.
The Correlation Matrix is interactive. If you click on any column header you will sort the matrix top to bottom by ascending or descending correlations. If you click on any row symbol you will sort the matrix left to right by ascending or descending correlations. Here’s a report that has been sorted to show everything correlated to AAPL in the upper left quadrant of the report:
If you have a specific symbol that you want to find Correlations for you can instead run the ‘Correlation, Alpha, Beta’ template and set the correlation symbol to your chosen symbol. The template will report the correlation, Alpha and Beta values of this symbol vs every symbol in your chosen list. It will report those values for 5 different time periods.
Here’s an example of the Correlation, Alpha, Beta report:
This report is also interactive. You can click on the column headers to sort the columns. You can also open up a chart of any stock in the report by double-clicking on the respective row. As you scroll around the report the chart will update to show the selected symbol.
This report is linked to a chart layout which shows the main symbol (row) as a candlechart with the correlation symbol (SPY) as a gray line superimposed on the chart. The lower chart areas show the Correlation, Alpha and Beta Values for the time period that was clicked on in the report. Here’s an example of a linked chart:
Correlation, Alpha and Beta are values that give a statistical measure of how one stock is related to another. Highly correlated stocks move together. Higher beta stocks move with greater magnitude and higher alpha stocks have higher excess returns than their beta value would suggest.
You can easily find correlations for every stock in your symbol list by running the Correlation Matrix template in EdgeRater. You can easily find correlation, alpha and beta values compared to a specific symbol by running the ‘Correlation, Alpha, Beta’ template in EdgeRater.