Economics & Investing

Thomas Huault

Thomas Huault

22 days ago

A Mean Reversion Trading Indicator Inspired by Classical Mechanics Is The Kinetic Detrender


Old pots produce the best soup.

Photo by engin akyurt on Unsplash

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:


Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:



L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA
BTD/USDT candle chart at 01-hs timeframe with the Kinetic detrender and its 2 red fixed level and black dynamic levels


We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.

Chritiaan Hetzner

1 month ago

Mystery of the $1 billion'meme stock' that went to $400 billion in days

Who is AMTD Digital?

An unknown Hong Kong corporation joined the global megacaps worth over $500 billion on Tuesday.

The American Depository Share (ADS) with the ticker code HKD gapped at the open, soaring 25% over the previous closing price as trading began, before hitting an intraday high of $2,555.

At its peak, its market cap was almost $450 billion, more than Facebook parent Meta or Alibaba.

Yahoo Finance reported a daily volume of 350,500 shares, the lowest since the ADS began trading and much below the average of 1.2 million.

Despite losing a fifth of its value on Wednesday, it's still worth more than Toyota, Nike, McDonald's, or Walt Disney.

The company sold 16 million shares at $7.80 each in mid-July, giving it a $1 billion market valuation.

Why the boom?

That market cap seems unjustified.

According to SEC reports, its income-generating assets barely topped $400 million in March. Fortune's emails and calls went unanswered.

Website discloses little about company model. Its one-minute business presentation film uses a Star Wars–like design to sell the company as a "one-stop digital solutions platform in Asia"

The SEC prospectus explains.

AMTD Digital sells a "SpiderNet Ecosystems Solutions" kind of club membership that connects enterprises. This is the bulk of its $25 million annual revenue in April 2021.

Pretax profits have been higher than top line over the past three years due to fair value accounting gains on Appier, DayDayCook, WeDoctor, and five Asian fintechs.

AMTD Group, the company's parent, specializes in investment banking, hotel services, luxury education, and media and entertainment. AMTD IDEA, a $14 billion subsidiary, is also traded on the NYSE.

“Significant volatility”

Why AMTD Digital listed in the U.S. is unknown, as it informed investors in its share offering prospectus that could delist under SEC guidelines.

Beijing's red tape prevents the Sarbanes-Oxley Board from inspecting its Chinese auditor.

This frustrates Chinese stock investors. If the U.S. and China can't achieve a deal, 261 Chinese companies worth $1.3 trillion might be delisted.

Calvin Choi left UBS to become AMTD Group's CEO.

His capitalist background and status as a Young Global Leader with the World Economic Forum don't stop him from praising China's Communist party or celebrating the "glory and dream of the Great Rejuvenation of the Chinese nation" a century after its creation.

Despite having an executive vice chairman with a record of battling corruption and ties to Carrie Lam, Beijing's previous proconsul in Hong Kong, Choi is apparently being targeted for a two-year industry ban by the city's securities regulator after an investor accused Choi of malfeasance.

Some CMIG-funded initiatives produced money, but he didn't give us the proceeds, a corporate official told China's Caixin in October 2020. We don't know if he misappropriated or lost some money.

A seismic anomaly

In fundamental analysis, where companies are valued based on future cash flows, AMTD Digital's mind-boggling market cap is a statistical aberration that should occur once every hundred years.

AMTD Digital doesn't know why it's so valuable. In a thank-you letter to new shareholders, it said it was confused by the stock's performance.

Since its IPO, the company has seen significant ADS price volatility and active trading volume, it said Tuesday. "To our knowledge, there have been no important circumstances, events, or other matters since the IPO date."

Permabears awoke after the jump. Jim Chanos asked if "we're all going to ignore the $400 billion meme stock in the room," while Nate Anderson called AMTD Group "sketchy."

It happened the same day SEC Chair Gary Gensler praised the 20th anniversary of the Sarbanes-Oxley Act, aimed to restore trust in America's financial markets after the Enron and WorldCom accounting fraud scandals.

The run-up revived unpleasant memories of Robinhood's decision to limit retail investors' ability to buy GameStop, regarded as a measure to protect hedge funds invested in the meme company.

Why wasn't HKD's buy button removed? Because retail wasn't behind it?" tweeted Gensler on Tuesday. "Real stock fraud. "You're worthless."

Ben Carlson

Ben Carlson

2 months ago

Bear market duration and how to invest during one

Bear markets don't last forever, but that's hard to remember. Jamie Cullen's illustration

A bear market is a 20% decline from peak to trough in stock prices.

The S&P 500 was down 24% from its January highs at its low point this year. Bear market.

The U.S. stock market has had 13 bear markets since WWII (including the current one). Previous 12 bear markets averaged –32.7% losses. From peak to trough, the stock market averaged 12 months. The average time from bottom to peak was 21 months.

In the past seven decades, a bear market roundtrip to breakeven has averaged less than three years.

Long-term averages can vary widely, as with all historical market data. Investors can learn from past market crashes.

Historical bear markets offer lessons.

Bear market duration

A bear market can cost investors money and time. Most of the pain comes from stock market declines, but bear markets can be long.

Here are the longest U.S. stock bear markets since World war 2:

Stock market crashes can make it difficult to break even. After the 2008 financial crisis, the stock market took 4.5 years to recover. After the dotcom bubble burst, it took seven years to break even.

The longer you're underwater in the market, the more suffering you'll experience, according to research. Suffering can lead to selling at the wrong time.

Bear markets require patience because stocks can take a long time to recover.

Stock crash recovery

Bear markets can end quickly. The Corona Crash in early 2020 is an example.

The S&P 500 fell 34% in 23 trading sessions, the fastest bear market from a high in 90 years. The entire crash lasted one month. Stocks broke even six months after bottoming. Stocks rose 100% from those lows in 15 months.

Seven bear markets have lasted two years or less since 1945.

The 2020 recovery was an outlier, but four other bear markets have made investors whole within 18 months.

During a bear market, you don't know if it will end quickly or feel like death by a thousand cuts.

Recessions vs. bear markets

Many people believe the U.S. economy is in or heading for a recession.

I agree. Four-decade high inflation. Since 1945, inflation has exceeded 5% nine times. Each inflationary spike caused a recession. Only slowing economic demand seems to stop price spikes.

This could happen again. Stocks seem to be pricing in a recession.

Recessions almost always cause a bear market, but a bear market doesn't always equal a recession. In 1946, the stock market fell 27% without a recession in sight. Without an economic slowdown, the stock market fell 22% in 1966. Black Monday in 1987 was the most famous stock market crash without a recession. Stocks fell 30% in less than a week. Many believed the stock market signaled a depression. The crash caused no slowdown.

Economic cycles are hard to predict. Even Wall Street makes mistakes.

Bears vs. bulls

Bear markets for U.S. stocks always end. Every stock market crash in U.S. history has been followed by new all-time highs.

How should investors view the recession? Investing risk is subjective.

You don't have as long to wait out a bear market if you're retired or nearing retirement. Diversification and liquidity help investors with limited time or income. Cash and short-term bonds drag down long-term returns but can ensure short-term spending.

Young people with years or decades ahead of them should view this bear market as an opportunity. Stock market crashes are good for net savers in the future. They let you buy cheap stocks with high dividend yields.

You need discipline, patience, and planning to buy stocks when it doesn't feel right.

Bear markets aren't fun because no one likes seeing their portfolio fall. But stock market downturns are a feature, not a bug. If stocks never crashed, they wouldn't offer such great long-term returns.

Sam Hickmann

Sam Hickmann

3 months ago

What is headline inflation?

Headline inflation is the raw Consumer price index (CPI) reported monthly by the Bureau of labour statistics (BLS). CPI measures inflation by calculating the cost of a fixed basket of goods. The CPI uses a base year to index the current year's prices.

Explaining Inflation

As it includes all aspects of an economy that experience inflation, headline inflation is not adjusted to remove volatile figures. Headline inflation is often linked to cost-of-living changes, which is useful for consumers.

The headline figure doesn't account for seasonality or volatile food and energy prices, which are removed from the core CPI. Headline inflation is usually annualized, so a monthly headline figure of 4% inflation would equal 4% inflation for the year if repeated for 12 months. Top-line inflation is compared year-over-year.

Inflation's downsides

Inflation erodes future dollar values, can stifle economic growth, and can raise interest rates. Core inflation is often considered a better metric than headline inflation. Investors and economists use headline and core results to set growth forecasts and monetary policy.

Core Inflation

Core inflation removes volatile CPI components that can distort the headline number. Food and energy costs are commonly removed. Environmental shifts that affect crop growth can affect food prices outside of the economy. Political dissent can affect energy costs, such as oil production.

From 1957 to 2018, the U.S. averaged 3.64 percent core inflation. In June 1980, the rate reached 13.60%. May 1957 had 0% inflation. The Fed's core inflation target for 2022 is 3%.

Central bank:

A central bank has privileged control over a nation's or group's money and credit. Modern central banks are responsible for monetary policy and bank regulation. Central banks are anti-competitive and non-market-based. Many central banks are not government agencies and are therefore considered politically independent. Even if a central bank isn't government-owned, its privileges are protected by law. A central bank's legal monopoly status gives it the right to issue banknotes and cash. Private commercial banks can only issue demand deposits.

What are living costs?

The cost of living is the amount needed to cover housing, food, taxes, and healthcare in a certain place and time. Cost of living is used to compare the cost of living between cities and is tied to wages. If expenses are higher in a city like New York, salaries must be higher so people can live there.

What's U.S. bureau of labor statistics?

BLS collects and distributes economic and labor market data about the U.S. Its reports include the CPI and PPI, both important inflation measures.

Sam Hickmann

Sam Hickmann

3 months ago

What is this Fed interest rate everybody is talking about that makes or breaks the stock market?

The Federal Funds Rate (FFR) is the target interest rate set by the Federal Reserve System (Fed)'s policy-making body (FOMC). This target is the rate at which the Fed suggests commercial banks borrow and lend their excess reserves overnight to each other.

The FOMC meets 8 times a year to set the target FFR. This is supposed to promote economic growth. The overnight lending market sets the actual rate based on commercial banks' short-term reserves. If the market strays too far, the Fed intervenes.

Banks must keep a certain percentage of their deposits in a Federal Reserve account. A bank's reserve requirement is a percentage of its total deposits. End-of-day bank account balances averaged over two-week reserve maintenance periods are used to determine reserve requirements.

If a bank expects to have end-of-day balances above what's needed, it can lend the excess to another institution.

The FOMC adjusts interest rates based on economic indicators that show inflation, recession, or other issues that affect economic growth. Core inflation and durable goods orders are indicators.

In response to economic conditions, the FFR target has changed over time. In the early 1980s, inflation pushed it to 20%. During the Great Recession of 2007-2009, the rate was slashed to 0.15 percent to encourage growth.

Inflation picked up in May 2022 despite earlier rate hikes, prompting today's 0.75 percent point increase. The largest increase since 1994. It might rise to around 3.375% this year and 3.1% by the end of 2024.