What Is T-Distribution in Trading? What Is T-Distribution in Trading?
In the financial markets, understanding T-distribution in probability is a valuable skill. This statistical concept, crucial for small sample sizes, offers insights into market trends and risks. By grasping T-distribution, traders gain a powerful tool for evaluating strategies, risks, and portfolios. Let's delve into what T-distribution is and how it's effectively used in the realm of trading.
Understanding T-Distribution
The T-distribution in probability distribution plays a crucial role in trading, especially in situations where sample sizes are small. William Sealy Gosset first introduced it under the pseudonym "Student". This distribution resembles the normal distribution with its bell-shaped curve but has thicker tails, meaning it predicts more outcomes in the extreme ends than a normal distribution would.
A key element of T-distribution is the concept of 'degrees of freedom', which essentially refers to the number of values in a calculation that are free to vary. It's usually the sample size minus one.
The degrees of freedom affect the shape of the T-distribution; with fewer degrees of freedom, the distribution has heavier tails. As the degrees of freedom increase, the distribution starts to resemble the normal distribution more closely. This is particularly significant in trading when dealing with small data sets, where the T-distribution provides a more accurate estimation of probability and risk than the normal distribution.
T-Distribution vs Normal Distribution
T-distribution and normal distribution are foundational in statistical analysis, yet they serve different purposes. While both exhibit a bell-shaped curve, the T-distribution has thicker tails, implying a higher probability of extreme values. This makes it more suitable for small sample sizes or when the standard deviation is unknown.
In contrast, the normal distribution, with its thinner tails, is ideal for larger sample sets where the standard deviation is known. Traders often use T-distribution for more accurate analysis in small-scale or uncertain data scenarios, while normal distribution is preferred for larger, more stable datasets, where extreme outcomes are less likely.
Application in Trading
In trading, T-distribution is a valuable tool for analysing financial data. It is primarily used in constructing confidence intervals and conducting hypothesis testing, which are essential for making informed trading decisions.
For instance, a trader might use T-distribution to test the effectiveness of a new trading strategy. Suppose a trader has developed a strategy using the technical analysis tools and wants to understand its potential effectiveness compared to the general market performance. They would collect a sample of returns from this strategy over a period, say, 30 days. Given the small sample size, using T-distribution is appropriate here.
The trader would then calculate the mean return of this sample and use T-distribution to create a confidence interval. This interval would provide a range within which the true mean return of the strategy is likely to lie, with a certain level of confidence. If this confidence interval shows a higher mean return than the market average, the trader might conclude that the strategy is potentially effective. However, it's important to note that this is an estimation and not a guarantee of future performance.
How to Plug Probability and Normal Distribution in Your T-Calculation
To use a T-calculator for integrating probability and normal distribution, follow these steps:
- Input Degrees of Freedom: For T-distribution, calculate the degrees of freedom (sample size minus one).
- Convert Z-Score to T-Value: If using normal distribution data, convert the Z-score (standard deviation units from the mean in a normal distribution) to a T-value using the formula: T = Z * (sqrt(n)), where 'n' is the sample size.
- Enter T-Value: Input this T-value into the calculator.
- Calculate Probability: The calculator will then output the probability, providing a statistical basis for trading decisions based on the T-distribution.
Limitations and Considerations of T-Distribution
While T-distribution is a powerful tool in trading analysis, it's important to recognise its limitations and considerations:
- Sample Size Sensitivity: T-distribution is most effective with small sample sizes. As the sample size increases, it converges to a normal distribution, reducing its distinct utility.
- Assumption of Normality: T-distribution assumes that the underlying data is approximately normally distributed. This may not hold true for all financial data sets, especially those with significant skewness or kurtosis.
- Degrees of Freedom Complications: Misestimating degrees of freedom can lead to inaccurate results. It's crucial to calculate this correctly based on the sample data.
- Outlier Sensitivity: T-distribution can be overly sensitive to outliers in the data, which can skew results.
Advanced Applications of T-Distribution in Trading
T-distribution extends beyond basic trading applications, playing a role in advanced financial analyses:
- Risk Modelling: Utilised in constructing sophisticated risk models, helping traders assess the probability of extreme losses.
- Algorithmic Trading: Integral in developing complex algorithms.
- Portfolio Optimisation: Assists in optimising portfolios by estimating returns and risks of various assets.
- Market Research: Used in advanced market research methodologies to analyse small sample behavioural studies.
The Bottom Line
The T-distribution is a powerful tool, offering nuanced insights in scenarios involving small sample sizes or uncertain standard deviations. Its ability to accommodate real-world data's quirks makes it invaluable for various trading applications, from strategy testing to risk assessment. However, understanding its limitations and proper application is crucial for accurate analysis.
This article represents the opinion of the Companies operating under the FXOpen brand only. It is not to be construed as an offer, solicitation, or recommendation with respect to products and services provided by the Companies operating under the FXOpen brand, nor is it to be considered financial advice.
Probability
Stop Hunting for Perfection - Start Managing Risk.Stop Hunting for Perfection — Start Managing Risk.
Hard truth:
Your obsession with perfect setups costs you money.
Markets don't reward perfectionists; they reward effective risk managers.
Here's why your perfect entry is killing your results:
You ignore good trades waiting for ideal setups — they rarely come.
You double-down on losing trades, convinced your entry was flawless.
You're blindsided by normal market moves because you didn’t plan for imperfection.
🎯 Solution?
Shift your focus from entry perfection to risk management. Define your maximum acceptable loss, stick to it, and scale into trades strategically.
TrendGo wasn't built to promise perfect entries. It was built to clarify probabilities and structure risk.
🔍 Stop chasing unicorns. Focus on managing the horses you actually ride.
Most Traders Want Certainty. The Best Ones Want Probability.Hard truth:
You’re trying to trade like an engineer in a casino.
You want certainty in an environment that only rewards probabilistic thinking.
Here’s how that kills your edge:
You wait for “confirmation” — and enter too late.
By the time it feels safe, the market has moved.
You fear losses — but they’re the cost of data.
Good traders don’t fear being wrong. They fear not knowing why.
You need to think in bets, not absolutes.
Outcomes don’t equal decisions. Losing on a great setup is still a good trade.
🎯 Fix it with better framing.
That’s exactly what we designed TrendGo f or — to help you see trend strength and structure without delusions of certainty.
Not perfect calls. Just cleaner probabilities.
🔍 Train your brain for the game you’re playing — or you’ll keep losing by default.
Probabilistic thinking. Using Technical logic to get odds.Markets are simple if you think about it.
moderate and long range resistance -- is the best odds for rally.
"horizontal" or 50-50 supports -- risky.
steep supports mean high demand, strong trends. Buying at such supports, at worst it bounces to the upside. (High market with strong trend can mean reversals)
rule: break outs always must coincide with 200dma rallies.
Bonus.
High market, strong trend -- best odds for reversal .
50-50 resistance, with weak support --> trickster market. (trap)
strong trend but no flying 200dma --> trap.
50-50 resistance with strong trend, high market, but weak 200dma ---> good odds for reversal.
keeping it simple.
P.S. this method shows why odds favor BTC reversal . Or why 110/120k had to be peak point. for now.
Trade high probabilities using game theoryAccording to statistics, 95% of traders are losing longterm. Not because they lack skill, but because they involve in high variance (or poor probability) situations.
What is game theory? we can define GT with three principles.
*People dont want to lose. (hence.. predictable).
*People buy good things at good price, or they are profit maximizing.
*Everyone is strategic.
** we assume that "nobody can predict future".
** markets respond to feedbacks or signals.
Practice: the higher something goes, potential narrows and risk increases. Deeper something falls, "potential" becomes attractive. Once market decides that it will fall -- people assume crash as possibility. People who can buy at a strong trend line - has benefit of having more information.
(1) Downtrending VIX highs and accumulating lows. a strong signal about SPX peak, with everyone expecting a market correction before US election. ---> GT in practice.
(2) pre-election. Markets be wobbly, pointing to 50-50 probability or risk. Maybe there was fear of NVDA/AAPL high valuations, or the fear due to Trump tariff policy (markets are 6m forward looking) as bond yields were rallying.
If we assume statistically, markets boom after elections. We can predict GT in action (or call it market forces). imo that still is a profitable risk.
People hate uncertainty and they love guarantees. So the "wobble" was reasonable.
(3) VIX higher low.. predictably (GT) sell off follows. Almost as by the book.
other way to put it? people maximize potential while minimize loses/risk. There are periods of volatile markets and periods for one directional rallies.
P.S. Blue arrows are longterm macd turning points.
Reality & FibonacciParallels between Schrödinger’s wave function and Fibonacci ratios in financial markets
Just as the electron finds its position within the interference pattern, price respects Fibonacci levels due to their harmonic relationship with the market's fractal geometry.
Interference Pattern ⚖️ Fibonacci Ratios
In the double-slit experiment, particles including photons behave like a wave of probability, passing through slits and landing at specific points within the interference pattern . These points represent zones of higher probability where the electron is most likely to end up.
Interference Pattern (Schrodinger's Wave Function)
Similarly, Fractal-based Fibonacci ratios act as "nodes" or key zones where price is more likely to react.
Here’s the remarkable connection: the peaks and troughs of the interference pattern align with Fibonacci ratios, such as 0.236, 0.382, 0.618, 0.786. These ratios emerge naturally from the mathematics of the wave function, dividing the interference pattern into predictable zones. The ratios act as nodes of resonance, marking areas where probabilities are highest or lowest—mirroring how Fibonacci levels act in financial markets.
Application
In markets, price action often behaves like a wave of probabilities, oscillating between levels of support and resistance. Just as an electron in the interference pattern is more likely to land at specific points, price reacts at Fibonacci levels due to their harmonic relationship with the broader market structure.
This connection is why tools like Fibonacci retracements work so effectively:
Fibonacci ratios predict price levels just as they predict the high-probability zones in the wave function.
Timing: Market cycles follow wave-like behavior, with Fibonacci ratios dividing these cycles into phase zones.
Indicators used in illustrations:
Exponential Grid
Fibonacci Time Periods
Have you noticed Fibonacci ratios acting as critical levels in your trading? Share your insights in the comments below!
Election Year Cycle & Stock Market Returns - VisualisedIn this chart, we're analysing the open value of the week the US election took place and comparing it to the open of the following election, showing the gain (or loss) in value between each election cycle.
Historically we can see prices in the Dow Jones Industrials Index tend to appreciate the week the election is held. Only twice has the return between the cycles produced a negative return.
Buying stocks on election day, 8 out of 10 times has yielded a profitable return between the election cycles. 80% of the time in the past 40 years returning a profit, has so far been a good strategy to take.
The typical cycle starts with the election results, an immediate positive movement and continued growth before finishing positive.
The Outliers
2000-2004 was the only year which ended negative without prices going higher than the election day.
2004-2008 increased 41.84% before ending negative.
2008-2012 began the cycle falling 30.62% before finishing positive.
The names of presidents who won their respective elections is to visualise who had the presidential term during that specific cycle.
Stock feedback loopStock market is a adaptive system or a stock, with feedback loops (for inflow, outflow function). Where nobody knows the outcome or future, but feedbacks (corrections or resistance) gives tells (makes inflows or outflows). Without a common leader.
Economists think in models (price is the result of supply-demand, or inflow-outflow) that helps to explain system behavior (short term moves), but models are just ideas to explain complex world (models work until they dont). System thinkers study the stock not aggregate behavior .
Looking at markets trough perspective of "eco system" helps better understand the drivers or moving forces?
Think in Probabilities Embracing Uncertainty Your Key To SuccessPicture this: You’re at your trading desk, eyes on the charts, heart pounding as the market swings unpredictably. Do you feel that fear creeping in?
Now, imagine knowing that this unpredictability doesn’t have to scare you. Instead, it can be the key to your success. Let's dive into why thinking in probabilities and staying calm in the face of uncertainty can turn trading from a gamble into a calculated path to consistent success.
Many traders struggle with uncertainty because they lack a solid, tested system. Trading randomly or without a proven strategy leads to anxiety and inconsistency. But once you have a reliable system that suits your lifestyle and mindset, and you fully understand your edge, you realize that while the outcome of each trade is random, the probabilities of your trading system will work out for you over time.
The Role of Probabilities in Trading
Trading isn’t about predicting the next big market move; it’s about understanding the odds and working them to your advantage. Each trade is a small part of a larger statistical framework, where the focus shifts from individual outcomes to the bigger picture.
Why Is Learning To Think In Probabilities So Important For Trading Success?
Reduces Emotional Bias : By thinking in probabilities, you understand that each trade is just one in a series of many. This helps reduce emotional reactions to individual losses or gains, such as revenge trading, doubling up on position sizing, or even smashing your new iPhone against the wall (been there, LOL).
For example, if you know that your strategy wins 60% of the time, you won't be devastated by a single loss. You'll see it as part of the statistical outcome.
Encourages Rational Decision-Making: Knowing your strategy has an actual edge helps you stick to your plan, even during losing streaks, and avoid impulsive decisions. To know your edge, you need to do plenty of backtesting and forward testing so you can gain confidence in the system.
For instance, if you experience a string of losses, understanding that this is normal and statistically probable helps you remain disciplined and not deviate from your strategy.
Builds Confidence in Your System : Confidence comes from knowing your strategy is backtested and has a proven edge over a large number of trades.
This knowledge helps you stay disciplined and focused on executing your plan. For example, if your backtesting shows a positive expectancy over 1,000 trades, you can trust your system even when short-term results are unfavorable.
Things That Have Helped Me Over the Years to Deal With the Uncertainty of Trading
Finding or Developing a System/Strategy That Suits You : As humans, we are all different, and this is especially true in trading. Some people are happy to be in and out of the market fast (scalpers) and have the ability to make big decisions quickly under pressure.
Others are slower thinkers and like to make decisions carefully, staying in the market for a longer period of time (swing traders).
You need to find what you're best at and stick to it. If you have a busy life with work and family, maybe swing trading suits you. If you’re younger and not as busy, then perhaps scalping is your style.
Playing Strategy Games and Games of Chance : This may not be something you've heard before, but I've met many traders, including myself, who have found that games like poker can really help your trading by teaching you to think in probabilities.
Another game I love to play is chess, as it encourages you to think ahead, and I’ve found it has helped me in my trading over the years.
Practicing Visualization : If you've ever read anything on the subconscious mind, you know it’s responsible for 95% of all your automatic behaviors, especially in trading. The subconscious doesn’t distinguish between what is real and what is imagined.
This is why visualization is such a powerful tool to help you embrace market uncertainty. By visualizing yourself placing trades confidently, managing risks well, and handling outcomes calmly, you prepare your mind for real trading scenarios.
This mental practice reinforces your belief in your system and prepares you for the market's ups and downs.
Books That Helped Me Think in Probabilities
Reading has been an invaluable part of my journey to understanding probabilities. Here are some books that have profoundly impacted my trading mindset:
"Thinking, Fast and Slow" by Daniel Kahneman
This book helped me understand how cognitive biases affect decision-making and how to overcome them by thinking more strategically.
"Fooled by Randomness" by Nassim Nicholas Taleb
Taleb's insights into the role of chance and randomness in our lives and the markets were eye-opening and changed how I view risk and probability.
"Beat the Dealer" by Edward O. Thorp
Although this book is about blackjack, Thorp’s exploration of probability and statistics offers valuable lessons for trading.
"The Theory of Poker" by David Sklansky
Sklansky breaks down the mathematics of poker, showing how to make decisions based on probability, a skill directly applicable to trading.
"The Intelligent Investor" by Benjamin Graham
This classic on value investing emphasizes the importance of long-term thinking and understanding market probabilities.
"A Man for All Markets" by Edward O. Thorp
This autobiography offers a fascinating look at how Thorp applied probability theory to beat the casino and the stock market.
"Sapiens: A Brief History of Humankind" by Yuval Noah Harari
Harari’s book provides context on human behavior and decision-making, offering insights into the psychological elements of trading.
"The Signal and the Noise" by Nate Silver
Silver’s exploration of how we can better understand predictions and probabilities is highly relevant to making informed trading decisions.
"Superforecasting: The Art and Science of Prediction" by Philip E. Tetlock and Dan M. Gardner
This book teaches how to improve forecasting skills through careful analysis and thinking in probabilities.
Thinking in probabilities was a game-changer for me. It shifted my focus from trying to predict every market move to playing the long game. By embracing this mindset, I turned fear into confidence and uncertainty into strategy.
Remember, trading isn’t about guessing the market. It’s about responding with a clear, composed mind. Trust your strategy, know your edge, and let the probabilities work in your favor. This approach transformed my trading journey, and it can do the same for you. Happy trading!
Odds and Psychology.Based on "Think fast and slow", people have two system thinking. System-1 is autonomous, always working in background (ie unconsciousness), lazy, intuitive, fast, has stereotypes. System-2 is rational, hard problem solving, takes effort and energy, cuts trough the BS, etc (ie consciousness).
Based on another book called "superforcasters" and some dude I forgot his name, best approach for odds is to have simple system; where 100% certain. 93% almost certain. 75% probable. 50% about even (or maybe). 25% probably not. 7% almost certainly not. 0% impossible. All forecast are subjective guesses.
The catch; If you think something is 100% - you would go allin with max lever. (If you dont) your beliefs or opinion go against your actions. If you dont believe it's wise to go allin - then odds are not actually 100%. If you are stressed about 93% spot, then maybe it might not be 93% after all. (1:14).
In key SPX areas, based on business cycle and TNX, logic says one odds (or System-2) and your intuition (or feel) says differently. You are either too bearish or too bullish.
This is a simple representation of concept.
Another key concept is that TIME <----> PROBABILITY are at opposite sides of coin. The closer or far away in time something - more or less risk, ie higher or lower probability.
What do you do when your trading plan fails? Yesterday I wrote about a beautiful chart pattern that was forming on the Bitcoin daily time frame that ended up failing not long after I wrote the post. That kind of thing will shake a trader to their core, especially if they thought it was going to play out, but ended up losing their shirt.
This is why it is important to set stop losses, so that if the trade does go the other way, you will be out of the trade before it gets too bad. This is simply called risk management, and is one of the biggest things that any trader, especially new traders need to master.
Trading is a business of statistics and probabilities. Just because something has worked for you in the past, doesn't mean it is going to work for you every time. So when something like a bullish pattern that you have traded many times fails, you have to reassess and move on to the next trade. Out of 100 trades, that pattern may only work 6 or 7 times which gives you a 60-70% chance of it working in your favor. That's how it works, nothing is ever 100% in this game. So you always have to be ready for things to not work out the way you think they should.
If they don't work out, don't freak out! Just learn from your mistakes, readjust your plan, and move along to the next trade! Hopefully things like this will help you better understand the importance of a good risk management plan.
Be safe out there everyone and trade logically!
How we have been trading Bitcoin D1How we have been trading Bitcoin (Daily chart) with our indicators + hand-drawn trend lines.
After 10 years of R&D (we have been testing different indicators every day for a decade), we have developed our own Suite of 26 indicators. Here are just a few of them.
Indicators names (from top to bottom):
- Strength
Shows the strength of the market, the direction, pullbacks, equilibrium, and flats.
- Bear&Bull Powers
Shows the battle between the bears and the bulls.
- Angle
Indicates the direction and angle of the trend and the pullbacks.
- Template
Our main central indicator simplifying charts and bringing clarity.
- Steepness
Displays how steep the trend is and comments:
Going Up/Down | Trending | Strong/Weak | Pulling Back | Retracement | Flat | 75% Blue Background | ...
- Odds
11 indicators calculating the odds.
- Probability
75 indicators calculating the probabilities.
How To Trade Probability Ranges The Critical Rule of 1/3Using the Rule of Thirds to Master Probabilities in trading and investing ranges
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Stocks typically remaining in consolidation ranges 70% of the time while trending the remainder.
Using the rule of thirds, we can use statistics, prior price action and the probabilities of success to determine when to enter trades where the odds are stacked in our favor.
1) We start by finding a stock that is in a consolidation range, and identify the nearest important support and important resistance levels based on your targeted trading timeframe.
2 ) We take the range between the support and resistance levels and divide it into thirds, so we have three zones within the consolidation range.
3) When going long, you want to BUY the stock when it is within the bottom third or the zone from support to the 1st third level. Once you buy, your objectives are to hold during the middle third of the range, and sell during the top third.
When you buy in the first third, this gives you a 66 percent chance of success. If you buy in the second third of the range, you only have a 50/50 chance of success. Going long in the top third of the range, gives you only a 33% chance of success because you are already close to the resistance level.
When going short, the sequence and odds are reversed. You sell during the top third of the range, hold during the middle third and exit in the bottom third. This again gives you a 66% chance of success when you enter in the top third, 50/50 chance if you enter in the middle third, and a 33% chance of success if you enter in the bottom third as you are already close to the support zone.
****Using this simple trick, you can quickly evaluate trades based on probabilities and selectively enter trades where the odds of success are the highest and avoid likely losing trades. The rule of thirds also also gives you the confidence to continue to hold trades based on previous important ranges, and provides clear levels where the stock is likely to either reverse or start trending.
Hope It Helps to your Trading & Investing Success
Marc
How to Calculate Probability in Price So many have asked for tutorials on some quant strategies. So this is my first tutorial for some basic quant trading strategies.
This is not really a strategy in and of itself, this is to help you determine realistic price points as part of your overall strategy.
You will need Excel to do this.
If you like this kind of tutorial/find it helpful, let me know and I can continue posting similar stuff on how to apply some more basic quant strategies into your trading.
Take care and trade safe!
How To Use Risk:Reward Like A ProWhatsup my friends
In this video I will be covering my risk:reward model and how I can use it to generate an edge in the market.
In this specific backtesting session, I used 0.5:2 risk:reward with TP at 4RR for every trade.
I got pretty good results - but remember this is simulated and it's easier to perform better.
However, don't take this type of training lightly - this is the best way to improve as a trader.
The next step would be to actually start journaling your trades and analyzing everything at a deeper level.
I hope you enjoyed this!
Cheers
Dil
What's the Probability of SPY 500 End of Year?This is not a forecast of AMEX:SPY getting to 500... this video will instead demonstrate how we can answer this question using Options Delta to assess the probability the market expects for an event to happen. I use a backtest of NASDAQ:TSLA Weekly Options to demonstrate.
Understanding draw down recovery 😬😥Morning traders.
Middle of the trading week all ready!
I thought I'd take this opportunity to discuss a topic we all fear and we all find ourselves in at some point in our trading journey.
That topic being draw down and your account in a loss of starting capital.
The table I have drawn on the chart shows the amount of gain required to get an account back to break even depending on how big the draw down is on your capital.
Scary stuff when viewed in a simple table format like and hits home just how big of task over turning losses could be.
No trading system or strategy has zero losses or draw down and all strategies endure losing runs.
To avoid excessive losses there is two crucial elements.
Sounds obvious but cut losing trades quickly is the first element, second element is factoring probability into the trading strategy.
Probability helps control risk management which in turns keep losses to a minimum, probability is obtained by carrying out back testing on your strategy.
You can't plan for probability in your risk management if you have no data for your strategy.
The example I am using for this Idea is on AUDCHF H1 timeframe and thanks to our built in strategy tester I can see if I traded this pair in the manner the strategy is set over the last 292 trades at 1% risk I am 22% down on my account. It would not take in the region of a 25% account gain to be back to near break even on my account!!!
You don't need a built in strategy tester to gain this information you can also manually back test a strategy in order to avoid losses and to know if you are entering markets with a proven edge.
A trading edge means your strategy creates bigger wins than losses. Which in turn means you avoid the situation shown in the table.
To avoid hefty draw down don't enter the markets blind with an unproven strategy.
Ensure you have back tested strategies with probability factored in to those strategies that way what is shown in the table wont apply to you then 👍
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Please hit the 👍 LIKE button if you like my ideas🙏
Also follow my profile, then you will receive a notification whenever I post a trading idea - so you don't miss them. 🙌
No one likes missing out, do they?
Also, see my 'related ideas' below to see more just like this.
The stats for this pair are shown below too.
Thank you.
Darren
How to use Chobotaru IndicatorOur indicator can now be used by everyone.
There are a lot of indicators trying to predict what will be the range of the stock in the future.
Some of the indicators, that are well known, are using STD of volatility like Bolinger Bands or using an advanced simulation like Monte-Carlo, and others that are using different methods.
Our approach to this subject is different. There is an official volatility predictor called Implied Volatility. (I explained it in a different post)
This number can be seen in the options chain in your broker platform. You don’t need to trade options to use this indicator.
This indicator shows you a probability cloud, giving you the probability of the stock moving to a certain price.
This can help in several ways like determine if your target price is possible, where to put stop-loss, you can also use other technical analyses, like support and resistance to choose which area is best for your trade. The sky is the limit.
We tested it on 30(+/-10) days of small market cap and higher. In our testing, the price finished inside the range more than 80% of the time (the result are higher but I’m trying to stay conservative).
The user can choose a different option’s time period than 30 days, but the longer the period the higher the chance for a rare event that is not currently priced in.
The indicator is based on the partial differential equations from the mathematical model of options, the Black-Scholes model.
In simple words, the prices of options give you some indication of how the market thinks the stock should perform. If you take the implied volatility and insert it into the indicator, you can see the probability range, transforming this data into a visual representation.
What inputs do you need to enter?
Instrument price –
The current price of the stock or futures contract.
In this example, the close price of the SPY on March 30, 2021, is 394.73
The interest rate –
Searching in google: “U.S. Department of the treasury daily yield curve rates”, Use the 3-month value (of the day of the entry or day before).
On 03/30/2021 the 3-month value was 0.02%
Days to expire (minus trading holidays) –
At the end of 03/30/2021, I searched for the option that is the closest to 30 days on the SPY. The option that ending on April 30, has 31 days, in this period we have a holiday “Good Friday”, so I subtract the original number of days from the holiday, 31-1 = 30
Implied Volatility –
This number in your trading platform will usually be shown in a percentage, you need to enter a positive decimal number.
In this example, the implied volatility of the option was 15.2%, the input is 0.152
The date – The last thing is the date of the entry, in this case, Day – 30, Month – 3, Year – 2021.
This indicator can be used on daily bars and everything smaller than that. We recommend using it on daily bars.
Try it for yourself on your charts and share your result, if you have any questions, tell us in the comments.
The Ace Spectrum as a Template for Support ProjectionDemonstrating the big idea: That straight lines in log-space form exponential curves.
This property of the log chart is useful for examining assets with exponential growth (like high-growth stocks, cryptos, etc).
Because the log scale asymptotically approaches the absolute scale as y slice decreases, this indicator is really applicable to any time scale.
This indicator samples a distribution of lines from the past and projects them into the future, these projected lines form indicators of prior support.
The idea is longer support at those specific lines is indicative of support strength, which this indicator approximately captures.
My initial goal was to capture this intuition about exponential growth in log spaces by applying a monte-carlo style sampling approach to visualize the latent support lines.
After I had captured that in a slightly more complex version of this indicator, my goal was to distill the concept into the simplest possible implementation.
5 Fundamental Truths of Trading:1. Anything can happen.
Why? Because there are always unknown forces operating in every market at every moment , it takes only one trader somewhere in the world to negate the positive outcome of your edge. That's all: only one. Regardless of how much time, effort, or money you've invested in your analysis, from the market's perspective there are no exceptions to this truth. Any exceptions that may exist in your mind will be a source of conflict and potentially cause you to perceive market information as threatening.
2. You don't need to know what is going to happen next in order to make money.
Why? Because there is a random distribution between wins and losses for any given set of variables that define an edge. (See number 3.) In other words, based on the past performance of your edge, you may know that out of the next 20 trades, 12 will be winners and 8 will be losers. What you don't know is the sequence of wins and losses or how much money the market is going to make available on the winning trades.
This truth makes trading a probability or numbers game.
3. There is a random distribution between wins and losses for any given set of variables that define an edge
If every loss puts you that much closer to a win, you will be looking forward to the next occurrence of your edge, ready and waiting to jump in without the slightest reservation or hesitation. On the other hand, if you still believe that trading is about analysis or about being right, then after a loss you will anticipate the occurrence of your next edge with trepidation, wondering if it's going to work. This, in turn, will cause you to start gathering evidence for or against the trade, so you will not be in the most conducive state of mind to produce consistent results .
4. An edge is nothing more than an indication of a higher probability of one thing happening over another.
Creating consistency requires that you completely accept that trading isn't about hoping, wondering, or gathering evidence one way or the other to determine if the next trade is going to work. The only evidence you need to gather is whether the variables you use to define an edge are present at any given moment. When you use "other" information, outside the parameters of your edge to decide whether you will take the trade, you are adding random variables to your trading regime. Adding random variables makes it extremely difficult, if not impossible, to determine what works and what doesn't.
Gathering "other" evidence makes about as much sense as trying to determine whether the next flip of a coin will be heads, after the last ten flips came up tails. Regardless of what evidence you find to support heads coming up, there is still a 50-percent chance that the next flip will come up tails.
If the market is offering you a legitimate edge,determine the risk and take the trade .
5. Every moment in the market is unique.
Take a moment and think about the concept of uniqueness. No two moments in the external environment will ever exactly duplicate themselves . To do so,every atom or every molecule would have to be in the exact same position they were in some previous moment. Not a very likely possibility.
Source: Mark Douglas - Trading in the zone
MaMA : Momentum adjusted Moving AverageA brand new Moving Average , calculated using Momentum, Acceleration and Probability (Psychological Effect).
Momentum adjusted Moving Average( MaMA ) is an indicator that measures Price Action by taking into consideration not only Price movements but also its Momentum, Acceleration and Probability. MaMA , provides faster responses comparing to the regular Moving Average
Here is the math of the MaMA idea
Momentum measures change in price over a specified time period
momentum = source – source(length)
where,
source, indicates current bar’s price value
source(length), indicates historical price value of length bars earlier
Lets play with this formula and rewrite it by moving source(length) to other side of the equation
source = source(length) + momentum
to avoid confusion let’s call the source that we aim to predict as adjustedSource
adjustedSource = source(length) + momentum
looks nice the next value of source simply can be calculated by summing of historical value of the source value and value of the momentum. I wish it was so easy, the formula holds true only when the momentum is conserved/constant/steady but momentum move up or down with the price fluctuations (accelerating or decelerating)
Let’s add acceleration effects on our formula, where acceleration is change in momentum for a given length. Then the formula will become as (skipped proof part of acceleration effects, you may google for further details)
adjustedSource = source(length) + momentum + 1/2 * acceleration
here again the formula holds true when the acceleration is constant and once again it is not the case for trading, acceleration also changes with the price fluctuations
Then, how we can benefit from all of this, it has value yet requires additional approaches for better outcome
Let’s simulate behaviour with some predictive approach such as using probability (also known as psychological effect), where probability is a measure for calculating the chances or the possibilities of the occurrence of a random event. As stated earlier above momentum and acceleration are changing with the price fluctuations, by using the probability approach we can add a predictive skill to determine the likelihood of momentum and acceleration changes (remember it is a predictive approach). With this approach, our equations can be expresses as follows
adjustedSource = source(length) + momentum * probability
adjustedSource = source(length) + ( momentum + 1/2 * acceleration ) * probability , with acceleration effect
Finally, we plot MaMA with the new predicted source adjustedSource, applying acceleration effect is made settable by the used from the dialog box, default value is true.
What to look for:
• Trend Identification
• Support and Resistance
• Price Crossovers
Recommended settings are applied as default settings, if you wish to change the length of the MaMA then you should also adjust length of Momentum (and/or Probability). For example for faster moving average such as 21 period it would be suggested to set momentum length to 13
Alternative usage, set moving average length to 1 and keep rest lengths with default values, it will produce a predictive price line based on momentum and probability. Experience acceleration factor by enabling and disabling it
Conclusion
MaMA provide an added level of confidence to a trading strategy and yet it is important to always be aware that it implements a predictive approach in a chaotic market use with caution just like with any indicator
Trading success is all about following your trading strategy and the indicators should fit within your trading strategy, and not to be traded upon solely
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