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
(Edited)

Hackernoon
4 years ago
👏 Awesome post! When is part 3 coming?

Trent Lapinski
4 years ago
Very complex topic, great explanation
More on Web3 & Crypto

Elnaz Sarraf
3 years ago
Why Bitcoin's Crash Could Be Good for Investors

The crypto market crashed in June 2022. Bitcoin and other cryptocurrencies hit their lowest prices in over a year, causing market panic. Some believe this crash will benefit future investors.
Before I discuss how this crash might help investors, let's examine why it happened. Inflation in the U.S. reached a 30-year high in 2022 after Russia invaded Ukraine. In response, the U.S. Federal Reserve raised interest rates by 0.5%, the most in almost 20 years. This hurts cryptocurrencies like Bitcoin. Higher interest rates make people less likely to invest in volatile assets like crypto, so many investors sold quickly.

The crypto market collapsed. Bitcoin, Ethereum, and Binance dropped 40%. Other cryptos crashed so hard they were delisted from almost every exchange. Bitcoin peaked in April 2022 at $41,000, but after the May interest rate hike, it crashed to $28,000. Bitcoin investors were worried. Even in bad times, this crash is unprecedented.
Bitcoin wasn't "doomed." Before the crash, LUNA was one of the top 5 cryptos by market cap. LUNA was trading around $80 at the start of May 2022, but after the rate hike?
Less than 1 cent. LUNA lost 99.99% of its value in days and was removed from every crypto exchange. Bitcoin's "crash" isn't as devastating when compared to LUNA.
Many people said Bitcoin is "due" for a LUNA-like crash and that the only reason it hasn't crashed is because it's bigger. Still false. If so, Bitcoin should be worth zero by now. We didn't. Instead, Bitcoin reached 28,000, then 29k, 30k, and 31k before falling to 18k. That's not the world's greatest recovery, but it shows Bitcoin's safety.
Bitcoin isn't falling constantly. It fell because of the initial shock of interest rates, but not further. Now, Bitcoin's value is more likely to rise than fall. Bitcoin's low price also attracts investors. They know what prices Bitcoin can reach with enough hype, and they want to capitalize on low prices before it's too late.

Bitcoin's crash was bad, but in a way it wasn't. To understand, consider 2021. In March 2021, Bitcoin surpassed $60k for the first time. Elon Musk's announcement in May that he would no longer support Bitcoin caused a massive crash in the crypto market. In May 2017, Bitcoin's price hit $29,000. Elon Musk's statement isn't worth more than the Fed raising rates. Many expected this big announcement to kill Bitcoin.

Not so. Bitcoin crashed from $58k to $31k in 2021. Bitcoin fell from $41k to $28k in 2022. This crash is smaller. Bitcoin's price held up despite tensions and stress, proving investors still believe in it. What happened after the initial crash in the past?
Bitcoin fell until mid-July. This is also something we’re not seeing today. After a week, Bitcoin began to improve daily. Bitcoin's price rose after mid-July. Bitcoin's price fluctuated throughout the rest of 2021, but it topped $67k in November. Despite no major changes, the peak occurred after the crash. Elon Musk seemed uninterested in crypto and wasn't likely to change his mind soon. What triggered this peak? Nothing, really. What really happened is that people got over the initial statement. They forgot.
Internet users have goldfish-like attention spans. People quickly forgot the crash's cause and were back investing in crypto months later. Despite the market's setbacks, more crypto investors emerged by the end of 2017. Who gained from these peaks? Bitcoin investors who bought low. Bitcoin not only recovered but also doubled its ROI. It was like a movie, and it shows us what to expect from Bitcoin in the coming months.
The current Bitcoin crash isn't as bad as the last one. LUNA is causing market panic. LUNA and Bitcoin are different cryptocurrencies. LUNA crashed because Terra wasn’t able to keep its peg with the USD. Bitcoin is unanchored. It's one of the most decentralized investments available. LUNA's distrust affected crypto prices, including Bitcoin, but it won't last forever.
This is why Bitcoin will likely rebound in the coming months. In 2022, people will get over the rise in interest rates and the crash of LUNA, just as they did with Elon Musk's crypto stance in 2021. When the world moves on to the next big controversy, Bitcoin's price will soar.
Bitcoin may recover for another reason. Like controversy, interest rates fluctuate. The Russian invasion caused this inflation. World markets will stabilize, prices will fall, and interest rates will drop.
Next, lower interest rates could boost Bitcoin's price. Eventually, it will happen. The U.S. economy can't sustain such high interest rates. Investors will put every last dollar into Bitcoin if interest rates fall again.
Bitcoin has proven to be a stable investment. This boosts its investment reputation. Even if Ethereum dethrones Bitcoin as crypto king one day (or any other crypto, for that matter). Bitcoin may stay on top of the crypto ladder for a while. We'll have to wait a few months to see if any of this is true.
This post is a summary. Read the full article here.

Miguel Saldana
3 years ago
Crypto Inheritance's Catch-22
Security, privacy, and a strategy!
How to manage digital assets in worst-case scenarios is a perennial crypto concern. Since blockchain and bitcoin technology is very new, this hasn't been a major issue. Many early developers are still around, and many groups created around this technology are young and feel they have a lot of life remaining. This is why inheritance and estate planning in crypto should be handled promptly. As cryptocurrency's intrinsic worth rises, many people in the ecosystem are holding on to assets that might represent generational riches. With that much value, it's crucial to have a plan. Creating a solid plan entails several challenges.
the initial hesitation in coming up with a plan
The technical obstacles to ensuring the assets' security and privacy
the passing of assets from a deceased or incompetent person
Legal experts' lack of comprehension and/or understanding of how to handle and treat cryptocurrency.
This article highlights several challenges, a possible web3-native solution, and how to learn more.
The Challenge of Inheritance:
One of the biggest hurdles to inheritance planning is starting the conversation. As humans, we don't like to think about dying. Early adopters will experience crazy gains as cryptocurrencies become more popular. Creating a plan is crucial if you wish to pass on your riches to loved ones. Without a plan, the technical and legal issues I barely mentioned above would erode value by requiring costly legal fees and/or taxes, and you could lose everything if wallets and assets are not distributed appropriately (associated with the private keys). Raising awareness of the consequences of not having a plan should motivate people to make one.
Controlling Change:
Having an inheritance plan for your digital assets is crucial, but managing the guts and bolts poses a new set of difficulties. Privacy and security provided by maintaining your own wallet provide different issues than traditional finances and assets. Traditional finance is centralized (say a stock brokerage firm). You can assign another person to handle the transfer of your assets. In crypto, asset transfer is reimagined. One may suppose future transaction management is doable, but the user must consent, creating an impossible loop.
I passed away and must send a transaction to the person I intended to deliver it to.
I have to confirm or authorize the transaction, but I'm dead.
In crypto, scheduling a future transaction wouldn't function. To transfer the wallet and its contents, we'd need the private keys and/or seed phrase. Minimizing private key exposure is crucial to protecting your crypto from hackers, social engineering, and phishing. People have lost private keys after utilizing Life Hack-type tactics to secure them. People that break and hide their keys, lose them, or make them unreadable won't help with managing and/or transferring. This will require a derived solution.
Legal Challenges and Implications
Unlike routine cryptocurrency transfers and transactions, local laws may require special considerations. Even in the traditional world, estate/inheritance taxes, how assets will be split, and who executes the will must be considered. Many lawyers aren't crypto-savvy, which complicates the matter. There will be many hoops to jump through to safeguard your crypto and traditional assets and give them to loved ones.
Knowing RUFADAA/UFADAA, depending on your state, is vital for Americans. UFADAA offers executors and trustees access to online accounts (which crypto wallets would fall into). RUFADAA was changed to limit access to the executor to protect assets. RUFADAA outlines how digital assets are administered following death and incapacity in the US.
A Succession Solution
Having a will and talking about who would get what is the first step to having a solution, but using a Dad Mans Switch is a perfect tool for such unforeseen circumstances. As long as the switch's controller has control, nothing happens. Losing control of the switch initiates a state transition.
Subway or railway operations are examples. Modern control systems need the conductor to hold a switch to keep the train going. If they can't, the train stops.
Enter Sarcophagus
Sarcophagus is a decentralized dead man's switch built on Ethereum and Arweave. Sarcophagus allows actors to maintain control of their possessions even while physically unable to do so. Using a programmable dead man's switch and dual encryption, anything can be kept and passed on. This covers assets, secrets, seed phrases, and other use cases to provide authority and control back to the user and release trustworthy services from this work. Sarcophagus is built on a decentralized, transparent open source codebase. Sarcophagus is there if you're unprepared.

Jonathan Vanian
4 years ago
What is Terra? Your guide to the hot cryptocurrency
With cryptocurrencies like Bitcoin, Ether, and Dogecoin gyrating in value over the past few months, many people are looking at so-called stablecoins like Terra to invest in because of their more predictable prices.
Terraform Labs, which oversees the Terra cryptocurrency project, has benefited from its rising popularity. The company said recently that investors like Arrington Capital, Lightspeed Venture Partners, and Pantera Capital have pledged $150 million to help it incubate various crypto projects that are connected to Terra.
Terraform Labs and its partners have built apps that operate on the company’s blockchain technology that helps keep a permanent and shared record of the firm’s crypto-related financial transactions.
Here’s what you need to know about Terra and the company behind it.
What is Terra?
Terra is a blockchain project developed by Terraform Labs that powers the startup’s cryptocurrencies and financial apps. These cryptocurrencies include the Terra U.S. Dollar, or UST, that is pegged to the U.S. dollar through an algorithm.
Terra is a stablecoin that is intended to reduce the volatility endemic to cryptocurrencies like Bitcoin. Some stablecoins, like Tether, are pegged to more conventional currencies, like the U.S. dollar, through cash and cash equivalents as opposed to an algorithm and associated reserve token.
To mint new UST tokens, a percentage of another digital token and reserve asset, Luna, is “burned.” If the demand for UST rises with more people using the currency, more Luna will be automatically burned and diverted to a community pool. That balancing act is supposed to help stabilize the price, to a degree.
“Luna directly benefits from the economic growth of the Terra economy, and it suffers from contractions of the Terra coin,” Terraform Labs CEO Do Kwon said.
Each time someone buys something—like an ice cream—using UST, that transaction generates a fee, similar to a credit card transaction. That fee is then distributed to people who own Luna tokens, similar to a stock dividend.
Who leads Terra?
The South Korean firm Terraform Labs was founded in 2018 by Daniel Shin and Kwon, who is now the company’s CEO. Kwon is a 29-year-old former Microsoft employee; Shin now heads the Chai online payment service, a Terra partner. Kwon said many Koreans have used the Chai service to buy goods like movie tickets using Terra cryptocurrency.
Terraform Labs does not make money from transactions using its crypto and instead relies on outside funding to operate, Kwon said. It has raised $57 million in funding from investors like HashKey Digital Asset Group, Divergence Digital Currency Fund, and Huobi Capital, according to deal-tracking service PitchBook. The amount raised is in addition to the latest $150 million funding commitment announced on July 16.
What are Terra’s plans?
Terraform Labs plans to use Terra’s blockchain and its associated cryptocurrencies—including one pegged to the Korean won—to create a digital financial system independent of major banks and fintech-app makers. So far, its main source of growth has been in Korea, where people have bought goods at stores, like coffee, using the Chai payment app that’s built on Terra’s blockchain. Kwon said the company’s associated Mirror trading app is experiencing growth in China and Thailand.
Meanwhile, Kwon said Terraform Labs would use its latest $150 million in funding to invest in groups that build financial apps on Terra’s blockchain. He likened the scouting and investing in other groups as akin to a “Y Combinator demo day type of situation,” a reference to the popular startup pitch event organized by early-stage investor Y Combinator.
The combination of all these Terra-specific financial apps shows that Terraform Labs is “almost creating a kind of bank,” said Ryan Watkins, a senior research analyst at cryptocurrency consultancy Messari.
In addition to cryptocurrencies, Terraform Labs has a number of other projects including the Anchor app, a high-yield savings account for holders of the group’s digital coins. Meanwhile, people can use the firm’s associated Mirror app to create synthetic financial assets that mimic more conventional ones, like “tokenized” representations of corporate stocks. These synthetic assets are supposed to be helpful to people like “a small retail trader in Thailand” who can more easily buy shares and “get some exposure to the upside” of stocks that they otherwise wouldn’t have been able to obtain, Kwon said. But some critics have said the U.S. Securities and Exchange Commission may eventually crack down on synthetic stocks, which are currently unregulated.
What do critics say?
Terra still has a long way to go to catch up to bigger cryptocurrency projects like Ethereum.
Most financial transactions involving Terra-related cryptocurrencies have originated in Korea, where its founders are based. Although Terra is becoming more popular in Korea thanks to rising interest in its partner Chai, it’s too early to say whether Terra-related currencies will gain traction in other countries.
Terra’s blockchain runs on a “limited number of nodes,” said Messari’s Watkins, referring to the computers that help keep the system running. That helps reduce latency that may otherwise slow processing of financial transactions, he said.
But the tradeoff is that Terra is less “decentralized” than other blockchain platforms like Ethereum, which is powered by thousands of interconnected computing nodes worldwide. That could make Terra less appealing to some blockchain purists.
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Dung Claire Tran
3 years ago
Is the future of brand marketing with virtual influencers?
Digital influences that mimic humans are rising.
Lil Miquela has 3M Instagram followers, 3.6M TikTok followers, and 30K Twitter followers. She's been on the covers of Prada, Dior, and Calvin Klein magazines. Miquela released Not Mine in 2017 and launched Hard Feelings at Lollapazoolas this year. This isn't surprising, given the rise of influencer marketing.
This may be unexpected. Miquela's fake. Brud, a Los Angeles startup, produced her in 2016.
Lil Miquela is one of many rising virtual influencers in the new era of social media marketing. She acts like a real person and performs the same tasks as sports stars and models.
The emergence of online influencers
Before 2018, computer-generated characters were rare. Since the virtual human industry boomed, they've appeared in marketing efforts worldwide.
In 2020, the WHO partnered up with Atlanta-based virtual influencer Knox Frost (@knoxfrost) to gather contributions for the COVID-19 Solidarity Response Fund.
Lu do Magalu (@magazineluiza) has been the virtual spokeswoman for Magalu since 2009, using social media to promote reviews, product recommendations, unboxing videos, and brand updates. Magalu's 10-year profit was $552M.
In 2020, PUMA partnered with Southeast Asia's first virtual model, Maya (@mayaaa.gram). She joined Singaporean actor Tosh Zhang in the PUMA campaign. Local virtual influencer Ava Lee-Graham (@avagram.ai) partnered with retail firm BHG to promote their in-house labels.
In Japan, Imma (@imma.gram) is the face of Nike, PUMA, Dior, Salvatore Ferragamo SpA, and Valentino. Imma's bubblegum pink bob and ultra-fine fashion landed her on the cover of Grazia magazine.
Lotte Home Shopping created Lucy (@here.me.lucy) in September 2020. She made her TV debut as a Christmas show host in 2021. Since then, she has 100K Instagram followers and 13K TikTok followers.
Liu Yiexi gained 3 million fans in five days on Douyin, China's TikTok, in 2021. Her two-minute video went viral overnight. She's posted 6 videos and has 830 million Douyin followers.
China's virtual human industry was worth $487 million in 2020, up 70% year over year, and is expected to reach $875.9 million in 2021.
Investors worldwide are interested. Immas creator Aww Inc. raised $1 million from Coral Capital in September 2020, according to Bloomberg. Superplastic Inc., the Vermont-based startup behind influencers Janky and Guggimon, raised $16 million by 2020. Craft Ventures, SV Angels, and Scooter Braun invested. Crunchbase shows the company has raised $47 million.
The industries they represent, including Augmented and Virtual reality, were worth $14.84 billion in 2020 and are projected to reach $454.73 billion by 2030, a CAGR of 40.7%, according to PR Newswire.
Advantages for brands
Forbes suggests brands embrace computer-generated influencers. Examples:
Unlimited creative opportunities: Because brands can personalize everything—from a person's look and activities to the style of their content—virtual influencers may be suited to a brand's needs and personalities.
100% brand control: Brand managers now have more influence over virtual influencers, so they no longer have to give up and rely on content creators to include brands into their storytelling and style. Virtual influencers can constantly produce social media content to promote a brand's identity and ideals because they are completely scandal-free.
Long-term cost savings: Because virtual influencers are made of pixels, they may be reused endlessly and never lose their beauty. Additionally, they can move anywhere around the world and even into space to fit a brand notion. They are also always available. Additionally, the expense of creating their content will not rise in step with their expanding fan base.
Introduction to the metaverse: Statista reports that 75% of American consumers between the ages of 18 and 25 follow at least one virtual influencer. As a result, marketers that support virtual celebrities may now interact with younger audiences that are more tech-savvy and accustomed to the digital world. Virtual influencers can be included into any digital space, including the metaverse, as they are entirely computer-generated 3D personas. Virtual influencers can provide brands with a smooth transition into this new digital universe to increase brand trust and develop emotional ties, in addition to the young generations' rapid adoption of the metaverse.
Better engagement than in-person influencers: A Hype Auditor study found that online influencers have roughly three times the engagement of their conventional counterparts. Virtual influencers should be used to boost brand engagement even though the data might not accurately reflect the entire sector.
Concerns about influencers created by computers
Virtual influencers could encourage excessive beauty standards in South Korea, which has a $10.7 billion plastic surgery industry.
A classic Korean beauty has a small face, huge eyes, and pale, immaculate skin. Virtual influencers like Lucy have these traits. According to Lee Eun-hee, a professor at Inha University's Department of Consumer Science, this could make national beauty standards more unrealistic, increasing demand for plastic surgery or cosmetic items.
Other parts of the world raise issues regarding selling items to consumers who don't recognize the models aren't human and the potential of cultural appropriation when generating influencers of other ethnicities, called digital blackface by some.
Meta, Facebook and Instagram's parent corporation, acknowledges this risk.
“Like any disruptive technology, synthetic media has the potential for both good and harm. Issues of representation, cultural appropriation and expressive liberty are already a growing concern,” the company stated in a blog post. “To help brands navigate the ethical quandaries of this emerging medium and avoid potential hazards, (Meta) is working with partners to develop an ethical framework to guide the use of (virtual influencers).”
Despite theoretical controversies, the industry will likely survive. Companies think virtual influencers are the next frontier in the digital world, which includes the metaverse, virtual reality, and digital currency.
In conclusion
Virtual influencers may garner millions of followers online and help marketers reach youthful audiences. According to a YouGov survey, the real impact of computer-generated influencers is yet unknown because people prefer genuine connections. Virtual characters can supplement brand marketing methods. When brands are metaverse-ready, the author predicts virtual influencer endorsement will continue to expand.

Ben Carlson
3 years 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.

Liam Vaughan
3 years ago
Investors can bet big on almost anything on a new prediction market.
Kalshi allows five-figure bets on the Grammys, the next Covid wave, and future SEC commissioners. Worst-case scenario
On Election Day 2020, two young entrepreneurs received a call from the CFTC chairman. Luana Lopes Lara and Tarek Mansour spent 18 months trying to start a new type of financial exchange. Instead of betting on stock prices or commodity futures, people could trade instruments tied to real-world events, such as legislation, the weather, or the Oscar winner.
Heath Tarbert, a Trump appointee, shouted "Congratulations." "You're competing with 1840s-era markets. I'm sure you'll become a powerhouse too."
Companies had tried to introduce similar event markets in the US for years, but Tarbert's agency, the CFTC, said no, arguing they were gambling and prone to cheating. Now the agency has reversed course, approving two 24-year-olds who will have first-mover advantage in what could become a huge new asset class. Kalshi Inc. raised $30 million from venture capitalists within weeks of Tarbert's call, his representative says. Mansour, 26, believes this will be bigger than crypto.
Anyone who's read The Wisdom of Crowds knows prediction markets' potential. Well-designed markets can help draw out knowledge from disparate groups, and research shows that when money is at stake, people make better predictions. Lopes Lara calls it a "bullshit tax." That's why Google, Microsoft, and even the US Department of Defense use prediction markets internally to guide decisions, and why university-linked political betting sites like PredictIt sometimes outperform polls.
Regulators feared Wall Street-scale trading would encourage investors to manipulate reality. If the stakes are high enough, traders could pressure congressional staffers to stall a bill or bet on whether Kanye West's new album will drop this week. When Lopes Lara and Mansour pitched the CFTC, senior regulators raised these issues. Politically appointed commissioners overruled their concerns, and one later joined Kalshi's board.
Will Kanye’s new album come out next week? Yes or no?
Kalshi's victory was due more to lobbying and legal wrangling than to Silicon Valley-style innovation. Lopes Lara and Mansour didn't invent anything; they changed a well-established concept's governance. The result could usher in a new era of market-based enlightenment or push Wall Street's destructive tendencies into the real world.
If Kalshi's founders lacked experience to bolster their CFTC application, they had comical youth success. Lopes Lara studied ballet at the Brazilian Bolshoi before coming to the US. Mansour won France's math Olympiad. They bonded over their work ethic in an MIT computer science class.
Lopes Lara had the idea for Kalshi while interning at a New York hedge fund. When the traders around her weren't working, she noticed they were betting on the news: Would Apple hit a trillion dollars? Kylie Jenner? "It was anything," she says.
Are mortgage rates going up? Yes or no?
Mansour saw the business potential when Lopes Lara suggested it. He interned at Goldman Sachs Group Inc., helping investors prepare for the UK leaving the EU. Goldman sold clients complex stock-and-derivative combinations. As he discussed it with Lopes Lara, they agreed that investors should hedge their risk by betting on Brexit itself rather than an imperfect proxy.
Lopes Lara and Mansour hypothesized how a marketplace might work. They settled on a "event contract," a binary-outcome instrument like "Will inflation hit 5% by the end of the month?" The contract would settle at $1 (if the event happened) or zero (if it didn't), but its price would fluctuate based on market sentiment. After a good debate, a politician's election odds may rise from 50 to 55. Kalshi would charge a commission on every trade and sell data to traders, political campaigns, businesses, and others.
In October 2018, five months after graduation, the pair flew to California to compete in a hackathon for wannabe tech founders organized by the Silicon Valley incubator Y Combinator. They built a website in a day and a night and presented it to entrepreneurs the next day. Their prototype barely worked, but they won a three-month mentorship program and $150,000. Michael Seibel, managing director of Y Combinator, said of their idea, "I had to take a chance!"
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Seibel's skepticism was rooted in America's historical wariness of gambling. Roulette, poker, and other online casino games are largely illegal, and sports betting was only legal in a few states until May 2018. Kalshi as a risk-hedging platform rather than a bookmaker seemed like a good idea, but convincing the CFTC wouldn't be easy. In 2012, the CFTC said trading on politics had no "economic purpose" and was "contrary to the public interest."
Lopes Lara and Mansour cold-called 60 Googled lawyers during their time at Y Combinator. Everyone advised quitting. Mansour recalls the pain. Jeff Bandman, a former CFTC official, helped them navigate the agency and its characters.
When they weren’t busy trying to recruit lawyers, Lopes Lara and Mansour were meeting early-stage investors. Alfred Lin of Sequoia Capital Operations LLC backed Airbnb, DoorDash, and Uber Technologies. Lin told the founders their idea could capitalize on retail trading and challenge how the financial world manages risk. "Come back with regulatory approval," he said.
In the US, even small bets on most events were once illegal. Under the Commodity Exchange Act, the CFTC can stop exchanges from listing contracts relating to "terrorism, assassination, war" and "gaming" if they are "contrary to the public interest," which was often the case.
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In 1988, as academic interest in the field grew, the agency allowed the University of Iowa to set up a prediction market for research purposes, as long as it didn't make a profit or advertise and limited bets to $500. PredictIt, the biggest and best-known political betting platform in the US, also got an exemption thanks to an association with Victoria University of Wellington in New Zealand. Today, it's a sprawling marketplace with its own subculture and lingo. PredictIt users call it "Rules Cuck Panther" when they lose on a technicality. Major news outlets cite PredictIt's odds on Discord and the Star Spangled Gamblers podcast.
CFTC limits PredictIt bets to $850. To keep traders happy, PredictIt will often run multiple variations of the same question, listing separate contracts for two dozen Democratic primary candidates, for example. A trader could have more than $10,000 riding on a single outcome. Some of the site's traders are current or former campaign staffers who can answer questions like "How many tweets will Donald Trump post from Nov. 20 to 27?" and "When will Anthony Scaramucci's role as White House communications director end?"
According to PredictIt co-founder John Phillips, politicians help explain the site's accuracy. "Prediction markets work well and are accurate because they attract people with superior information," he said in a 2016 podcast. “In the financial stock market, it’s called inside information.”
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Trading on nonpublic information is illegal outside of academia, which presented a dilemma for Lopes Lara and Mansour. Kalshi's forecasts needed to be accurate. Kalshi must eliminate insider trading as a regulated entity. Lopes Lara and Mansour wanted to build a high-stakes PredictIt without the anarchy or blurred legal lines—a "New York Stock Exchange for Events." First, they had to convince regulators event trading was safe.
When Lopes Lara and Mansour approached the CFTC in the spring of 2019, some officials in the Division of Market Oversight were skeptical, according to interviews with people involved in the process. For all Kalshi's talk of revolutionizing finance, this was just a turbocharged version of something that had been rejected before.
The DMO couldn't see the big picture. The staff review was supposed to ensure Kalshi could complete a checklist, "23 Core Principles of a Designated Contract Market," which included keeping good records and having enough money. The five commissioners decide. With Trump as president, three of them were ideologically pro-market.
Lopes Lara, Mansour, and their lawyer Bandman, an ex-CFTC official, answered the DMO's questions while lobbying the commissioners on Zoom about the potential of event markets to mitigate risks and make better decisions. Before each meeting, they would write a script and memorize it word for word.
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Several prediction markets that hadn't sought regulatory approval bolstered Kalshi's case. Polymarket let customers bet hundreds of thousands of dollars anonymously using cryptocurrencies, making it hard to track. Augur, which facilitates private wagers between parties using blockchain, couldn't regulate bets and hadn't stopped users from betting on assassinations. Kalshi, by comparison, argued it was doing everything right. (The CFTC fined Polymarket $1.4 million for operating an unlicensed exchange in January 2022. Polymarket says it's now compliant and excited to pioneer smart contract-based financial solutions with regulators.
Kalshi was approved unanimously despite some DMO members' concerns about event contracts' riskiness. "Once they check all the boxes, they're in," says a CFTC insider.
Three months after CFTC approval, Kalshi announced funding from Sequoia, Charles Schwab, and Henry Kravis. Sequoia's Lin, who joined the board, said Tarek, Luana, and team created a new way to invest and engage with the world.
The CFTC hadn't asked what markets the exchange planned to run since. After approval, Lopes Lara and Mansour had the momentum. Kalshi's March list of 30 proposed contracts caused chaos at the DMO. The division handles exchanges that create two or three new markets a year. Kalshi’s business model called for new ones practically every day.
Uncontroversial proposals included weather and GDP questions. Others, on the initial list and later, were concerning. DMO officials feared Covid-19 contracts amounted to gambling on human suffering, which is why war and terrorism markets are banned. (Similar logic doomed ex-admiral John Poindexter's Policy Analysis Market, a Bush-era plan to uncover intelligence by having security analysts bet on Middle East events.) Regulators didn't see how predicting the Grammy winners was different from betting on the Patriots to win the Super Bowl. Who, other than John Legend, would need to hedge the best R&B album winner?
Event contracts raised new questions for the DMO's product review team. Regulators could block gaming contracts that weren't in the public interest under the Commodity Exchange Act, but no one had defined gaming. It was unclear whether the CFTC had a right or an obligation to consider whether a contract was in the public interest. How was it to determine public interest? Another person familiar with the CFTC review says, "It was a mess." The agency didn't comment.
CFTC staff feared some event contracts could be cheated. Kalshi wanted to run a bee-endangerment market. The DMO pushed back, saying it saw two problems symptomatic of the asset class: traders could press government officials for information, and officials could delay adding the insects to the list to cash in.
The idea that traders might manipulate prediction markets wasn't paranoid. In 2013, academics David Rothschild and Rajiv Sethi found that an unidentified party lost $7 million buying Mitt Romney contracts on Intrade, a now-defunct, unlicensed Irish platform, in the runup to the 2012 election. The authors speculated that the trader, whom they dubbed the “Romney Whale,” may have been looking to boost morale and keep donations coming in.
Kalshi said manipulation and insider trading are risks for any market. It built a surveillance system and said it would hire a team to monitor it. "People trade on events all the time—they just use options and other instruments. This brings everything into the open, Mansour says. Kalshi didn't include election contracts, a red line for CFTC Democrats.
Lopes Lara and Mansour were ready to launch kalshi.com that summer, but the DMO blocked them. Product reviewers were frustrated by spending half their time on an exchange that represented a tiny portion of the derivatives market. Lopes Lara and Mansour pressed politically appointed commissioners during the impasse.
Tarbert, the chairman, had moved on, but Kalshi found a new supporter in Republican Brian Quintenz, a crypto-loving former hedge fund manager. He was unmoved by the DMO's concerns, arguing that speculation on Kalshi's proposed events was desirable and the agency had no legal standing to prevent it. He supported a failed bid to allow NFL futures earlier this year. Others on the commission were cautious but supportive. Given the law's ambiguity, they worried they'd be on shaky ground if Kalshi sued if they blocked a contract. Without a permanent chairman, the agency lacked leadership.
To block a contract, DMO staff needed a majority of commissioners' support, which they didn't have in all but a few cases. "We didn't have the votes," a reviewer says, paraphrasing Hamilton. By the second half of 2021, new contract requests were arriving almost daily at the DMO, and the demoralized and overrun division eventually accepted defeat and stopped fighting back. By the end of the year, three senior DMO officials had left the agency, making it easier for Kalshi to list its contracts unimpeded.
Today, Kalshi is growing. 32 employees work in a SoHo office with big windows and exposed brick. Quintenz, who left the CFTC 10 months after Kalshi was approved, is on its board. He joined because he was interested in the market's hedging and risk management opportunities.
Mid-May, the company's website had 75 markets, such as "Will Q4 GDP be negative?" Will NASA land on the moon by 2025? The exchange recently reached 2 million weekly contracts, a jump from where it started but still a small number compared to other futures exchanges. Early adopters are PredictIt and Polymarket fans. Bets on the site are currently capped at $25,000, but Kalshi hopes to increase that to $100,000 and beyond.
With the regulatory drawbridge down, Lopes Lara and Mansour must move quickly. Chicago's CME Group Inc. plans to offer index-linked event contracts. Kalshi will release a smartphone app to attract customers. After that, it hopes to partner with a big brokerage. Sequoia is a major investor in Robinhood Markets Inc. Robinhood users could have access to Kalshi so that after buying GameStop Corp. shares, they'd be prompted to bet on the Oscars or the next Fed commissioner.
Some, like Illinois Democrat Sean Casten, accuse Robinhood and its competitors of gamifying trading to encourage addiction, but Kalshi doesn't seem worried. Mansour says Kalshi's customers can't bet more than they've deposited, making debt difficult. Eventually, he may introduce leveraged bets.
Tension over event contracts recalls another CFTC episode. Brooksley Born proposed regulating the financial derivatives market in 1994. Alan Greenspan and others in the government opposed her, saying it would stifle innovation and push capital overseas. Unrestrained, derivatives grew into a trillion-dollar industry until 2008, when they sparked the financial crisis.
Today, with a midterm election looming, it seems reasonable to ask whether Kalshi plans to get involved. Elections have historically been the biggest draw in prediction markets, with 125 million shares traded on PredictIt for 2020. “We can’t discuss specifics,” Mansour says. “All I can say is, you know, we’re always working on expanding the universe of things that people can trade on.”
Any election contracts would need CFTC approval, which may be difficult with three Democratic commissioners. A Republican president would change the equation.
