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.

Every week I meet many people interested in VC. Many of them ask me what it's like to be a junior analyst in VC or what I've learned so far.

Looking back, I've learned many things as a junior VC, having gone through an almost-euphoric peak bull market, failed tech IPOs of 2019 including WeWorks' catastrophic fall, and the beginnings of a bearish market.

1. Network, network, network!

VCs spend 80% of their time networking. Junior VCs source deals or manage portfolios. You spend your time bringing startups to your fund or helping existing portfolio companies grow. Knowing stakeholders (corporations, star talent, investors) in your particular areas of investment helps you develop your portfolio.

Networking was one of my strengths. When I first started in the industry, I'd go to startup events and meet 50 people a month. Over time, I realized these relationships were shallow and I was only getting business cards. So I stopped seeing networking as a transaction. VC is a long-term game, so you should work with people you like. Now I know who I click with and can build deeper relationships with them. My network is smaller but more valuable than before.

2. The Most Important Metric Is Founder

People often ask how we pick investments. Why some companies can raise money and others can't is a mystery. The founder is the most important metric for VCs. When a company is young, the product, environment, and team all change, but the founder remains constant. VCs bet on the founder, not the company.

How do we decide which founders are best after 2-3 calls? When looking at a founder's profile, ask why this person can solve this problem. The founders' track record will tell. If the founder is a serial entrepreneur, you know he/she possesses the entrepreneur DNA and will likely succeed again. If it's his/her first startup, focus on industry knowledge to deliver the best solution.

3. A company's fate can be determined by macrotrends.

Macro trends are crucial. A company can have the perfect product, founder, and team, but if it's solving the wrong problem, it won't succeed. I've also seen average companies ride the wave to success. When you're on the right side of a trend, there's so much demand that more companies can get a piece of the pie.

In COVID-19, macro trends made or broke a company. Ed-tech and health-tech companies gained unicorn status and raised funding at inflated valuations due to sudden demand. With the easing of pandemic restrictions and the start of a bear market, many of these companies' valuations are in question.

4. Look for methods to ACTUALLY add value.

You only need to go on VC twitter (read: @vcstartterkit and @vcbrags) for 5 minutes or look at fin-meme accounts on Instagram to see how much VCs claim to add value but how little they actually do. VC is a long-term game, though. Long-term, founders won't work with you if you don't add value.

How can we add value when we're young and have no network? Leaning on my strengths helped me. Instead of viewing my age and limited experience as a disadvantage, I realized that I brought a unique perspective to the table.

As a VC, you invest in companies that will be big in 5-7 years, and millennials and Gen Z will have the most purchasing power. Because you can relate to that market, you can offer insights that most Partners at 40 can't. I added value by helping with hiring because I had direct access to university talent pools and by finding university students for product beta testing.

5. Develop your personal brand.

Generalists or specialists run most funds. This means that funds either invest across industries or have a specific mandate. Most funds are becoming specialists, I've noticed. Top-tier founders don't lack capital, so funds must find other ways to attract them. Why would a founder work with a generalist fund when a specialist can offer better industry connections and partnership opportunities?

Same for fund members. Founders want quality investors. Become a thought leader in your industry to meet founders. Create content and share your thoughts on industry-related social media. When I first started building my brand, I found it helpful to interview industry veterans to create better content than I could on my own. Over time, my content attracted quality founders so I didn't have to look for them.

These are my biggest VC lessons. This list isn't exhaustive, but it's my industry survival guide.

Zero-Knowledge Proofs for Beginners

Published here originally.

Introduction

I Spy—did you play as a kid? One person chose a room object, and the other had to guess it by answering yes or no questions. I Spy was entertaining, but did you know it could teach you cryptography?

Zero Knowledge Proofs let you show your pal you know what they picked without exposing how. Math replaces electronics in this secret spy mission. Zero-knowledge proofs (ZKPs) are sophisticated cryptographic tools that allow one party to prove they have particular knowledge without revealing it. This proves identification and ownership, secures financial transactions, and more. This article explains zero-knowledge proofs and provides examples to help you comprehend this powerful technology.

What is a Proof of Zero Knowledge?

Zero-knowledge proofs prove a proposition is true without revealing any other information. This lets the prover show the verifier that they know a fact without revealing it. So, a zero-knowledge proof is like a magician's trick: the prover proves they know something without revealing how or what. Complex mathematical procedures create a proof the verifier can verify.

Want to find an easy way to test it out? Try out with tis awesome example! ZK Crush

Describe it as if I'm 5

Alex and Jack found a cave with a center entrance that only opens when someone knows the secret. Alex knows how to open the cave door and wants to show Jack without telling him.

Alex and Jack name both pathways (let’s call them paths A and B).

1. In the first phase, Alex is already inside the cave and is free to select either path, in this case A or B.

2. As Alex made his decision, Jack entered the cave and asked him to exit from the B path.

3. Jack can confirm that Alex really does know the key to open the door because he came out for the B path and used it.

To conclude, Alex and Jack repeat:

1. Alex walks into the cave.

2. Alex follows a random route.

3. Jack walks into the cave.

4. Alex is asked to follow a random route by Jack.

5. Alex follows Jack's advice and heads back that way.

What is a Zero Knowledge Proof?

At a high level, the aim is to construct a secure and confidential conversation between the prover and the verifier, where the prover convinces the verifier that they have the requisite information without disclosing it. The prover and verifier exchange messages and calculate in each round of the dialogue.

The prover uses their knowledge to prove they have the information the verifier wants during these rounds. The verifier can verify the prover's truthfulness without learning more by checking the proof's mathematical statement or computation.

Zero knowledge proofs use advanced mathematical procedures and cryptography methods to secure communication. These methods ensure the evidence is authentic while preventing the prover from creating a phony proof or the verifier from extracting unnecessary information.

ZK proofs require examples to grasp. Before the examples, there are some preconditions.

Criteria for Proofs of Zero Knowledge

1. Completeness: If the proposition being proved is true, then an honest prover will persuade an honest verifier that it is true.

2. Soundness: If the proposition being proved is untrue, no dishonest prover can persuade a sincere verifier that it is true.

3. Zero-knowledge: The verifier only realizes that the proposition being proved is true. In other words, the proof only establishes the veracity of the proposition being supported and nothing more.

The zero-knowledge condition is crucial. Zero-knowledge proofs show only the secret's veracity. The verifier shouldn't know the secret's value or other details.

Example after example after example

To illustrate, take a zero-knowledge proof with several examples:

Initial Password Verification Example

You want to confirm you know a password or secret phrase without revealing it.

Use a zero-knowledge proof:

1. You and the verifier settle on a mathematical conundrum or issue, such as figuring out a big number's components.

2. The puzzle or problem is then solved using the hidden knowledge that you have learned. You may, for instance, utilize your understanding of the password to determine the components of a particular number.

3. You provide your answer to the verifier, who can assess its accuracy without knowing anything about your private data.

4. You go through this process several times with various riddles or issues to persuade the verifier that you actually are aware of the secret knowledge.

You solved the mathematical puzzles or problems, proving to the verifier that you know the hidden information. The proof is zero-knowledge since the verifier only sees puzzle solutions, not the secret information.

In this scenario, the mathematical challenge or problem represents the secret, and solving it proves you know it. The evidence does not expose the secret, and the verifier just learns that you know it.

My simple example meets the zero-knowledge proof conditions:

1. Completeness: If you actually know the hidden information, you will be able to solve the mathematical puzzles or problems, hence the proof is conclusive.

2. Soundness: The proof is sound because the verifier can use a publicly known algorithm to confirm that your answer to the mathematical conundrum or difficulty is accurate.

3. Zero-knowledge: The proof is zero-knowledge because all the verifier learns is that you are aware of the confidential information. Beyond the fact that you are aware of it, the verifier does not learn anything about the secret information itself, such as the password or the factors of the number. As a result, the proof does not provide any new insights into the secret.

Explanation #2: Toss a coin.

One coin is biased to come up heads more often than tails, while the other is fair (i.e., comes up heads and tails with equal probability). You know which coin is which, but you want to show a friend you can tell them apart without telling them.

Use a zero-knowledge proof:

1. One of the two coins is chosen at random, and you secretly flip it more than once.

2. You show your pal the following series of coin flips without revealing which coin you actually flipped.

3. Next, as one of the two coins is flipped in front of you, your friend asks you to tell which one it is.

4. Then, without revealing which coin is which, you can use your understanding of the secret order of coin flips to determine which coin your friend flipped.

5. To persuade your friend that you can actually differentiate between the coins, you repeat this process multiple times using various secret coin-flipping sequences.

In this example, the series of coin flips represents the knowledge of biased and fair coins. You can prove you know which coin is which without revealing which is biased or fair by employing a different secret sequence of coin flips for each round.

The evidence is zero-knowledge since your friend does not learn anything about which coin is biased and which is fair other than that you can tell them differently. The proof does not indicate which coin you flipped or how many times you flipped it.

The coin-flipping example meets zero-knowledge proof requirements:

1. Completeness: If you actually know which coin is biased and which is fair, you should be able to distinguish between them based on the order of coin flips, and your friend should be persuaded that you can.

2. Soundness: Your friend may confirm that you are correctly recognizing the coins by flipping one of them in front of you and validating your answer, thus the proof is sound in that regard. Because of this, your acquaintance can be sure that you are not just speculating or picking a coin at random.

3. Zero-knowledge: The argument is that your friend has no idea which coin is biased and which is fair beyond your ability to distinguish between them. Your friend is not made aware of the coin you used to make your decision or the order in which you flipped the coins. Consequently, except from letting you know which coin is biased and which is fair, the proof does not give any additional information about the coins themselves.

Figure out the prime number in Example #3.

You want to prove to a friend that you know their product n=pq without revealing p and q. Zero-knowledge proof?

Use a variant of the RSA algorithm. Method:

1. You determine a new number s = r2 mod n by computing a random number r.

2. You email your friend s and a declaration that you are aware of the values of p and q necessary for n to equal pq.

3. A random number (either 0 or 1) is selected by your friend and sent to you.

4. You send your friend r as evidence that you are aware of the values of p and q if e=0. You calculate and communicate your friend's s/r if e=1.

5. Without knowing the values of p and q, your friend can confirm that you know p and q (in the case where e=0) or that s/r is a legitimate square root of s mod n (in the situation where e=1).

This is a zero-knowledge proof since your friend learns nothing about p and q other than their product is n and your ability to verify it without exposing any other information. You can prove that you know p and q by sending r or by computing s/r and sending that instead (if e=1), and your friend can verify that you know p and q or that s/r is a valid square root of s mod n without learning anything else about their values. This meets the conditions of completeness, soundness, and zero-knowledge.

Zero-knowledge proofs satisfy the following:

1. Completeness: The prover can demonstrate this to the verifier by computing q = n/p and sending both p and q to the verifier. The prover also knows a prime number p and a factorization of n as p*q.

2. Soundness: Since it is impossible to identify any pair of numbers that correctly factorize n without being aware of its prime factors, the prover is unable to demonstrate knowledge of any p and q that do not do so.

3. Zero knowledge: The prover only admits that they are aware of a prime number p and its associated factor q, which is already known to the verifier. This is the extent of their knowledge of the prime factors of n. As a result, the prover does not provide any new details regarding n's prime factors.

Types of Proofs of Zero Knowledge

Each zero-knowledge proof has pros and cons. Most zero-knowledge proofs are:

1. Interactive Zero Knowledge Proofs: The prover and the verifier work together to establish the proof in this sort of zero-knowledge proof. The verifier disputes the prover's assertions after receiving a sequence of messages from the prover. When the evidence has been established, the prover will employ these new problems to generate additional responses.

2. Non-Interactive Zero Knowledge Proofs: For this kind of zero-knowledge proof, the prover and verifier just need to exchange a single message. Without further interaction between the two parties, the proof is established.

3. A statistical zero-knowledge proof is one in which the conclusion is reached with a high degree of probability but not with certainty. This indicates that there is a remote possibility that the proof is false, but that this possibility is so remote as to be unimportant.

4. Succinct Non-Interactive Argument of Knowledge (SNARKs): SNARKs are an extremely effective and scalable form of zero-knowledge proof. They are utilized in many different applications, such as machine learning, blockchain technology, and more. Similar to other zero-knowledge proof techniques, SNARKs enable one party—the prover—to demonstrate to another—the verifier—that they are aware of a specific piece of information without disclosing any more information about that information.

5. The main characteristic of SNARKs is their succinctness, which refers to the fact that the size of the proof is substantially smaller than the amount of the original data being proved. Because to its high efficiency and scalability, SNARKs can be used in a wide range of applications, such as machine learning, blockchain technology, and more.

Uses for Zero Knowledge Proofs

ZKP applications include:

1. Verifying Identity ZKPs can be used to verify your identity without disclosing any personal information. This has uses in access control, digital signatures, and online authentication.

2. Proof of Ownership ZKPs can be used to demonstrate ownership of a certain asset without divulging any details about the asset itself. This has uses for protecting intellectual property, managing supply chains, and owning digital assets.

3. Financial Exchanges Without disclosing any details about the transaction itself, ZKPs can be used to validate financial transactions. Cryptocurrency, internet payments, and other digital financial transactions can all use this.

4. By enabling parties to make calculations on the data without disclosing the data itself, Data Privacy ZKPs can be used to preserve the privacy of sensitive data. Applications for this can be found in the financial, healthcare, and other sectors that handle sensitive data.

5. By enabling voters to confirm that their vote was counted without disclosing how they voted, elections ZKPs can be used to ensure the integrity of elections. This is applicable to electronic voting, including internet voting.

6. Cryptography Modern cryptography's ZKPs are a potent instrument that enable secure communication and authentication. This can be used for encrypted messaging and other purposes in the business sector as well as for military and intelligence operations.

Proofs of Zero Knowledge and Compliance

Kubernetes and regulatory compliance use ZKPs in many ways. Examples:

1. Security for Kubernetes ZKPs offer a mechanism to authenticate nodes without disclosing any sensitive information, enhancing the security of Kubernetes clusters. ZKPs, for instance, can be used to verify, without disclosing the specifics of the program, that the nodes in a Kubernetes cluster are running permitted software.

2. Compliance Inspection Without disclosing any sensitive information, ZKPs can be used to demonstrate compliance with rules like the GDPR, HIPAA, and PCI DSS. ZKPs, for instance, can be used to demonstrate that data has been encrypted and stored securely without divulging the specifics of the mechanism employed for either encryption or storage.

3. Access Management Without disclosing any private data, ZKPs can be used to offer safe access control to Kubernetes resources. ZKPs can be used, for instance, to demonstrate that a user has the necessary permissions to access a particular Kubernetes resource without disclosing the details of those permissions.

4. Safe Data Exchange Without disclosing any sensitive information, ZKPs can be used to securely transmit data between Kubernetes clusters or between several businesses. ZKPs, for instance, can be used to demonstrate the sharing of a specific piece of data between two parties without disclosing the details of the data itself.

5. Kubernetes deployments audited Without disclosing the specifics of the deployment or the data being processed, ZKPs can be used to demonstrate that Kubernetes deployments are working as planned. This can be helpful for auditing purposes and for ensuring that Kubernetes deployments are operating as planned.

ZKPs preserve data and maintain regulatory compliance by letting parties prove things without revealing sensitive information. ZKPs will be used more in Kubernetes as it grows.

Don't say this in public!

Want to wow your audience? Want to deliver a successful presentation? Do you want practical takeaways from your presentation?

Then avoid these phrases.

Public speaking is difficult. People fear public speaking, according to research.

"Public speaking is people's biggest fear, according to studies. Number two is death. "Sounds right?" — Comedian Jerry Seinfeld

Yes, public speaking is scary. These words and phrases will make your presentation harder.

Using unnecessary words can weaken your message.

You may have prepared well for your presentation and feel confident. During your presentation, you may freeze up. You may blank or forget.

Effective delivery is even more important than skillful public speaking.

Here are 10 presentation pitfalls.

1. I or Me

Presentations are about the audience, not you. Replace "I or me" with "you, we, or us." Focus on your audience. Reward them with expertise and intriguing views about your issue.

Serve your audience actionable items during your presentation, and you'll do well. Your audience will have a harder time listening and engaging if you're self-centered.

2. Sorry if/for

Your presentation is fine. These phrases make you sound insecure and unprepared. Don't pressure the audience to tell you not to apologize. Your audience should focus on your presentation and essential messages.

3. Excuse the Eye Chart, or This slide's busy

Why add this slide if you're utilizing these phrases? If you don't like this slide, change it before presenting. After the presentation, extra data can be provided.

Don't apologize for unclear slides. Hide or delete a broken PowerPoint slide. If so, divide your message into multiple slides or remove the "business" slide.

4. Sorry I'm Nervous

Some think expressing yourself will win over the audience. Nerves are horrible. Even public speakers are nervous.

Nerves aren't noticeable. What's the point? Let the audience judge your nervousness. Please don't make this obvious.

5. I'm not a speaker or I've never done this before.

These phrases destroy credibility. People won't listen and will check their phones or computers.

Why present if you use these phrases?

Good speakers aren't necessarily public speakers. Be confident in what you say. When you're confident, many people will like your presentation.

6. Our Key Differentiators Are

Overused term. It's widely utilized. This seems "salesy," and your "important differentiators" are probably like a competitor's.

This statement has been diluted; say, "what makes us different is..."

7. Next Slide

Many slides or stories? Your presentation needs transitions. They help your viewers understand your argument.

You didn't transition well when you said "next slide." Think about organic transitions.

8. I Didn’t Have Enough Time, or I’m Running Out of Time

The phrase "I didn't have enough time" implies that you didn't care about your presentation. This shows the viewers you rushed and didn't care.

Saying "I'm out of time" shows poor time management. It means you didn't rehearse enough and plan your time well.

9. I've been asked to speak on

This phrase is used to emphasize your importance. This phrase conveys conceit.

When you say this sentence, you tell others you're intelligent, skilled, and appealing. Don't utilize this term; focus on your topic.

10. Moving On, or All I Have

These phrases don't consider your transitions or presentation's end. People recall a presentation's beginning and end.

How you end your discussion affects how people remember it. You must end your presentation strongly and use natural transitions.

Conclusion

10 phrases to avoid in a presentation. I or me, sorry if or sorry for, pardon the Eye Chart or this busy slide, forgive me if I appear worried, or I'm really nervous, and I'm not good at public speaking, I'm not a speaker, or I've never done this before.

Please don't use these phrases: next slide, I didn't have enough time, I've been asked to speak about, or that's all I have.

We shouldn't make public speaking more difficult than it is. We shouldn't exacerbate a difficult issue. Better public speakers avoid these words and phrases.

“Remember not only to say the right thing in the right place, but far more difficult still, to leave unsaid the wrong thing at the tempting moment.” — Benjamin Franklin, Founding Father

This is a summary. See the original post here.