Pair Creation🙏🏻 The one and only pair construction tech you need, unlike others:
Applies one consistent operation to all the data features (not only prices). Then, the script outputs these, so you can apply other calculations on these outputs.
calculates a very fast and native volatility based hedge ratio, that also takes into account point value (think SPY vs ES) so you can easily use it in position sizing
Has built-in forward pricing aka cost of carry model , so you can de-drift pairs from cost of carry, discover spot price of oil based on futures, and ofc find arbitrage opportunities
Also allows to make a pair as a product of 2 series, useful for triangular arbitrage
This script can make a pair in 2 ways:
Ratio, by dividing leg 1 by leg 2
Product, by multiplying leg 1 by leg 2
The real mathematically right way to construct a pair is a ratio/product (Spreads are in fact = 2 legged portfolio, but I ain't told ya that ok). Why? Because a pair of 2 entities has a mathematically unique beauty, it allows direct comparisons and relationship analysis, smth you can't do directly with 3 and more components.
Multiplication (think inversions like (EURUSD -> USDEUR), and use cases for triangular arbitrage) is useful sometimes too.
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Quickguide:
First, "Legs" are pair components: make a pair of related assets. Don’t be guided exclusively by clustering, cointegrations, mutual information etc. Common sense and exogenous info can easily made them all Forward pricing model: is useful when u work with spot vs futures pairs. Otherwise: put financing, storage and yield all on zeros, this way u will turn it off and have a pure ratio/product of 2 legs.
Look at the 2 numbers on the script’s status line: the first one would always be 1), and the second one is a variable.
First number (always 1) is multiplier for your position size on leg 1
The second number is the multiplier for your position size on leg 2 in the opposite direction.
If both legs are related, trading your sizes with these multipliers makes you do statistical arbitrage -> trading ~ volatility in risk free mode, while the relationship between the assets is still in place.
Also guys srsly, nobody ‘ever’ made a universal law that somewhy somehow for whatever secret conspiracy reason one shall only trade pairs in mean reverting style xd. You can do whatever you want:
Tilt hedge ratio significantly based on relative strength of legs
Trade the pair in momentum style
Ignore hedge ratio all together
And more and more, the limit is your imagination, e.g.:
Anticipate hedge ratio changes based on exogenous info and act accordingly
Scalp a pair just like any other asset
Make a pair out of 2 pairs
Like I mean it, whatever you desire
About forward pricing model:
It’s applied only to leg 2;
Direct: takes spot price and finds out implied futures price
Inverse: takes futures price and finds out implied spot price (try on oil)
Pls read online how to choose parameters, it’s open access reliable info
About the hedge ratio I use:
You prolly noticed the way I prefer to use inferred volumes vs the “real” ones. In pairs it’s especially meaningful, because real volumes lose sense in pair creation. And while volumes are closely tied to volatility, the inferred volumes ‘Are’ volatility irl (and later can be converted to currency space by using point value, allowing direct comparisons symbol vs symbol).
This hedge ratio is a good example of how discovering the real nature of entities beats making 100s of inventions, why domain knowledge and proper feature engineering beats difficult bulky models, neural networks etc. How simple data understanding & operations on it is all you need.
This script simply does this:
Takes inferred volume delta of both assets, makes a ratio, normalizes it by tick sizes and points values of both legs, calculates a typical value of this series.
That’s it, no step 2, we’re done. No Kalman filters, no TLS regression, no vine copulas, or whatever new fancy keywords you can come up with etc.
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^^ comparing real ES prices vs theoretical ones by forward-pricing model. Financing: 0.04, yield 0.0175
^^ EURUSD, 6E futures with theoretical futures price calculated with interest rate differential 0.02 (4% USD - 2% EUR interest rates)
^^4 different pairs (RTY/ES, YM/ES, NQ/ES, ES/ZN) each with different plot style (pick one you like in script's Style settings)
^^ YM/RTY pair, each plot represents ratio of different features: ratio of prices, ratio of inferred volume deltas, ratio of inferred volumes, ratio of inferred tick counts (also can be turned on/off in Style settings)
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How can u upgrade it and make a step forward yourself:
On tradingview missing values are automatically fixed by backfilling, and this never becomes a thing until you hit high frequency data. You can do better and use Kalman filter for filling missing values.
Script contains the functions I use everywhere to calculate inferred volume delta, inferred volume, and inferred tick count.
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Hedgeratio
Static Beta for Pair and Quant Trading A beta coefficient shows the volatility of an individual stock compared to the systematic risk of the entire market. Beta represents the slope of the line through a regression of data points. In finance, each point represents an individual stock's returns against the market.
Beta effectively describes the activity of a security's returns as it responds to swings in the market. It is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets. CAPM is used to price risky securities and to estimate the expected returns of assets, considering the risk of those assets and the cost of capital.
Calculating Beta
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. The calculation helps investors understand whether a stock moves in the same direction as the rest of the market. It also provides insights into how volatile—or how risky—a stock is relative to the rest of the market.
For beta to provide useful insight, the market used as a benchmark should be related to the stock. For example, a bond ETF's beta with the S&P 500 as the benchmark would not be helpful to an investor because bonds and stocks are too dissimilar.
Beta Values
Beta equal to 1: A stock with a beta of 1.0 means its price activity correlates with the market. Adding a stock to a portfolio with a beta of 1.0 doesn’t add any risk to the portfolio, but it doesn’t increase the likelihood that the portfolio will provide an excess return.
Beta less than 1: A beta value less than 1.0 means the security is less volatile than the market. Including this stock in a portfolio makes it less risky than the same portfolio without the stock. Utility stocks often have low betas because they move more slowly than market averages.
Beta greater than 1: A beta greater than 1.0 indicates that the security's price is theoretically more volatile than the market. If a stock's beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks tend to have higher betas than the market benchmark. Adding the stock to a portfolio will increase the portfolio’s risk, but may also increase its return.
Negative beta: A beta of -1.0 means that the stock is inversely correlated to the market benchmark on a 1:1 basis. Put options and inverse ETFs are designed to have negative betas. There are also a few industry groups, like gold miners, where a negative beta is common.
LET'S START
Now I'll give my own definition.
Beta:
If we assume market caps are equal ,
it is an indicator that shows how much of the second instrument we should buy if we buy one of the first, taking into account the price volatility of two instruments.
But if the market caps are not equal:
For example, the ETF for A is $300.
The ETF for B is $600.
If static beta predicted by this script is 0.5:
300 * 1 * a = 600 * 0.5 * b
Then we should use 1 b for 1 a.
(Long a and short b or vice versa )
So, we can try pair trading for a/b or a-b.
However, these values are generally close to each other, such as 0.8 and 0.93. However, the closer we can adjust our lot purchases to bring the double beta to a value closer to 1, the higher the hedge ratio will be.
Large commercials use dynamic betas, which are updated periodically, in addition to static betas
However, scaling this is very difficult for individual investors with limited investment tools.
But a static beta of 5,000 bars is still much better than not considering any beta at all.
Note: The presence of a beta value for two instruments does not necessarily mean they can be included in pair trading.
It is also important (%99) to consider historically very high correlations and cointegration relationships, as well as the compatibility of security structures.
Note 2 : This script is designed for low timeframes.
Do not use betas from different timeframes.
Beta dynamics are different for each timeframe.
Note 3 : I created this script with the help of ChatGPT.
Source for beta definition ( ) :
www.investopedia.com
Regards.
