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

Modern Eremite
3 years ago
The complete, easy-to-understand guide to bitcoin
Introduction
Markets rely on knowledge.
The internet provided practically endless knowledge and wisdom. Humanity has never seen such leverage. Technology's progress drives us to adapt to a changing world, changing our routines and behaviors.
In a digital age, people may struggle to live in the analogue world of their upbringing. Can those who can't adapt change their lives? I won't answer. We should teach those who are willing to learn, nevertheless. Unravel the modern world's riddles and give them wisdom.
Adapt or die . Accept the future or remain behind.
This essay will help you comprehend Bitcoin better than most market participants and the general public. Let's dig into Bitcoin.
Join me.
Ascension
Bitcoin.org was registered in August 2008. Bitcoin whitepaper was published on 31 October 2008. The document intrigued and motivated people around the world, including technical engineers and sovereignty seekers. Since then, Bitcoin's whitepaper has been read and researched to comprehend its essential concept.
I recommend reading the whitepaper yourself. You'll be able to say you read the Bitcoin whitepaper instead of simply Googling "what is Bitcoin" and reading the fundamental definition without knowing the revolution's scope. The article links to Bitcoin's whitepaper. To avoid being overwhelmed by the whitepaper, read the following article first.
Bitcoin isn't the first peer-to-peer digital currency. Hashcash or Bit Gold were once popular cryptocurrencies. These two Bitcoin precursors failed to gain traction and produce the network effect needed for general adoption. After many struggles, Bitcoin emerged as the most successful cryptocurrency, leading the way for others.
Satoshi Nakamoto, an active bitcointalk.org user, created Bitcoin. Satoshi's identity remains unknown. Satoshi's last bitcointalk.org login was 12 December 2010. Since then, he's officially disappeared. Thus, conspiracies and riddles surround Bitcoin's creators. I've heard many various theories, some insane and others well-thought-out.
It's not about who created it; it's about knowing its potential. Since its start, Satoshi's legacy has changed the world and will continue to.
Block-by-block blockchain
Bitcoin is a distributed ledger. What's the meaning?
Everyone can view all blockchain transactions, but no one can undo or delete them.
Imagine you and your friends routinely eat out, but only one pays. You're careful with money and what others owe you. How can everyone access the info without it being changed?
You'll keep a notebook of your evening's transactions. Everyone will take a page home. If one of you changed the page's data, the group would notice and reject it. The majority will establish consensus and offer official facts.
Miners add a new Bitcoin block to the main blockchain every 10 minutes. The appended block contains miner-verified transactions. Now that the next block has been added, the network will receive the next set of user transactions.
Bitcoin Proof of Work—prove you earned it
Any firm needs hardworking personnel to expand and serve clients. Bitcoin isn't that different.
Bitcoin's Proof of Work consensus system needs individuals to validate and create new blocks and check for malicious actors. I'll discuss Bitcoin's blockchain consensus method.
Proof of Work helps Bitcoin reach network consensus. The network is checked and safeguarded by CPU, GPU, or ASIC Bitcoin-mining machines (Application-Specific Integrated Circuit).
Every 10 minutes, miners are rewarded in Bitcoin for securing and verifying the network. It's unlikely you'll finish the block. Miners build pools to increase their chances of winning by combining their processing power.
In the early days of Bitcoin, individual mining systems were more popular due to high maintenance costs and larger earnings prospects. Over time, people created larger and larger Bitcoin mining facilities that required a lot of space and sophisticated cooling systems to keep machines from overheating.
Proof of Work is a vital part of the Bitcoin network, as network security requires the processing power of devices purchased with fiat currency. Miners must invest in mining facilities, which creates a new business branch, mining facilities ownership. Bitcoin mining is a topic for a future article.
More mining, less reward
Bitcoin is usually scarce.
Why is it rare? It all comes down to 21,000,000 Bitcoins.
Were all Bitcoins mined? Nope. Bitcoin's supply grows until it hits 21 million coins. Initially, 50BTC each block was mined, and each block took 10 minutes. Around 2140, the last Bitcoin will be mined.
But 50BTC every 10 minutes does not give me the year 2140. Indeed careful reader. So important is Bitcoin's halving process.
What is halving?
The block reward is halved every 210,000 blocks, which takes around 4 years. The initial payout was 50BTC per block and has been decreased to 25BTC after 210,000 blocks. First halving occurred on November 28, 2012, when 10,500,000 BTC (50%) had been mined. As of April 2022, the block reward is 6.25BTC and will be lowered to 3.125BTC by 19 March 2024.
The halving method is tied to Bitcoin's hashrate. Here's what "hashrate" means.
What if we increased the number of miners and hashrate they provide to produce a block every 10 minutes? Wouldn't we manufacture blocks faster?
Every 10 minutes, blocks are generated with little asymmetry. Due to the built-in adaptive difficulty algorithm, the overall hashrate does not affect block production time. With increased hashrate, it's harder to construct a block. We can estimate when the next halving will occur because 10 minutes per block is fixed.
Building with nodes and blocks
For someone new to crypto, the unusual terms and words may be overwhelming. You'll also find everyday words that are easy to guess or have a vague idea of what they mean, how they work, and what they do. Consider blockchain technology.
Nodes and blocks: Think about that for a moment. What is your first idea?
The blockchain is a chain of validated blocks added to the main chain. What's a "block"? What's inside?
The block is another page in the blockchain book that has been filled with transaction information and accepted by the majority.
We won't go into detail about what each block includes and how it's built, as long as you understand its purpose.
What about nodes?
Nodes, along with miners, verify the blockchain's state independently. But why?
To create a full blockchain node, you must download the whole Bitcoin blockchain and check every transaction against Bitcoin's consensus criteria.
What's Bitcoin's size?
In April 2022, the Bitcoin blockchain was 389.72GB.
Bitcoin's blockchain has miners and node runners.
Let's revisit the US gold rush. Miners mine gold with their own power (physical and monetary resources) and are rewarded with gold (Bitcoin). All become richer with more gold, and so does the country.
Nodes are like sheriffs, ensuring everything is done according to consensus rules and that there are no rogue miners or network users.
Lost and held bitcoin
Does the Bitcoin exchange price match each coin's price? How many coins remain after 21,000,000? 21 million or less?
Common reason suggests a 21 million-coin supply.
What if I lost 1BTC from a cold wallet?
What if I saved 1000BTC on paper in 2010 and it was damaged?
What if I mined Bitcoin in 2010 and lost the keys?
Satoshi Nakamoto's coins? Since then, those coins haven't moved.
How many BTC are truly in circulation?
Many people are trying to answer this question, and you may discover a variety of studies and individual research on the topic. Be cautious of the findings because they can't be evaluated and the statistics are hazy guesses.
On the other hand, we have long-term investors who won't sell their Bitcoin or will sell little amounts to cover mining or living needs.
The price of Bitcoin is determined by supply and demand on exchanges using liquid BTC. How many BTC are left after subtracting lost and non-custodial BTC?
We have significantly less Bitcoin in circulation than you think, thus the price may not reflect demand if we knew the exact quantity of coins available.
True HODLers and diamond-hand investors won't sell you their coins, no matter the market.
What's UTXO?
Unspent (U) Transaction (TX) Output (O)
Imagine taking a $100 bill to a store. After choosing a drink and munchies, you walk to the checkout to pay. The cashier takes your $100 bill and gives you $25.50 in change. It's in your wallet.
Is it simply 100$? No way.
The $25.50 in your wallet is unrelated to the $100 bill you used. Your wallet's $25.50 is just bills and coins. Your wallet may contain these coins and bills:
2x 10$ 1x 10$
1x 5$ or 3x 5$
1x 0.50$ 2x 0.25$
Any combination of coins and bills can equal $25.50. You don't care, and I'd wager you've never ever considered it.
That is UTXO. Now, I'll detail the Bitcoin blockchain and how UTXO works, as it's crucial to know what coins you have in your (hopefully) cold wallet.
You purchased 1BTC. Is it all? No. UTXOs equal 1BTC. Then send BTC to a cold wallet. Say you pay 0.001BTC and send 0.999BTC to your cold wallet. Is it the 1BTC you got before? Well, yes and no. The UTXOs are the same or comparable as before, but the blockchain address has changed. It's like if you handed someone a wallet, they removed the coins needed for a network charge, then returned the rest of the coins and notes.
UTXO is a simple concept, but it's crucial to grasp how it works to comprehend dangers like dust attacks and how coins may be tracked.
Lightning Network: fast cash
You've probably heard of "Layer 2 blockchain" projects.
What does it mean?
Layer 2 on a blockchain is an additional layer that increases the speed and quantity of transactions per minute and reduces transaction fees.
Imagine going to an obsolete bank to transfer money to another account and having to pay a charge and wait. You can transfer funds via your bank account or a mobile app without paying a fee, or the fee is low, and the cash appear nearly quickly. Layer 1 and 2 payment systems are different.
Layer 1 is not obsolete; it merely has more essential things to focus on, including providing the blockchain with new, validated blocks, whereas Layer 2 solutions strive to offer Layer 1 with previously processed and verified transactions. The primary blockchain, Bitcoin, will only receive the wallets' final state. All channel transactions until shutting and balancing are irrelevant to the main chain.
Layer 2 and the Lightning Network's goal are now clear. Most Layer 2 solutions on multiple blockchains are created as blockchains, however Lightning Network is not. Remember the following remark, as it best describes Lightning.
Lightning Network connects public and private Bitcoin wallets.
Opening a private channel with another wallet notifies just two parties. The creation and opening of a public channel tells the network that anyone can use it.
Why create a public Lightning Network channel?
Every transaction through your channel generates fees.
Money, if you don't know.
See who benefits when in doubt.
Anonymity, huh?
Bitcoin anonymity? Bitcoin's anonymity was utilized to launder money.
Well… You've heard similar stories. When you ask why or how it permits people to remain anonymous, the conversation ends as if it were just a story someone heard.
Bitcoin isn't private. Pseudonymous.
What if someone tracks your transactions and discovers your wallet address? Where is your anonymity then?
Bitcoin is like bulletproof glass storage; you can't take or change the money. If you dig and analyze the data, you can see what's inside.
Every online action leaves a trace, and traces may be tracked. People often forget this guideline.
A tool like that can help you observe what the major players, or whales, are doing with their coins when the market is uncertain. Many people spend time analyzing on-chain data. Worth it?
Ask yourself a question. What are the big players' options? Do you think they're letting you see their wallets for a small on-chain data fee?
Instead of short-term behaviors, focus on long-term trends.
More wallet transactions leave traces. Having nothing to conceal isn't a defect. Can it lead to regulating Bitcoin so every transaction is tracked like in banks today?
But wait. How can criminals pay out Bitcoin? They're doing it, aren't they?
Mixers can anonymize your coins, letting you to utilize them freely. This is not a guide on how to make your coins anonymous; it could do more harm than good if you don't know what you're doing.
Remember, being anonymous attracts greater attention.
Bitcoin isn't the only cryptocurrency we can use to buy things. Using cryptocurrency appropriately can provide usability and anonymity. Monero (XMR), Zcash (ZEC), and Litecoin (LTC) following the Mimblewimble upgrade are examples.
Summary
Congratulations! You've reached the conclusion of the article and learned about Bitcoin and cryptocurrency. You've entered the future.
You know what Bitcoin is, how its blockchain works, and why it's not anonymous. I bet you can explain Lightning Network and UTXO to your buddies.
Markets rely on knowledge. Prepare yourself for success before taking the first step. Let your expertise be your edge.
This article is a summary of this one.

William Brucee
3 years ago
This person is probably Satoshi Nakamoto.
Who founded bitcoin is the biggest mystery in technology today, not how it works.
On October 31, 2008, Satoshi Nakamoto posted a whitepaper to a cryptography email list. Still confused by the mastermind who changed monetary history.
Journalists and bloggers have tried in vain to uncover bitcoin's creator. Some candidates self-nominated. We're still looking for the mystery's perpetrator because none of them have provided proof.
One person. I'm confident he invented bitcoin. Let's assess Satoshi Nakamoto before I reveal my pick. Or what he wants us to know.
Satoshi's P2P Foundation biography says he was born in 1975. He doesn't sound or look Japanese. First, he wrote the whitepaper and subsequent articles in flawless English. His sleeping habits are unusual for a Japanese person.
Stefan Thomas, a Bitcoin Forum member, displayed Satoshi's posting timestamps. Satoshi Nakamoto didn't publish between 2 and 8 p.m., Japanese time. Satoshi's identity may not be real.
Why would he disguise himself?
There is a legitimate explanation for this
Phil Zimmermann created PGP to give dissidents an open channel of communication, like Pretty Good Privacy. US government seized this technology after realizing its potential. Police investigate PGP and Zimmermann.
This technology let only two people speak privately. Bitcoin technology makes it possible to send money for free without a bank or other intermediary, removing it from government control.
How much do we know about the person who invented bitcoin?
Here's what we know about Satoshi Nakamoto now that I've covered my doubts about his personality.
Satoshi Nakamoto first appeared with a whitepaper on metzdowd.com. On Halloween 2008, he presented a nine-page paper on a new peer-to-peer electronic monetary system.
Using the nickname satoshi, he created the bitcointalk forum. He kept developing bitcoin and created bitcoin.org. Satoshi mined the genesis block on January 3, 2009.
Satoshi Nakamoto worked with programmers in 2010 to change bitcoin's protocol. He engaged with the bitcoin community. Then he gave Gavin Andresen the keys and codes and transferred community domains. By 2010, he'd abandoned the project.
The bitcoin creator posted his goodbye on April 23, 2011. Mike Hearn asked Satoshi if he planned to rejoin the group.
“I’ve moved on to other things. It’s in good hands with Gavin and everyone.”
Nakamoto Satoshi
The man who broke the banking system vanished. Why?
Satoshi's wallets held 1,000,000 BTC. In December 2017, when the price peaked, he had over US$19 billion. Nakamoto had the 44th-highest net worth then. He's never cashed a bitcoin.
This data suggests something happened to bitcoin's creator. I think Hal Finney is Satoshi Nakamoto .
Hal Finney had ALS and died in 2014. I suppose he created the future of money, then he died, leaving us with only rumors about his identity.
Hal Finney, who was he?
Hal Finney graduated from Caltech in 1979. Student peers voted him the smartest. He took a doctoral-level gravitational field theory course as a freshman. Finney's intelligence meets the first requirement for becoming Satoshi Nakamoto.
Students remember Finney holding an Ayn Rand book. If he'd read this, he may have developed libertarian views.
His beliefs led him to a small group of freethinking programmers. In the 1990s, he joined Cypherpunks. This action promoted the use of strong cryptography and privacy-enhancing technologies for social and political change. Finney helped them achieve a crypto-anarchist perspective as self-proclaimed privacy defenders.
Zimmermann knew Finney well.
Hal replied to a Cypherpunk message about Phil Zimmermann and PGP. He contacted Phil and became PGP Corporation's first member, retiring in 2011. Satoshi Nakamoto quit bitcoin in 2011.
Finney improved the new PGP protocol, but he had to do so secretly. He knew about Phil's PGP issues. I understand why he wanted to hide his identity while creating bitcoin.
Why did he pretend to be from Japan?
His envisioned persona was spot-on. He resided near scientist Dorian Prentice Satoshi Nakamoto. Finney could've assumed Nakamoto's identity to hide his. Temple City has 36,000 people, so what are the chances they both lived there? A cryptographic genius with the same name as Bitcoin's creator: coincidence?
Things went differently, I think.
I think Hal Finney sent himself Satoshis messages. I know it's odd. If you want to conceal your involvement, do as follows. He faked messages and transferred the first bitcoins to himself to test the transaction mechanism, so he never returned their money.
Hal Finney created the first reusable proof-of-work system. The bitcoin protocol. In the 1990s, Finney was intrigued by digital money. He invented CRypto cASH in 1993.
Legacy
Hal Finney's contributions should not be forgotten. Even if I'm wrong and he's not Satoshi Nakamoto, we shouldn't forget his bitcoin contribution. He helped us achieve a better future.

CyberPunkMetalHead
3 years ago
I talked to ChatGPT about the adoption of cryptocurrencies.
OpenAI's ChatGPT is an amazing AI-powered chatbot. It can write poetry, fiction, and marketing ideas. I was impressed how well ChatGPT followed the interview, albeit there were a few classics “I’m afraid I can’t do that”.
Full interview below.
Me: I'm your interviewer. We'll discuss crypto. Thanks for being interviewed. What do you think about cryptocurrency?
CGPT: Cryptocurrency is an innovative technology that could transform money and financial activities. It might boost the efficiency and security of financial institutions and let consumers deal directly without banks. Cryptocurrency is still a new and untested technology with many unknowns and hurdles before it can be broadly accepted.
Me: Over 22,000 cryptocurrencies exist, and many have little use. We need how much cryptocurrencies?
CGPT: The appropriate quantity will rely on a multitude of factors, including each cryptocurrency's use cases, adoption rate, and market rivalry. Only a few cryptocurrencies will likely receive widespread adoption and be successful. Many existing cryptocurrencies may not survive since they can't deliver new or valued solutions or compete with more established cryptocurrencies.
Me: Will cryptocurrencies grow? What's next for worldwide adoption?
CGPT: It's hard to forecast the future of cryptocurrencies because the acceptance of new technologies is unpredictable. I believe cryptocurrencies will expand and acquire popularity in the future years. Regulatory ambiguity, security concerns, and scalability issues must be overcome for this to happen. Cryptocurrency companies and organizations must engage together with governments and authorities to address these obstacles and establish a growth-friendly climate. Continued innovation and improvement of the technology, including public education and awareness, will drive acceptance.
Me: Do bear markets affect bitcoin adoption?
CGPT: On the one hand, a bear market might induce uncertainty and hesitation among potential consumers. Bear markets can present opportunities for long-term investors who can acquire cryptocurrencies at cheaper prices and are more likely to hang onto their assets. A bear market can also test the tenacity and power of the underlying technology and community, which can boost long-term confidence and adoption. A bear market might have profound and nuanced effects on bitcoin adoption.
Me: What are some likely outcomes if Bitcoin reaches $100,000 by next year?
CGPT: If Bitcoin saw rapid growth, it would undoubtedly have repercussions for the cryptocurrency market and economy. Possible scenarios include increased public interest and awareness of cryptocurrency, a surge in demand for Bitcoin and other cryptocurrencies, and a growth in the cryptocurrency industry's market value. By shifting their focus and cash to the cryptocurrency market, investors and traders may also affect other asset classes, such as traditional equities and commodities. Governments and financial organizations may focus more on the cryptocurrency sector as they try to grasp Bitcoin's rapid rise.
Me: Will other countries accept crypto as currency?
CGPT: It's hard to say if additional governments will adopt cryptocurrencies as legal tender. Some countries have recognized the promise of bitcoin and are exploring its use, while others are cautious. Adoption of bitcoin as legal cash may vary by country, based on financial infrastructure, rules, and political atmosphere. As cryptocurrency technology evolves and becomes more accepted, more governments may embrace it as legal tender.
Me: Final question: will the recent cryptocurrency hacks affect long term adoption?
CGPT: Hacks might tarnish cryptocurrency's reputation and public faith in its security, the technology underpinning it is continually improving. Many cryptocurrency projects have developed strong security mechanisms to prevent hacks and other dangers, and these safeguards will undoubtedly improve over time. The decentralized nature of cryptocurrency makes it more resistant to attacks. Hacks and other security breaches are a concern, but they may not affect cryptocurrency adoption.
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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.

Sam Warain
3 years ago
The Brilliant Idea Behind Kim Kardashian's New Private Equity Fund
Kim Kardashian created Skky Partners. Consumer products, internet & e-commerce, consumer media, hospitality, and luxury are company targets.
Some call this another Kardashian publicity gimmick.
This maneuver is brilliance upon closer inspection. Why?
1) Kim has amassed a sizable social media fan base:
Over 320 million Instagram and 70 million Twitter users follow Kim Kardashian.
Kim Kardashian's Instagram account ranks 8th. Three Kardashians in top 10 is ridiculous.
This gives her access to consumer data. She knows what people are discussing. Investment firms need this data.
Quality, not quantity, of her followers matters. Studies suggest that her following are more engaged than Selena Gomez and Beyonce's.
Kim's followers are worth roughly $500 million to her brand, according to a research. They trust her and buy what she recommends.
2) She has a special aptitude for identifying trends.
Kim Kardashian can sense trends.
She's always ahead of fashion and beauty trends. She's always trying new things, too. She doesn't mind making mistakes when trying anything new. Her desire to experiment makes her a good business prospector.
Kim has also created a lifestyle brand that followers love. Kim is an entrepreneur, mom, and role model, not just a reality TV star or model. She's established a brand around her appearance, so people want to buy her things.
Her fragrance collection has sold over $100 million since its 2009 introduction, and her Sears apparel line did over $200 million in its first year.
SKIMS is her latest $3.2bn brand. She can establish multibillion-dollar firms with her enormous distribution platform.
Early founders would kill for Kim Kardashian's network.
Making great products is hard, but distribution is more difficult. — David Sacks, All-in-Podcast
3) She can delegate the financial choices to Jay Sammons, one of the greatest in the industry.
Jay Sammons is well-suited to develop Kim Kardashian's new private equity fund.
Sammons has 16 years of consumer investing experience at Carlyle. This will help Kardashian invest in consumer-facing enterprises.
Sammons has invested in Supreme and Beats Electronics, both of which have grown significantly. Sammons' track record and competence make him the obvious choice.
Kim Kardashian and Jay Sammons have joined forces to create a new business endeavor. The agreement will increase Kardashian's commercial empire. Sammons can leverage one of the world's most famous celebrities.
“Together we hope to leverage our complementary expertise to build the next generation consumer and media private equity firm” — Kim Kardashian
Kim Kardashian is a successful businesswoman. She developed an empire by leveraging social media to connect with fans. By developing a global lifestyle brand, she has sold things and experiences that have made her one of the world's richest celebrities.
She's a shrewd entrepreneur who knows how to maximize on herself and her image.
Imagine how much interest Kim K will bring to private equity and venture capital.
I'm curious about the company's growth.

DC Palter
3 years ago
Is Venture Capital a Good Fit for Your Startup?
5 VC investment criteria
I reviewed 200 startup business concepts last week. Brainache.
The enterprises sold various goods and services. The concepts were achingly similar: give us money, we'll produce a product, then get more to expand. No different from daily plans and pitches.
Most of those 200 plans sounded plausible. But 10% looked venture-worthy. 90% of startups need alternatives to venture finance.
With the success of VC-backed businesses and the growth of venture funds, a common misperception is that investors would fund any decent company idea. Finding investors that believe in the firm and founders is the key to funding.
Incorrect. Venture capital needs investing in certain enterprises. If your startup doesn't match the model, as most early-stage startups don't, you can revise your business plan or locate another source of capital.
Before spending six months pitching angels and VCs, make sure your startup fits these criteria.
Likely to generate $100 million in sales
First, I check the income predictions in a pitch deck. If it doesn't display $100M, don't bother.
The math doesn't work for venture financing in smaller businesses.
Say a fund invests $1 million in a startup valued at $5 million that is later acquired for $20 million. That's a win everyone should celebrate. Most VCs don't care.
Consider a $100M fund. The fund must reach $360M in 7 years with a 20% return. Only 20-30 investments are possible. 90% of the investments will fail, hence the 23 winners must return $100M-$200M apiece. $15M isn't worth the work.
Angel investors and tiny funds use the same ideas as venture funds, but their smaller scale affects the calculations. If a company can support its growth through exit on less than $2M in angel financing, it must have $25M in revenues before large companies will consider acquiring it.
Aiming for Hypergrowth
A startup's size isn't enough. It must expand fast.
Developing a great business takes time. Complex technology must be constructed and tested, a nationwide expansion must be built, or production procedures must go from lab to pilot to factories. These can be enormous, world-changing corporations, but venture investment is difficult.
The normal 10-year venture fund life. Investments are made during first 3–4 years.. 610 years pass between investment and fund dissolution. Funds need their investments to exit within 5 years, 7 at the most, therefore add a safety margin.
Longer exit times reduce ROI. A 2-fold return in a year is excellent. Loss at 2x in 7 years.
Lastly, VCs must prove success to raise their next capital. The 2nd fund is raised from 1st fund portfolio increases. Third fund is raised using 1st fund's cash return. Fund managers must raise new money quickly to keep their jobs.
Branding or technology that is protected
No big firm will buy a startup at a high price if they can produce a competing product for less. Their development teams, consumer base, and sales and marketing channels are large. Who needs you?
Patents, specialist knowledge, or brand name are the only answers. The acquirer buys this, not the thing.
I've heard of several promising startups. It's not a decent investment if there's no exit strategy.
A company that installs EV charging stations in apartments and shopping areas is an example. It's profitable, repeatable, and big. A terrific company. Not a startup.
This building company's operations aren't secret. No technology to protect, no special information competitors can't figure out, no go-to brand name. Despite the immense possibilities, a large construction company would be better off starting their own.
Most venture businesses build products, not services. Services can be profitable but hard to safeguard.
Probable purchase at high multiple
Once a software business proves its value, acquiring it is easy. Pharma and medtech firms have given up on their own research and instead acquire startups after regulatory permission. Many startups, especially in specialized areas, have this weakness.
That doesn't mean any lucrative $25M-plus business won't be acquired. In many businesses, the venture model requires a high exit premium.
A startup invents a new glue. 3M, BASF, Henkel, and others may buy them. Adding more adhesive to their catalogs won't boost commerce. They won't compete to buy the business. They'll only buy a startup at a profitable price. The acquisition price represents a moderate EBITDA multiple.
The company's $100M revenue presumably yields $10m in profits (assuming they’ve reached profitability at all). A $30M-$50M transaction is likely. Not terrible, but not what venture investors want after investing $25M to create a plant and develop the business.
Private equity buys profitable companies for a moderate profit multiple. It's a good exit for entrepreneurs, but not for investors seeking 10x or more what PE firms pay. If a startup offers private equity as an exit, the conversation is over.
Constructed for purchase
The startup wants a high-multiple exit. Unless the company targets $1B in revenue and does an IPO, exit means acquisition.
If they're constructing the business for acquisition or themselves, founders must decide.
If you want an indefinitely-running business, I applaud you. We need more long-term founders. Most successful organizations are founded around consumer demands, not venture capital's urge to grow fast and exit. Not venture funding.
if you don't match the venture model, what to do
VC funds moonshots. The 10% that succeed are extraordinary. Not every firm is a rocketship, and launching the wrong startup into space, even with money, will explode.
But just because your startup won't make $100M in 5 years doesn't mean it's a bad business. Most successful companies don't follow this model. It's not venture capital-friendly.
Although venture capital gets the most attention due to a few spectacular triumphs (and disasters), it's not the only or even most typical option to fund a firm.
Other ways to support your startup:
Personal and family resources, such as credit cards, second mortgages, and lines of credit
bootstrapping off of sales
government funding and honors
Private equity & project financing
collaborating with a big business
Including a business partner
Before pitching angels and VCs, be sure your startup qualifies. If so, include them in your pitch.
