Covariance — Indicators and Strategies

Correlation Coefficient Master Table The Correlation Coefficient Master Table is a comprehensive tool designed to calculate and visualize the correlation coefficient between a selected base asset and multiple other assets over various time periods. It provides traders and analysts with a clear understanding of the relationships between assets, enabling them to analyze trends, diversification opportunities, and market dynamics. You can define key parameters such as the base asset’s data source (e.g., close price), the assets to compare against (up to six symbols), and multiple lookback periods for granular analysis. The indicator calculates the covariance and normalizes it by the product of the standard deviations. The correlation coefficient ranges from -1 to +1, with +1 indicating a perfect positive relationship, -1 a perfect negative relationship, and 0 no relationship. You can specify the lookback periods (e.g., 15, 30, 90, or 120 bars) to tailor the calculation to their analysis needs. The results are visualized as both a line plot and a table. The line plot shows the correlation over the primary lookback period (the Chart Length), which can be used to inspect a certain length close up, or could be used in conjunction with the table to provide you with five lookback periods at once for the same base asset. The dynamically created table provides a detailed breakdown of correlation values for up to six target assets across the four user-defined lengths. The table’s cells are formatted with rounded values and color-coded for easy interpretation. This indicator is ideal for traders, portfolio managers, and market researchers who need an in-depth understanding of asset interdependencies. By providing both the numerical correlation coefficients and their visual representation, users can easily identify patterns, assess diversification strategies, and monitor correlations across multiple timeframes, making it a valuable tool for decision-making.

FunctionMatrixCovariance Library "FunctionMatrixCovariance" In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions. As an example, the variation in a collection of random points in two-dimensional space cannot be characterized fully by a single number, nor would the variances in the `x` and `y` directions contain all of the necessary information; a `2 × 2` matrix would be necessary to fully characterize the two-dimensional variation. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). The covariance matrix of a random vector `X` is typically denoted by `Kxx`, `Σ` or `S`. ~wikipedia. method cov(M, bias) Estimate Covariance matrix with provided data. Namespace types: matrix Parameters: M (matrix) : `matrix` Matrix with vectors in column order. bias (bool) Returns: Covariance matrix of provided vectors. --- en.wikipedia.org numpy.org

Beta Screener This script allows you to screen up to 38 symbols for their beta. It also allows you to compare the list to not only SPY but also CRYPTO10! Features include custom time frame and custom colors. Here is a refresher on what beta is: Beta (β) is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole (usually the S&P 500 ). Stocks with betas higher than 1.0 can be interpreted as more volatile than the S&P 500 . Beta is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets (usually stocks). CAPM is widely used as a method for pricing risky securities and for generating estimates of the expected returns of assets, considering both the risk of those assets and the cost of capital. How Beta Works A beta coefficient can measure the volatility of an individual stock compared to the systematic risk of the entire market. In statistical terms, beta represents the slope of the line through a regression of data points. In finance, each of these data points represents an individual stock's returns against those of the market as a whole. Beta effectively describes the activity of a security's returns as it responds to swings in the market. A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period. cov (a,b)/var(b)

Correlation Meter This script calculates the covariance and correlation coefficient between two markets using arrays. Lookback: How many bars to perform the calculation on. Source: Price source to calculate the correlation on. Reference Market: The reference market to compare to the current market. It's a simple indicator, but very useful for determining how correlated your preferred markets to trade are. A correlation reading of +1.0 means the markets are perfectly positively correlated, a reading of -1.0 means they are perfectly negatively correlated. If you're not sure what correlation & covariance are then Google the terms with "Investopedia" added to the end - they have some great definitions and examples. For traders this can be useful for deciding how much risk to spread across two markets that have a high correlation, or how to hedge existing positions by trading a negatively correlated market. For investors this can be useful for building a truly diversified portfolio. If a market has a high positive correlation, the black line will stay above zero most of the time. If a market has a high negative correlation, the black line will stay below zero most of the time. A market with no or little correlation will bounce between the two or hover around zero most of the time. The example market above is comparing Apple's weekly price action to the S&P500's over the past 20 weeks. It has a high positive correlation as the black line is above zero most of the time. Good luck with your trading!

Functions Allowing Series As Length - PineCoders FAQ █ WARNING Improvements to the following Pine built-ins have deprecated the vast majority of this publication's functions, as the built-ins now accept "series int" `length` arguments: ta.wma() ta.linreg() ta.variance() ta.stdev() ta.correlation() NOTE For an EMA function that allows a "series int" argument for `length`, please see `ema2()` in the ta library by TradingView . █ ORIGINAL DESCRIPTION Pinescript requires many of its built-in functions to use a simple int as their period length, which entails the period length cannot vary during the script's execution. These functions allow using a series int or series float for their period length, which means it can vary on each bar. The functions shared in this script include: Rolling sum: Sum(src,p) Simple moving average: Sma(src,p) Rolling variance: Variance(src,p) Rolling standard deviation: Stdev(src,p) Rolling covariance: Covariance(x,y,p) Rolling correlation: Correlation(x,y,p) If p is a float then it is rounded to the nearest int . How to Use the Script Most of the functions in the script are dependent on the Sma function. The Correlation function uses the Covariance and Stdev functions. Be sure you include all the required functions in your script. Make sure the series you use as the length argument is greater than 0, else the functions will return na . When using a series as length argument, the following error might appear: Pine cannot determine the referencing length of a series. Try using max_bars_back in the study or strategy function. This can be frequent if you use barssince(condition) where condition is a relatively rare event. You can fix it by including max_bars_back=5000 in your study declaration statement as follows: study("Title",overlay=true,max_bars_back=5000) Example The chart shows the Sma , Stdev , Covariance and Correlation functions. The Sma uses the closing price as input and bars as period length where: bars = barssince(change(security(syminfo.tickerid,"D",close ,lookahead=true))) The Stdev uses the closing price as input and bars + 9 as period length. The Covariance and Correlation use the closing price as x and bar_index as y , with bars + 9 as period length. Look first. Then leap.

Function Covariance Covariance Function as described here: www.investopedia.com can be used for example to calculate Beta:

Moving CO-covariance (covariance on covariance)This is Covariance on Covariance. It shows you how much a given covariance period has deviated from it mean over another defined period. Because it is a time series, It can allow you to spot changes in how covariance changes. You can apply trend lines, Fibonacci retracements, etc. This is also volume weighting covariance. This is not a directional indicator nor is moving covariance. This is used for forecasting volatility. This must be used in conjunction with moving covariance.

Moving Covariance Co-variance is a representation of the average percent data points deviate from there mean. A standard calculation of Co-variance uses One standard Deviation. Using the empirical rule, we can assume that about 68.26% of Data points lie in this range. The advantage to plotting co variance as a time series is that it will show you how volatility of a trailing period changes. Therefore trend lines and other methods of analysis such as Fibonacci retracements could be applied in order to generate volatility targets. For the purpose of this indicator I have the mean using a vwma derived from vwap. This makes this measurement of co-variance more sensitive to changes in volume, likewise are more representative a change in volatility, thus giving this indicator a "leading aspect".