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Adam Hayes

Adam Hayes

3 years ago

Bernard Lawrence "Bernie" Madoff, the largest Ponzi scheme in history

Madoff who?

Bernie Madoff ran the largest Ponzi scheme in history, defrauding thousands of investors over at least 17 years, and possibly longer. He pioneered electronic trading and chaired Nasdaq in the 1990s. On April 14, 2021, he died while serving a 150-year sentence for money laundering, securities fraud, and other crimes.

Understanding Madoff

Madoff claimed to generate large, steady returns through a trading strategy called split-strike conversion, but he simply deposited client funds into a single bank account and paid out existing clients. He funded redemptions by attracting new investors and their capital, but the market crashed in late 2008. He confessed to his sons, who worked at his firm, on Dec. 10, 2008. Next day, they turned him in. The fund reported $64.8 billion in client assets.

Madoff pleaded guilty to 11 federal felony counts, including securities fraud, wire fraud, mail fraud, perjury, and money laundering. Ponzi scheme became a symbol of Wall Street's greed and dishonesty before the financial crisis. Madoff was sentenced to 150 years in prison and ordered to forfeit $170 billion, but no other Wall Street figures faced legal ramifications.

Bernie Madoff's Brief Biography

Bernie Madoff was born in Queens, New York, on April 29, 1938. He began dating Ruth (née Alpern) when they were teenagers. Madoff told a journalist by phone from prison that his father's sporting goods store went bankrupt during the Korean War: "You watch your father, who you idolize, build a big business and then lose everything." Madoff was determined to achieve "lasting success" like his father "whatever it took," but his career had ups and downs.

Early Madoff investments

At 22, he started Bernard L. Madoff Investment Securities LLC. First, he traded penny stocks with $5,000 he earned installing sprinklers and as a lifeguard. Family and friends soon invested with him. Madoff's bets soured after the "Kennedy Slide" in 1962, and his father-in-law had to bail him out.

Madoff felt he wasn't part of the Wall Street in-crowd. "We weren't NYSE members," he told Fishman. "It's obvious." According to Madoff, he was a scrappy market maker. "I was happy to take the crumbs," he told Fishman, citing a client who wanted to sell eight bonds; a bigger firm would turn it down.

Recognition

Success came when he and his brother Peter built electronic trading capabilities, or "artificial intelligence," that attracted massive order flow and provided market insights. "I had all these major banks coming down, entertaining me," Madoff told Fishman. "It was mind-bending."

By the late 1980s, he and four other Wall Street mainstays processed half of the NYSE's order flow. Controversially, he paid for much of it, and by the late 1980s, Madoff was making in the vicinity of $100 million a year.  He was Nasdaq chairman from 1990 to 1993.

Madoff's Ponzi scheme

It is not certain exactly when Madoff's Ponzi scheme began. He testified in court that it began in 1991, but his account manager, Frank DiPascali, had been at the firm since 1975.

Why Madoff did the scheme is unclear. "I had enough money to support my family's lifestyle. "I don't know why," he told Fishman." Madoff could have won Wall Street's respect as a market maker and electronic trading pioneer.

Madoff told Fishman he wasn't solely responsible for the fraud. "I let myself be talked into something, and that's my fault," he said, without saying who convinced him. "I thought I could escape eventually. I thought it'd be quick, but I couldn't."

Carl Shapiro, Jeffry Picower, Stanley Chais, and Norm Levy have been linked to Bernard L. Madoff Investment Securities LLC for years. Madoff's scheme made these men hundreds of millions of dollars in the 1960s and 1970s.

Madoff told Fishman, "Everyone was greedy, everyone wanted to go on." He says the Big Four and others who pumped client funds to him, outsourcing their asset management, must have suspected his returns or should have. "How can you make 15%-18% when everyone else is making less?" said Madoff.

How Madoff Got Away with It for So Long

Madoff's high returns made clients look the other way. He deposited their money in a Chase Manhattan Bank account, which merged to become JPMorgan Chase & Co. in 2000. The bank may have made $483 million from those deposits, so it didn't investigate.

When clients redeemed their investments, Madoff funded the payouts with new capital he attracted by promising unbelievable returns and earning his victims' trust. Madoff created an image of exclusivity by turning away clients. This model let half of Madoff's investors profit. These investors must pay into a victims' fund for defrauded investors.

Madoff wooed investors with his philanthropy. He defrauded nonprofits, including the Elie Wiesel Foundation for Peace and Hadassah. He approached congregants through his friendship with J. Ezra Merkin, a synagogue officer. Madoff allegedly stole $1 billion to $2 billion from his investors.

Investors believed Madoff for several reasons:

  • His public portfolio seemed to be blue-chip stocks.
  • His returns were high (10-20%) but consistent and not outlandish. In a 1992 interview with Madoff, the Wall Street Journal reported: "[Madoff] insists the returns were nothing special, given that the S&P 500-stock index returned 16.3% annually from 1982 to 1992. 'I'd be surprised if anyone thought matching the S&P over 10 years was remarkable,' he says.
  • "He said he was using a split-strike collar strategy. A collar protects underlying shares by purchasing an out-of-the-money put option.

SEC inquiry

The Securities and Exchange Commission had been investigating Madoff and his securities firm since 1999, which frustrated many after he was prosecuted because they felt the biggest damage could have been prevented if the initial investigations had been rigorous enough.

Harry Markopolos was a whistleblower. In 1999, he figured Madoff must be lying in an afternoon. The SEC ignored his first Madoff complaint in 2000.

Markopolos wrote to the SEC in 2005: "The largest Ponzi scheme is Madoff Securities. This case has no SEC reward, so I'm turning it in because it's the right thing to do."

Many believed the SEC's initial investigations could have prevented Madoff's worst damage.

Markopolos found irregularities using a "Mosaic Method." Madoff's firm claimed to be profitable even when the S&P fell, which made no mathematical sense given what he was investing in. Markopolos said Madoff Securities' "undisclosed commissions" were the biggest red flag (1 percent of the total plus 20 percent of the profits).

Markopolos concluded that "investors don't know Bernie Madoff manages their money." Markopolos learned Madoff was applying for large loans from European banks (seemingly unnecessary if Madoff's returns were high).

The regulator asked Madoff for trading account documentation in 2005, after he nearly went bankrupt due to redemptions. The SEC drafted letters to two of the firms on his six-page list but didn't send them. Diana Henriques, author of "The Wizard of Lies: Bernie Madoff and the Death of Trust," documents the episode.

In 2008, the SEC was criticized for its slow response to Madoff's fraud.

Confession, sentencing of Bernie Madoff

Bernard L. Madoff Investment Securities LLC reported 5.6% year-to-date returns in November 2008; the S&P 500 fell 39%. As the selling continued, Madoff couldn't keep up with redemption requests, and on Dec. 10, he confessed to his sons Mark and Andy, who worked at his firm. "After I told them, they left, went to a lawyer, who told them to turn in their father, and I never saw them again. 2008-12-11: Bernie Madoff arrested.

Madoff insists he acted alone, but several of his colleagues were jailed. Mark Madoff died two years after his father's fraud was exposed. Madoff's investors committed suicide. Andy Madoff died of cancer in 2014.

2009 saw Madoff's 150-year prison sentence and $170 billion forfeiture. Marshals sold his three homes and yacht. Prisoner 61727-054 at Butner Federal Correctional Institution in North Carolina.

Madoff's lawyers requested early release on February 5, 2020, claiming he has a terminal kidney disease that may kill him in 18 months. Ten years have passed since Madoff's sentencing.

Bernie Madoff's Ponzi scheme aftermath

The paper trail of victims' claims shows Madoff's complexity and size. Documents show Madoff's scam began in the 1960s. His final account statements show $47 billion in "profit" from fake trades and shady accounting.

Thousands of investors lost their life savings, and multiple stories detail their harrowing loss.

Irving Picard, a New York lawyer overseeing Madoff's bankruptcy, has helped investors. By December 2018, Picard had recovered $13.3 billion from Ponzi scheme profiteers.

A Madoff Victim Fund (MVF) was created in 2013 to help compensate Madoff's victims, but the DOJ didn't start paying out the $4 billion until late 2017. Richard Breeden, a former SEC chair who oversees the fund, said thousands of claims were from "indirect investors"

Breeden and his team had to reject many claims because they weren't direct victims. Breeden said he based most of his decisions on one simple rule: Did the person invest more than they withdrew? Breeden estimated 11,000 "feeder" investors.

Breeden wrote in a November 2018 update for the Madoff Victim Fund, "We've paid over 27,300 victims 56.65% of their losses, with thousands more to come." In December 2018, 37,011 Madoff victims in the U.S. and around the world received over $2.7 billion. Breeden said the fund expected to make "at least one more significant distribution in 2019"


This post is a summary. Read full article here

More on Economics & Investing

Thomas Huault

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.

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:

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 = 1.6

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:

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.ema

The 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.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

Conclusion

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.

Theresa W. Carey

Theresa W. Carey

3 years ago

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

Trevor Stark

Trevor Stark

3 years ago

Economics is complete nonsense.

Mainstream economics haven't noticed.

Photo by Hans Eiskonen on Unsplash

What come to mind when I say the word "economics"?

Probably GDP, unemployment, and inflation.

If you've ever watched the news or listened to an economist, they'll use data like these to defend a political goal.

The issue is that these statistics are total bunk.

I'm being provocative, but I mean it:

  • The economy is not measured by GDP.

  • How many people are unemployed is not counted in the unemployment rate.

  • Inflation is not measured by the CPI.

All orthodox economists' major economic statistics are either wrong or falsified.

Government institutions create all these stats. The administration wants to reassure citizens the economy is doing well.

GDP does not reflect economic expansion.

GDP measures a country's economic size and growth. It’s calculated by the BEA, a government agency.

The US has the world's largest (self-reported) GDP, growing 2-3% annually.

If GDP rises, the economy is healthy, say economists.

Why is the GDP flawed?

GDP measures a country's yearly spending.

The government may adjust this to make the economy look good.

GDP = C + G + I + NX

C = Consumer Spending

G = Government Spending

I = Investments (Equipment, inventories, housing, etc.)

NX = Exports minus Imports

GDP is a country's annual spending.

The government can print money to boost GDP. The government has a motive to increase and manage GDP.

Because government expenditure is part of GDP, printing money and spending it on anything will raise GDP.

They've done this. Since 1950, US government spending has grown 8% annually, faster than GDP.

In 2022, government spending accounted for 44% of GDP. It's the highest since WWII. In 1790-1910, it was 3% of GDP.

Who cares?

The economy isn't only spending. Focus on citizens' purchasing power or quality of life.

Since GDP just measures spending, the government can print money to boost GDP.

Even if Americans are poorer than last year, economists can say GDP is up and everything is fine.

How many people are unemployed is not counted in the unemployment rate.

The unemployment rate measures a country's labor market. If unemployment is high, people aren't doing well economically.

The BLS estimates the (self-reported) unemployment rate as 3-4%.

Why is the unemployment rate so high?

The US government surveys 100k persons to measure unemployment. They extrapolate this data for the country.

They come into 3 categories:

  • Employed

People with jobs are employed … duh.

  • Unemployed

People who are “jobless, looking for a job, and available for work” are unemployed

  • Not in the labor force

The “labor force” is the employed + the unemployed.

The unemployment rate is the percentage of unemployed workers.

Problem is unemployed definition. You must actively seek work to be considered unemployed.

You're no longer unemployed if you haven't interviewed in 4 weeks.

This shit makes no goddamn sense.

Why does this matter?

You can't interview if there are no positions available. You're no longer unemployed after 4 weeks.

In 1994, the BLS redefined "unemployed" to exclude discouraged workers.

If you haven't interviewed in 4 weeks, you're no longer counted in the unemployment rate.

Unemployment Data Including “Long-term Discouraged Workers” (Source)

If unemployment were measured by total unemployed, it would be 25%.

Because the government wants to keep the unemployment rate low, they modify the definition.

If every US resident was unemployed and had no job interviews, economists would declare 0% unemployment. Excellent!

Inflation is not measured by the CPI.

The BLS measures CPI. This month was the highest since 1981.

CPI measures the cost of a basket of products across time. Food, energy, shelter, and clothes are included.

A 9.1% CPI means the basket of items is 9.1% more expensive.

What is the CPI problem?

Here's a more detailed explanation of CPI's flaws.

In summary, CPI is manipulated to be understated.

Housing costs are understated to manipulate CPI. Housing accounts for 33% of the CPI because it's the biggest expense for most people.

This signifies it's the biggest CPI weight.

Rather than using actual house prices, the Bureau of Labor Statistics essentially makes shit up. You can read more about the process here.

Surprise! It’s bullshit

The BLS stated Shelter's price rose 5.5% this month.

House prices are up 11-21%. (Source 1Source 2Source 3)

Rents are up 14-26%. (Source 1Source 2)

Why is this important?

If CPI included housing prices, it would be 12-15 percent this month, not 9.1 percent.

9% inflation is nuts. Your money's value halves every 7 years at 9% inflation.

Worse is 15% inflation. Your money halves every 4 years at 15% inflation.

If everyone realized they needed to double their wage every 4-5 years to stay wealthy, there would be riots.

Inflation drains our money's value so the government can keep printing it.

The Solution

Most individuals know the existing system doesn't work, but can't explain why.

People work hard yet lag behind. The government lies about the economy's data.

In reality:

  • GDP has been down since 2008

  • 25% of Americans are unemployed

  • Inflation is actually 15%

People might join together to vote out kleptocratic politicians if they knew the reality.

Having reliable economic data is the first step.

People can't understand the situation without sufficient information. Instead of immigrants or billionaires, people would blame liar politicians.

Here’s the vision:

A decentralized, transparent, and global dashboard that tracks economic data like GDP, unemployment, and inflation for every country on Earth.

Government incentives influence economic statistics.

ShadowStats has already started this effort, but the calculations must be transparent, decentralized, and global to be effective.

If interested, email me at trevorstark02@gmail.com.

Here are some links to further your research:

  1. MIT Billion Prices Project

  2. 1729 Decentralized Inflation Dashboard Project

  3. Balaji Srinivasan on “Fiat Information VS. Crypto Information”

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Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

  • x+5
  • x^4
  • x^3+3x^2+3x+1
  • 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

  • A(0)+B(0)=C(0)
  • A(1)+B(1)=C(1)
  • A(2)+B(2)=C(2)
  • A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

  • 12+1=13
  • 10+8=18
  • 15+8=23
  • 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

  • A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
  • B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
  • C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

see part 3

NonConformist

NonConformist

3 years ago

Before 6 AM, read these 6 quotations.

These quotes will change your perspective.

I try to reflect on these quotes daily. Reading it in the morning can affect your day, decisions, and priorities. Let's start.

1. Friedrich Nietzsche once said, "He who has a why to live for can bear almost any how."

What's your life goal?

80% of people don't know why they live or what they want to accomplish in life if you ask them randomly.

Even those with answers may not pursue their why. Without a purpose, life can be dull.

Your why can guide you through difficult times.

Create a life goal. Growing may change your goal. Having a purpose in life prevents feeling lost.

2. Seneca said, "He who fears death will never do anything fit for a man in life."

FAILURE STINKS Yes.

This quote is great if you're afraid to try because of failure. What if I'm not made for it? What will they think if I fail?

This wastes most of our lives. Many people prefer not failing over trying something with a better chance of success, according to studies.

Failure stinks in the short term, but it can transform our lives over time.

3. Two men peered through the bars of their cell windows; one saw mud, the other saw stars. — Dale Carnegie

It’s not what you look at that matters; it’s what you see.

The glass-full-or-empty meme is everywhere. It's hard to be positive when facing adversity.

This is a skill. Positive thinking can change our future.

We should stop complaining about our life and how easy success is for others.

Seductive pessimism. Realize this and start from first principles.

4. “Smart people learn from everything and everyone, average people from their experiences, and stupid people already have all the answers.” — Socrates.

Knowing we're ignorant can be helpful.

Every person and situation teaches you something. You can learn from others' experiences so you don't have to. Analyzing your and others' actions and applying what you learn can be beneficial.

Reading (especially non-fiction or biographies) is a good use of time. Walter Issacson wrote Benjamin Franklin's biography. Ben Franklin's early mistakes and successes helped me in some ways.

Knowing everything leads to disaster. Every incident offers lessons.

5. “We must all suffer one of two things: the pain of discipline or the pain of regret or disappointment.“ — James Rohn

My favorite Jim Rohn quote.

Exercise hurts. Healthy eating can be painful. But they're needed to get in shape. Avoiding pain can ruin our lives.

Always choose progress over hopelessness. Myth: overnight success Everyone who has mastered a craft knows that mastery comes from overcoming laziness.

Turn off your inner critic and start working. Try Can't Hurt Me by David Goggins.

6. “A champion is defined not by their wins, but by how they can recover when they fail.“ — Serena Williams

Have you heard of Traf-o-Data?

Gates and Allen founded Traf-O-Data. After some success, it failed. Traf-o-Data's failure led to Microsoft.

Allen said Traf-O-Data's setback was important for Microsoft's first product a few years later. Traf-O-Data was a business failure, but it helped them understand microprocessors, he wrote in 2017.

“The obstacle in the path becomes the path. Never forget, within every obstacle is an opportunity to improve our condition.” — Ryan Holiday.

Bonus Quotes

More helpful quotes:

“Those who cannot change their minds cannot change anything.” — George Bernard Shaw.

“Do something every day that you don’t want to do; this is the golden rule for acquiring the habit of doing your duty without pain.” — Mark Twain.

“Never give up on a dream just because of the time it will take to accomplish it. The time will pass anyway.” — Earl Nightingale.

“A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.” — George Bernard Shaw.

“We don’t stop playing because we grow old; we grow old because we stop playing.” — George Bernard Shaw.

Conclusion

Words are powerful. Utilize it. Reading these inspirational quotes will help you.

Nik Nicholas

Nik Nicholas

3 years ago

A simple go-to-market formula

Poor distribution, not poor goods, is the main reason for failure” — Peter Thiel.

Here's an easy way to conceptualize "go-to-market" for your distribution plan.

One equation captures the concept:

Distribution = Ecosystem Participants + Incentives

Draw your customers' ecosystem. Set aside your goods and consider your consumer's environment. Who do they deal with daily? 

  1. First, list each participant. You want an exhaustive list, but here are some broad categories.

  • In-person media services

  • Websites

  • Events\Networks

  • Financial education and banking

  • Shops

  • Staff

  • Advertisers

  • Twitter influencers

  1. Draw influence arrows. Who's affected? I'm not just talking about Instagram selfie-posters. Who has access to your consumer and could promote your product if motivated?

The thicker the arrow, the stronger the relationship. Include more "influencers" if needed. Customer ecosystems are complex.

3. Incentivize ecosystem players. “Show me the incentive and I will show you the result.“, says Warren Buffet's business partner Charlie Munger.

Strong distribution strategies encourage others to promote your product to your target market by incentivizing the most prominent players. Incentives can be financial or non-financial.

Financial rewards

Usually, there's money. If you pay Facebook, they'll run your ad. Salespeople close deals for commission. Giving customers bonus credits will encourage referrals.

Most businesses underuse non-financial incentives.

Non-cash incentives

Motivate key influencers without spending money to expand quickly and cheaply. What can you give a client-connector for free?

Here are some ideas:

Are there any other features or services available?

Titles or status? Tinder paid college "ambassadors" for parties to promote its dating service.

Can I get early/free access? Facebook gave a select group of developers "exclusive" early access to their AR platform.

Are you a good host? Pharell performed at YPlan's New York launch party.

Distribution? Apple's iPod earphones are white so others can see them.

Have an interesting story? PR rewards journalists by giving them a compelling story to boost page views.

Prioritize distribution.

More time spent on distribution means more room in your product design and business plan. Once you've identified the key players in your customer's ecosystem, talk to them.

Money isn't your only resource. Creative non-monetary incentives may be more effective and scalable. Give people something useful and easy to deliver.