How Payment for Order Flow (PFOF) Works
What is PFOF?
PFOF is a brokerage firm's compensation for directing orders to different parties for trade execution. The brokerage firm receives fractions of a penny per share for directing the order to a market maker.
Each optionable stock could have thousands of contracts, so market makers dominate options trades. Order flow payments average less than $0.50 per option contract.
Order Flow Payments (PFOF) Explained
The proliferation of exchanges and electronic communication networks has complicated equity and options trading (ECNs) Ironically, Bernard Madoff, the Ponzi schemer, pioneered pay-for-order-flow.
In a December 2000 study on PFOF, the SEC said, "Payment for order flow is a method of transferring trading profits from market making to brokers who route customer orders to specialists for execution."
Given the complexity of trading thousands of stocks on multiple exchanges, market making has grown. Market makers are large firms that specialize in a set of stocks and options, maintaining an inventory of shares and contracts for buyers and sellers. Market makers are paid the bid-ask spread. Spreads have narrowed since 2001, when exchanges switched to decimals. A market maker's ability to play both sides of trades is key to profitability.
Benefits, requirements
A broker receives fees from a third party for order flow, sometimes without a client's knowledge. This invites conflicts of interest and criticism. Regulation NMS from 2005 requires brokers to disclose their policies and financial relationships with market makers.
Your broker must tell you if it's paid to send your orders to specific parties. This must be done at account opening and annually. The firm must disclose whether it participates in payment-for-order-flow and, upon request, every paid order. Brokerage clients can request payment data on specific transactions, but the response takes weeks.
Order flow payments save money. Smaller brokerage firms can benefit from routing orders through market makers and getting paid. This allows brokerage firms to send their orders to another firm to be executed with other orders, reducing costs. The market maker or exchange benefits from additional share volume, so it pays brokerage firms to direct traffic.
Retail investors, who lack bargaining power, may benefit from order-filling competition. Arrangements to steer the business in one direction invite wrongdoing, which can erode investor confidence in financial markets and their players.
Pay-for-order-flow criticism
It has always been controversial. Several firms offering zero-commission trades in the late 1990s routed orders to untrustworthy market makers. During the end of fractional pricing, the smallest stock spread was $0.125. Options spreads widened. Traders found that some of their "free" trades cost them a lot because they weren't getting the best price.
The SEC then studied the issue, focusing on options trades, and nearly decided to ban PFOF. The proliferation of options exchanges narrowed spreads because there was more competition for executing orders. Options market makers said their services provided liquidity. In its conclusion, the report said, "While increased multiple-listing produced immediate economic benefits to investors in the form of narrower quotes and effective spreads, these improvements have been muted with the spread of payment for order flow and internalization."
The SEC allowed payment for order flow to continue to prevent exchanges from gaining monopoly power. What would happen to trades if the practice was outlawed was also unclear. SEC requires brokers to disclose financial arrangements with market makers. Since then, the SEC has watched closely.
2020 Order Flow Payment
Rule 605 and Rule 606 show execution quality and order flow payment statistics on a broker's website. Despite being required by the SEC, these reports can be hard to find. The SEC mandated these reports in 2005, but the format and reporting requirements have changed over the years, most recently in 2018.
Brokers and market makers formed a working group with the Financial Information Forum (FIF) to standardize order execution quality reporting. Only one retail brokerage (Fidelity) and one market maker remain (Two Sigma Securities). FIF notes that the 605/606 reports "do not provide the level of information that allows a retail investor to gauge how well a broker-dealer fills a retail order compared to the NBBO (national best bid or offer’) at the time the order was received by the executing broker-dealer."
In the first quarter of 2020, Rule 606 reporting changed to require brokers to report net payments from market makers for S&P 500 and non-S&P 500 equity trades and options trades. Brokers must disclose payment rates per 100 shares by order type (market orders, marketable limit orders, non-marketable limit orders, and other orders).
Richard Repetto, Managing Director of New York-based Piper Sandler & Co., publishes a report on Rule 606 broker reports. Repetto focused on Charles Schwab, TD Ameritrade, E-TRADE, and Robinhood in Q2 2020. Repetto reported that payment for order flow was higher in the second quarter than the first due to increased trading activity, and that options paid more than equities.
Repetto says PFOF contributions rose overall. Schwab has the lowest options rates, while TD Ameritrade and Robinhood have the highest. Robinhood had the highest equity rating. Repetto assumes Robinhood's ability to charge higher PFOF reflects their order flow profitability and that they receive a fixed rate per spread (vs. a fixed rate per share by the other brokers).
Robinhood's PFOF in equities and options grew the most quarter-over-quarter of the four brokers Piper Sandler analyzed, as did their implied volumes. All four brokers saw higher PFOF rates.
TD Ameritrade took the biggest income hit when cutting trading commissions in fall 2019, and this report shows they're trying to make up the shortfall by routing orders for additional PFOF. Robinhood refuses to disclose trading statistics using the same metrics as the rest of the industry, offering only a vague explanation on their website.
Summary
Payment for order flow has become a major source of revenue as brokers offer no-commission equity (stock and ETF) orders. For retail investors, payment for order flow poses a problem because the brokerage may route orders to a market maker for its own benefit, not the investor's.
Infrequent or small-volume traders may not notice their broker's PFOF practices. Frequent traders and those who trade larger quantities should learn about their broker's order routing system to ensure they're not losing out on price improvement due to a broker prioritizing payment for order flow.
This post is a summary. Read full article here
More on Economics & Investing

Jan-Patrick Barnert
3 years ago
Wall Street's Bear Market May Stick Around
If history is any guide, this bear market might be long and severe.
This is the S&P 500 Index's fourth such incident in 20 years. The last bear market of 2020 was a "shock trade" caused by the Covid-19 pandemic, although earlier ones in 2000 and 2008 took longer to bottom out and recover.
Peter Garnry, head of equities strategy at Saxo Bank A/S, compares the current selloff to the dotcom bust of 2000 and the 1973-1974 bear market marked by soaring oil prices connected to an OPEC oil embargo. He blamed high tech valuations and the commodity crises.
"This drop might stretch over a year and reach 35%," Garnry wrote.
Here are six bear market charts.
Time/depth
The S&P 500 Index plummeted 51% between 2000 and 2002 and 58% during the global financial crisis; it took more than 1,000 trading days to recover. The former took 638 days to reach a bottom, while the latter took 352 days, suggesting the present selloff is young.
Valuations
Before the tech bubble burst in 2000, valuations were high. The S&P 500's forward P/E was 25 times then. Before the market fell this year, ahead values were near 24. Before the global financial crisis, stocks were relatively inexpensive, but valuations dropped more than 40%, compared to less than 30% now.
Earnings
Every stock crash, especially earlier bear markets, returned stocks to fundamentals. The S&P 500 decouples from earnings trends but eventually recouples.
Support
Central banks won't support equity investors just now. The end of massive monetary easing will terminate a two-year bull run that was among the strongest ever, and equities may struggle without cheap money. After years of "don't fight the Fed," investors must embrace a new strategy.
Bear Haunting Bear
If the past is any indication, rising government bond yields are bad news. After the financial crisis, skyrocketing rates and a falling euro pushed European stock markets back into bear territory in 2011.
Inflation/rates
The current monetary policy climate differs from past bear markets. This is the first time in a while that markets face significant inflation and rising rates.
This post is a summary. Read full article here

Arthur Hayes
3 years ago
Contagion
(The author's opinions should not be used to make investment decisions or as a recommendation to invest.)
The pandemic and social media pseudoscience have made us all epidemiologists, for better or worse. Flattening the curve, social distancing, lockdowns—remember? Some of you may remember R0 (R naught), the number of healthy humans the average COVID-infected person infects. Thankfully, the world has moved on from Greater China's nightmare. Politicians have refocused their talent for misdirection on getting their constituents invested in the war for Russian Reunification or Russian Aggression, depending on your side of the iron curtain.
Humanity battles two fronts. A war against an invisible virus (I know your Commander in Chief might have told you COVID is over, but viruses don't follow election cycles and their economic impacts linger long after the last rapid-test clinic has closed); and an undeclared World War between US/NATO and Eurasia/Russia/China. The fiscal and monetary authorities' current policies aim to mitigate these two conflicts' economic effects.
Since all politicians are short-sighted, they usually print money to solve most problems. Printing money is the easiest and fastest way to solve most problems because it can be done immediately without much discussion. The alternative—long-term restructuring of our global economy—would hurt stakeholders and require an honest discussion about our civilization's state. Both of those requirements are non-starters for our short-sighted political friends, so whether your government practices capitalism, communism, socialism, or fascism, they all turn to printing money-ism to solve all problems.
Free money stimulates demand, so people buy crap. Overbuying shit raises prices. Inflation. Every nation has food, energy, or goods inflation. The once-docile plebes demand action when the latter two subsets of inflation rise rapidly. They will be heard at the polls or in the streets. What would you do to feed your crying hungry child?
Global central banks During the pandemic, the Fed, PBOC, BOJ, ECB, and BOE printed money to aid their governments. They worried about inflation and promised to remove fiat liquidity and tighten monetary conditions.
Imagine Nate Diaz's round-house kick to the face. The financial markets probably felt that way when the US and a few others withdrew fiat wampum. Sovereign debt markets suffered a near-record bond market rout.
The undeclared WW3 is intensifying, with recent gas pipeline attacks. The global economy is already struggling, and credit withdrawal will worsen the situation. The next pandemic, the Yield Curve Control (YCC) virus, is spreading as major central banks backtrack on inflation promises. All central banks eventually fail.
Here's a scorecard.
In order to save its financial system, BOE recently reverted to Quantitative Easing (QE).
BOJ Continuing YCC to save their banking system and enable affordable government borrowing.
ECB printing money to buy weak EU member bonds, but will soon start Quantitative Tightening (QT).
PBOC Restarting the money printer to give banks liquidity to support the falling residential property market.
Fed raising rates and QT-shrinking balance sheet.
80% of the world's biggest central banks are printing money again. Only the Fed has remained steadfast in the face of a financial market bloodbath, determined to end the inflation for which it is at least partially responsible—the culmination of decades of bad economic policies and a world war.
YCC printing is the worst for fiat currency and society. Because it necessitates central banks fixing a multi-trillion-dollar bond market. YCC central banks promise to infinitely expand their balance sheets to keep a certain interest rate metric below an unnatural ceiling. The market always wins, crushing humanity with inflation.
BOJ's YCC policy is longest-standing. The BOE joined them, and my essay this week argues that the ECB will follow. The ECB joining YCC would make 60% of major central banks follow this terrible policy. Since the PBOC is part of the Chinese financial system, the number could be 80%. The Chinese will lend any amount to meet their economic activity goals.
The BOE committed to a 13-week, GBP 65bn bond price-fixing operation. However, BOEs YCC may return. If you lose to the market, you're stuck. Since the BOE has announced that it will buy your Gilt at inflated prices, why would you not sell them all? Market participants taking advantage of this policy will only push the bank further into the hole it dug itself, so I expect the BOE to re-up this program and count them as YCC.
In a few trading days, the BOE went from a bank determined to slay inflation by raising interest rates and QT to buying an unlimited amount of UK Gilts. I expect the ECB to be dragged kicking and screaming into a similar policy. Spoiler alert: big daddy Fed will eventually die from the YCC virus.
Threadneedle St, London EC2R 8AH, UK
Before we discuss the BOE's recent missteps, a chatroom member called the British royal family the Kardashians with Crowns, which made me laugh. I'm sad about royal attention. If the public was as interested in energy and economic policies as they are in how the late Queen treated Meghan, Duchess of Sussex, UK politicians might not have been able to get away with energy and economic fairy tales.
The BOE printed money to recover from COVID, as all good central banks do. For historical context, this chart shows the BOE's total assets as a percentage of GDP since its founding in the 18th century.
The UK has had a rough three centuries. Pandemics, empire wars, civil wars, world wars. Even so, the BOE's recent money printing was its most aggressive ever!
BOE Total Assets as % of GDP (white) vs. UK CPI
Now, inflation responded slowly to the bank's most aggressive monetary loosening. King Charles wishes the gold line above showed his popularity, but it shows his subjects' suffering.
The BOE recognized early that its money printing caused runaway inflation. In its August 2022 report, the bank predicted that inflation would reach 13% by year end before aggressively tapering in 2023 and 2024.
Aug 2022 BOE Monetary Policy Report
The BOE was the first major central bank to reduce its balance sheet and raise its policy rate to help.
The BOE first raised rates in December 2021. Back then, JayPow wasn't even considering raising rates.
UK policymakers, like most developed nations, believe in energy fairy tales. Namely, that the developed world, which grew in lockstep with hydrocarbon use, could switch to wind and solar by 2050. The UK's energy import bill has grown while coal, North Sea oil, and possibly stranded shale oil have been ignored.
WW3 is an economic war that is balkanizing energy markets, which will continue to inflate. A nation that imports energy and has printed the most money in its history cannot avoid inflation.
The chart above shows that energy inflation is a major cause of plebe pain.
The UK is hit by a double whammy: the BOE must remove credit to reduce demand, and energy prices must rise due to WW3 inflation. That's not economic growth.
Boris Johnson was knocked out by his country's poor economic performance, not his lockdown at 10 Downing St. Prime Minister Truss and her merry band of fools arrived with the tried-and-true government remedy: goodies for everyone.
She released a budget full of economic stimulants. She cut corporate and individual taxes for the rich. She plans to give poor people vouchers for higher energy bills. Woohoo! Margret Thatcher's new pants suit.
My buddy Jim Bianco said Truss budget's problem is that it works. It will boost activity at a time when inflation is over 10%. Truss' budget didn't include austerity measures like tax increases or spending cuts, which the bond market wanted. The bond market protested.
30-year Gilt yield chart. Yields spiked the most ever after Truss announced her budget, as shown. The Gilt market is the longest-running bond market in the world.
The Gilt market showed the pole who's boss with Cardi B.
Before this, the BOE was super-committed to fighting inflation. To their credit, they raised short-term rates and shrank their balance sheet. However, rapid yield rises threatened to destroy the entire highly leveraged UK financial system overnight, forcing them to change course.
Accounting gimmicks allowed by regulators for pension funds posed a systemic threat to the UK banking system. UK pension funds could use interest rate market levered derivatives to match liabilities. When rates rise, short rate derivatives require more margin. The pension funds spent all their money trying to pick stonks and whatever else their sell side banker could stuff them with, so the historic rate spike would have bankrupted them overnight. The FT describes BOE-supervised chicanery well.
To avoid a financial apocalypse, the BOE in one morning abandoned all their hard work and started buying unlimited long-dated Gilts to drive prices down.
Another reminder to never fight a central bank. The 30-year Gilt is shown above. After the BOE restarted the money printer on September 28, this bond rose 30%. Thirty-fucking-percent! Developed market sovereign bonds rarely move daily. You're invested in His Majesty's government obligations, not a Chinese property developer's offshore USD bond.
The political need to give people goodies to help them fight the terrible economy ran into a financial reality. The central bank protected the UK financial system from asset-price deflation because, like all modern economies, it is debt-based and highly levered. As bad as it is, inflation is not their top priority. The BOE example demonstrated that. To save the financial system, they abandoned almost a year of prudent monetary policy in a few hours. They also started the endgame.
Let's play Central Bankers Say the Darndest Things before we go to the continent (and sorry if you live on a continent other than Europe, but you're not culturally relevant).
Pre-meltdown BOE output:
FT, October 17, 2021 On Sunday, the Bank of England governor warned that it must act to curb inflationary pressure, ignoring financial market moves that have priced in the first interest rate increase before the end of the year.
On July 19, 2022, Gov. Andrew Bailey spoke. Our 2% inflation target is unwavering. We'll do our job.
August 4th 2022 MPC monetary policy announcement According to its mandate, the MPC will sustainably return inflation to 2% in the medium term.
Catherine Mann, MPC member, September 5, 2022 speech. Fast and forceful monetary tightening, possibly followed by a hold or reversal, is better than gradualism because it promotes inflation expectations' role in bringing inflation back to 2% over the medium term.
When their financial system nearly collapsed in one trading session, they said:
The Bank of England's Financial Policy Committee warned on 28 September that gilt market dysfunction threatened UK financial stability. It advised action and supported the Bank's urgent gilt market purchases for financial stability.
It works when the price goes up but not down. Is my crypto portfolio dysfunctional enough to get a BOE bailout?
Next, the EU and ECB. The ECB is also fighting inflation, but it will also succumb to the YCC virus for the same reasons as the BOE.
Frankfurt am Main, ECB Tower, Sonnemannstraße 20, 60314
Only France and Germany matter economically in the EU. Modern European history has focused on keeping Germany and Russia apart. German manufacturing and cheap Russian goods could change geopolitics.
France created the EU to keep Germany down, and the Germans only cooperated because of WWII guilt. France's interests are shared by the US, which lurks in the shadows to prevent a Germany-Russia alliance. A weak EU benefits US politics. Avoid unification of Eurasia. (I paraphrased daddy Felix because I thought quoting a large part of his most recent missive would get me spanked.)
As with everything, understanding Germany's energy policy is the best way to understand why the German economy is fundamentally fucked and why that spells doom for the EU. Germany, the EU's main economic engine, is being crippled by high energy prices, threatening a depression. This economic downturn threatens the union. The ECB may have to abandon plans to shrink its balance sheet and switch to YCC to save the EU's unholy political union.
France did the smart thing and went all in on nuclear energy, which is rare in geopolitics. 70% of electricity is nuclear-powered. Their manufacturing base can survive Russian gas cuts. Germany cannot.
My boy Zoltan made this great graphic showing how screwed Germany is as cheap Russian gas leaves the industrial economy.
$27 billion of Russian gas powers almost $2 trillion of German economic output, a 75x energy leverage. The German public was duped into believing the same energy fairy tales as their politicians, and they overwhelmingly allowed the Green party to dismantle any efforts to build a nuclear energy ecosystem over the past several decades. Germany, unlike France, must import expensive American and Qatari LNG via supertankers due to Nordstream I and II pipeline sabotage.
American gas exports to Europe are touted by the media. Gas is cheap because America isn't the Western world's swing producer. If gas prices rise domestically in America, the plebes would demand the end of imports to avoid paying more to heat their homes.
German goods would cost much more in this scenario. German producer prices rose 46% YoY in August. The German current account is rapidly approaching zero and will soon be negative.
German PPI Change YoY
German Current Account
The reason this matters is a curious construction called TARGET2. Let’s hear from the horse’s mouth what exactly this beat is:
TARGET2 is the real-time gross settlement (RTGS) system owned and operated by the Eurosystem. Central banks and commercial banks can submit payment orders in euro to TARGET2, where they are processed and settled in central bank money, i.e. money held in an account with a central bank.
Source: ECB
Let me explain this in plain English for those unfamiliar with economic dogma.
This chart shows intra-EU credits and debits. TARGET2. Germany, Europe's powerhouse, is owed money. IOU-buying Greeks buy G-wagons. The G-wagon pickup truck is badass.
If all EU countries had fiat currencies, the Deutsche Mark would be stronger than the Italian Lira, according to the chart above. If Europe had to buy goods from non-EU countries, the Euro would be much weaker. Credits and debits between smaller political units smooth out imbalances in other federal-provincial-state political systems. Financial and fiscal unions allow this. The EU is financial, so the centre cannot force the periphery to settle their imbalances.
Greece has never had to buy Fords or Kias instead of BMWs, but what if Germany had to shut down its auto manufacturing plants due to energy shortages?
Italians have done well buying ammonia from Germany rather than China, but what if BASF had to close its Ludwigshafen facility due to a lack of affordable natural gas?
I think you're seeing the issue.
Instead of Germany, EU countries would owe foreign producers like America, China, South Korea, Japan, etc. Since these countries aren't tied into an uneconomic union for politics, they'll demand hard fiat currency like USD instead of Euros, which have become toilet paper (or toilet plastic).
Keynesian economists have a simple solution for politicians who can't afford market prices. Government debt can maintain production. The debt covers the difference between what a business can afford and the international energy market price.
Germans are monetary policy conservative because of the Weimar Republic's hyperinflation. The Bundesbank is the only thing preventing ECB profligacy. Germany must print its way out without cheap energy. Like other nations, they will issue more bonds for fiscal transfers.
More Bunds mean lower prices. Without German monetary discipline, the Euro would have become a trash currency like any other emerging market that imports energy and food and has uncompetitive labor.
Bunds price all EU country bonds. The ECB's money printing is designed to keep the spread of weak EU member bonds vs. Bunds low. Everyone falls with Bunds.
Like the UK, German politicians seeking re-election will likely cause a Bunds selloff. Bond investors will understandably reject their promises of goodies for industry and individuals to offset the lack of cheap Russian gas. Long-dated Bunds will be smoked like UK Gilts. The ECB will face a wave of ultra-levered financial players who will go bankrupt if they mark to market their fixed income derivatives books at higher Bund yields.
Some treats People: Germany will spend 200B to help consumers and businesses cope with energy prices, including promoting renewable energy.
That, ladies and germs, is why the ECB will immediately abandon QT, move to a stop-gap QE program to normalize the Bund and every other EU bond market, and eventually graduate to YCC as the market vomits bonds of all stripes into Christine Lagarde's loving hands. She probably has soft hands.
The 30-year Bund market has noticed Germany's economic collapse. 2021 yields skyrocketed.
30-year Bund Yield
ECB Says the Darndest Things:
Because inflation is too high and likely to stay above our target for a long time, we took today's decision and expect to raise interest rates further.- Christine Lagarde, ECB Press Conference, Sept 8.
The Governing Council will adjust all of its instruments to stabilize inflation at 2% over the medium term. July 21 ECB Monetary Decision
Everyone struggles with high inflation. The Governing Council will ensure medium-term inflation returns to two percent. June 9th ECB Press Conference
I'm excited to read the after. Like the BOE, the ECB may abandon their plans to shrink their balance sheet and resume QE due to debt market dysfunction.
Eighty Percent
I like YCC like dark chocolate over 80%. ;).
Can 80% of the world's major central banks' QE and/or YCC overcome Sir Powell's toughness on fungible risky asset prices?
Gold and crypto are fungible global risky assets. Satoshis and gold bars are the same in New York, London, Frankfurt, Tokyo, and Shanghai.
As more Euros, Yen, Renminbi, and Pounds are printed, people will move their savings into Dollars or other stores of value. As the Fed raises rates and reduces its balance sheet, the USD will strengthen. Gold/EUR and BTC/JPY may also attract buyers.
Gold and crypto markets are much smaller than the trillions in fiat money that will be printed, so they will appreciate in non-USD currencies. These flows only matter in one instance because we trade the global or USD price. Arbitrage occurs when BTC/EUR rises faster than EUR/USD. Here is how it works:
An investor based in the USD notices that BTC is expensive in EUR terms.
Instead of buying BTC, this investor borrows USD and then sells it.
After that, they sell BTC and buy EUR.
Then they choose to sell EUR and buy USD.
The investor receives their profit after repaying the USD loan.
This triangular FX arbitrage will align the global/USD BTC price with the elevated EUR, JPY, CNY, and GBP prices.
Even if the Fed continues QT, which I doubt they can do past early 2023, small stores of value like gold and Bitcoin may rise as non-Fed central banks get serious about printing money.
“Arthur, this is just more copium,” you might retort.
Patience. This takes time. Economic and political forcing functions take time. The BOE example shows that bond markets will reject politicians' policies to appease voters. Decades of bad energy policy have no immediate fix. Money printing is the only politically viable option. Bond yields will rise as bond markets see more stimulative budgets, and the over-leveraged fiat debt-based financial system will collapse quickly, followed by a monetary bailout.
America has enough food, fuel, and people. China, Europe, Japan, and the UK suffer. America can be autonomous. Thus, the Fed can prioritize domestic political inflation concerns over supplying the world (and most of its allies) with dollars. A steady flow of dollars allows other nations to print their currencies and buy energy in USD. If the strongest player wins, everyone else loses.
I'm making a GDP-weighted index of these five central banks' money printing. When ready, I'll share its rate of change. This will show when the 80%'s money printing exceeds the Fed's tightening.

Thomas Huault
3 years ago
A Mean Reversion Trading Indicator Inspired by Classical Mechanics Is The Kinetic Detrender
DATA MINING WITH SUPERALGORES
Old pots produce the best soup.
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:
With
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:
With
and
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 = 1.6Upper 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:
variable.allClose.push(candle.close)
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.emaThe Z calculation reuses code from Z-Normalization-based indicators:
variable.allE.push(variable.E)
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
}
variable.allZ.push(variable.Z)
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.sigZWe also update the EMA value.
variable.prevEMA = variable.EMAConclusion
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.
You might also like

mbvissers.eth
3 years ago
Why does every smart contract seem to implement ERC165?
ERC165 (or EIP-165) is a standard utilized by various open-source smart contracts like Open Zeppelin or Aavegotchi.
What's it? You must implement? Why do we need it? I'll describe the standard and answer any queries.
What is ERC165
ERC165 detects and publishes smart contract interfaces. Meaning? It standardizes how interfaces are recognized, how to detect if they implement ERC165, and how a contract publishes the interfaces it implements. How does it work?
Why use ERC165? Sometimes it's useful to know which interfaces a contract implements, and which version.
Identifying interfaces
An interface function's selector. This verifies an ABI function. XORing all function selectors defines an interface in this standard. The following code demonstrates.
// SPDX-License-Identifier: UNLICENCED
pragma solidity >=0.8.0 <0.9.0;
interface Solidity101 {
function hello() external pure;
function world(int) external pure;
}
contract Selector {
function calculateSelector() public pure returns (bytes4) {
Solidity101 i;
return i.hello.selector ^ i.world.selector;
// Returns 0xc6be8b58
}
function getHelloSelector() public pure returns (bytes4) {
Solidity101 i;
return i.hello.selector;
// Returns 0x19ff1d21
}
function getWorldSelector() public pure returns (bytes4) {
Solidity101 i;
return i.world.selector;
// Returns 0xdf419679
}
}This code isn't necessary to understand function selectors and how an interface's selector can be determined from the functions it implements.
Run that sample in Remix to see how interface function modifications affect contract function output.
Contracts publish their implemented interfaces.
We can identify interfaces. Now we must disclose the interfaces we're implementing. First, import IERC165 like so.
pragma solidity ^0.4.20;
interface ERC165 {
/// @notice Query if a contract implements an interface
/// @param interfaceID The interface identifier, as specified in ERC-165
/// @dev Interface identification is specified in ERC-165.
/// @return `true` if the contract implements `interfaceID` and
/// `interfaceID` is not 0xffffffff, `false` otherwise
function supportsInterface(bytes4 interfaceID) external view returns (bool);
}We still need to build this interface in our smart contract. ERC721 from OpenZeppelin is a good example.
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/ERC721.sol)
pragma solidity ^0.8.0;
import "./IERC721.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/introspection/ERC165.sol";
// ...
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
// ...
function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
return
interfaceId == type(IERC721).interfaceId ||
interfaceId == type(IERC721Metadata).interfaceId ||
super.supportsInterface(interfaceId);
}
// ...
}I deleted unnecessary code. The smart contract imports ERC165, IERC721 and IERC721Metadata. The is keyword at smart contract declaration implements all three.
Kind (interface).
Note that type(interface).interfaceId returns the same as the interface selector.
We override supportsInterface in the smart contract to return a boolean that checks if interfaceId is the same as one of the implemented contracts.
Super.supportsInterface() calls ERC165 code. Checks if interfaceId is IERC165.
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
return interfaceId == type(IERC165).interfaceId;
}So, if we run supportsInterface with an interfaceId, our contract function returns true if it's implemented and false otherwise. True for IERC721, IERC721Metadata, andIERC165.
Conclusion
I hope this post has helped you understand and use ERC165 and why it's employed.
Have a great day, thanks for reading!

Scott Galloway
3 years ago
Text-ure
While we played checkers, we thought billionaires played 3D chess. They're playing the same game on a fancier board.
Every medium has nuances and norms. Texting is authentic and casual. A smaller circle has access, creating intimacy and immediacy. Most people read all their texts, but not all their email and mail. Many of us no longer listen to our voicemails, and calling your kids ages you.
Live interviews and testimony under oath inspire real moments, rare in a world where communications departments sanitize everything powerful people say. When (some of) Elon's text messages became public in Twitter v. Musk, we got a glimpse into tech power. It's bowels.
These texts illuminate the tech community's upper caste.
Checkers, Not Chess
Elon texts with Larry Ellison, Joe Rogan, Sam Bankman-Fried, Satya Nadella, and Jack Dorsey. They reveal astounding logic, prose, and discourse. The world's richest man and his followers are unsophisticated, obtuse, and petty. Possibly. While we played checkers, we thought billionaires played 3D chess. They're playing the same game on a fancier board.
They fumble with their computers.
They lean on others to get jobs for their kids (no surprise).
No matter how rich, they always could use more (money).
Differences A social hierarchy exists. Among this circle, the currency of deference is... currency. Money increases sycophantry. Oculus and Elon's "friends'" texts induce nausea.
Autocorrect frustrates everyone.
Elon doesn't stand out to me in these texts; he comes off mostly OK in my view. It’s the people around him. It seems our idolatry of innovators has infected the uber-wealthy, giving them an uncontrollable urge to kill the cool kid for a seat at his cafeteria table. "I'd grenade for you." If someone says this and they're not fighting you, they're a fan, not a friend.
Many powerful people are undone by their fake friends. Facilitators, not well-wishers. When Elon-Twitter started, I wrote about power. Unchecked power is intoxicating. This is a scientific fact, not a thesis. Power causes us to downplay risk, magnify rewards, and act on instincts more quickly. You lose self-control and must rely on others.
You'd hope the world's richest person has advisers who push back when necessary (i.e., not yes men). Elon's reckless, childish behavior and these texts show there is no truth-teller. I found just one pushback in the 151-page document. It came from Twitter CEO Parag Agrawal, who, in response to Elon’s unhelpful “Is Twitter dying?” tweet, let Elon know what he thought: It was unhelpful. Elon’s response? A childish, terse insult.
Scale
The texts are mostly unremarkable. There are some, however, that do remind us the (super-)rich are different. Specifically, the discussions of possible equity investments from crypto-billionaire Sam Bankman-Fried (“Does he have huge amounts of money?”) and this exchange with Larry Ellison:
Ellison, who co-founded $175 billion Oracle, is wealthy. Less clear is whether he can text a billion dollars. Who hasn't been texted $1 billion? Ellison offered 8,000 times the median American's net worth, enough to buy 3,000 Ferraris or the Chicago Blackhawks. It's a bedrock principle of capitalism to have incredibly successful people who are exponentially wealthier than the rest of us. It creates an incentive structure that inspires productivity and prosperity. When people offer billions over text to help a billionaire's vanity project in a country where 1 in 5 children are food insecure, isn't America messed up?
Elon's Morgan Stanley banker, Michael Grimes, tells him that Web3 ventures investor Bankman-Fried can invest $5 billion in the deal: “could do $5bn if everything vision lock... Believes in your mission." The message bothers Elon. In Elon's world, $5 billion doesn't warrant a worded response. $5 billion is more than many small nations' GDP, twice the SEC budget, and five times the NRC budget.
If income inequality worries you after reading this, trust your gut.
Billionaires aren't like the rich.
As an entrepreneur, academic, and investor, I've met modest-income people, rich people, and billionaires. Rich people seem different to me. They're smarter and harder working than most Americans. Monty Burns from The Simpsons is a cartoon about rich people. Rich people have character and know how to make friends. Success requires supporters.
I've never noticed a talent or intelligence gap between wealthy and ultra-wealthy people. Conflating talent and luck infects the tech elite. Timing is more important than incremental intelligence when going from millions to hundreds of millions or billions. Proof? Elon's texting. Any man who electrifies the auto industry and lands two rockets on barges is a genius. His mega-billions come from a well-regulated capital market, enforceable contracts, thousands of workers, and billions of dollars in government subsidies, including a $465 million DOE loan that allowed Tesla to produce the Model S. So, is Mr. Musk a genius or an impressive man in a unique time and place?
The Point
Elon's texts taught us more? He can't "fix" Twitter. For two weeks in April, he was all in on blockchain Twitter, brainstorming Dogecoin payments for tweets with his brother — i.e., paid speech — while telling Twitter's board he was going to make a hostile tender offer. Kimbal approved. By May, he was over crypto and "laborious blockchain debates." (Mood.)
Elon asked the Twitter CEO for "an update from the Twitter engineering team" No record shows if he got the meeting. It doesn't "fix" Twitter either. And this is Elon's problem. He's a grown-up child with all the toys and no boundaries. His yes-men encourage his most facile thoughts, and shitposts and errant behavior diminish his genius and ours.
Post-Apocalyptic
The universe's titans have a sense of humor.
Every day, we must ask: Who keeps me real? Who will disagree with me? Who will save me from my psychosis, which has brought down so many successful people? Elon Musk doesn't need anyone to jump on a grenade for him; he needs to stop throwing them because one will explode in his hand.

The woman
3 years ago
I received a $2k bribe to replace another developer in an interview
I can't believe they’d even think it works!
Developers are usually interviewed before being hired, right? Every organization wants candidates who meet their needs. But they also want to avoid fraud.
There are cheaters in every field. Only two come to mind for the hiring process:
Lying on a resume.
Cheating on an online test.
Recently, I observed another one. One of my coworkers invited me to replace another developer during an online interview! I was astonished, but it’s not new.
The specifics
My ex-colleague recently texted me. No one from your former office will ever approach you after a year unless they need something.
Which was the case. My coworker said his wife needed help as a programmer. I was glad someone asked for my help, but I'm still a junior programmer.
Then he informed me his wife was selected for a fantastic job interview. He said he could help her with the online test, but he needed someone to help with the online interview.
Okay, I guess. Preparing for an online interview is beneficial. But then he said she didn't need to be ready. She needed someone to take her place.
I told him it wouldn't work. Every remote online interview I've ever seen required an open camera.
What followed surprised me. She'd ask to turn off the camera, he said.
I asked why.
He told me if an applicant is unwell, the interviewer may consider an off-camera interview. His wife will say she's sick and prefers no camera.
The plan left me speechless. I declined politely. He insisted and promised $2k if she got the job.
I felt insulted and told him if he persisted, I'd inform his office. I was furious. Later, I apologized and told him to stop.
I'm not sure what they did after that
I'm not sure if they found someone or listened to me. They probably didn't. How would she do the job if she even got it?
It's an internship, he said. With great pay, though. What should an intern do?
I suggested she do the interview alone. Even if she failed, she'd gain confidence and valuable experience.
Conclusion
Many interviewees cheat. My profession is vital to me, thus I'd rather improve my abilities and apply honestly. It's part of my identity.
Am I truthful? Most professionals are not. They fabricate their CVs. Often.
When you support interview cheating, you encourage more cheating! When someone cheats, another qualified candidate may not obtain the job.
One day, that could be you or me.
