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.

DATA MINING WITH SUPERALGORES

Old pots produce the best soup.

Science has always inspired indicator design. From physics to signal processing, many indicators use concepts from mechanical engineering, electronics, and probability. In Superalgos' Data Mining section, we've explored using thermodynamics and information theory to construct indicators and using statistical and probabilistic techniques like reduced normal law to take advantage of low probability events.

An asset's price is like a mechanical object revolving around its moving average. Using this approach, we could design an indicator using the oscillator's Total Energy. An oscillator's energy is finite and constant. Since we don't expect the price to follow the harmonic oscillator, this energy should deviate from the perfect situation, and the maximum of divergence may provide us valuable information on the price's moving average.

Definition of the Harmonic Oscillator in Few Words

Sinusoidal function describes a harmonic oscillator. The time-constant energy equation for a harmonic oscillator is:

With

Time saves energy.

In a mechanical harmonic oscillator, total energy equals kinetic energy plus potential energy. The formula for energy is the same for every kind of harmonic oscillator; only the terms of total energy must be adapted to fit the relevant units. Each oscillator has a velocity component (kinetic energy) and a position to equilibrium component (potential energy).

The Price Oscillator and the Energy Formula

Considering the harmonic oscillator definition, we must specify kinetic and potential components for our price oscillator. We define oscillator velocity as the rate of change and equilibrium position as the price's distance from its moving average.

Price kinetic energy:

It's like:

With

and

L is the number of periods for the rate of change calculation and P for the close price EMA calculation.

Total price oscillator energy =

Given that an asset's price can theoretically vary at a limitless speed and be endlessly far from its moving average, we don't expect this formula's outcome to be constrained. We'll normalize it using Z-Score for convenience of usage and readability, which also allows probabilistic interpretation.

Over 20 periods, we'll calculate E's moving average and standard deviation.

We calculated Z on BTC/USDT with L = 10 and P = 21 using Knime Analytics.

The graph is detrended. We added two horizontal lines at +/- 1.6 to construct a 94.5% probability zone based on reduced normal law tables. Price cycles to its moving average oscillate clearly. Red and green arrows illustrate where the oscillator crosses the top and lower limits, corresponding to the maximum/minimum price oscillation. Since the results seem noisy, we may apply a non-lagging low-pass or multipole filter like Butterworth or Laguerre filters and employ dynamic bands at a multiple of Z's standard deviation instead of fixed levels.

Kinetic Detrender Implementation in Superalgos

The Superalgos Kinetic detrender features fixed upper and lower levels and dynamic volatility bands.

The code is pretty basic and does not require a huge amount of code lines.

It starts with the standard definitions of the candle pointer and the constant declaration :

let candle = record.current
let len = 10
let P = 21
let T = 20
let up = 1.6
let low = 1.6

Upper and lower dynamic volatility band constants are up and low.

We proceed to the initialization of the previous value for EMA :

if (variable.prevEMA === undefined) {
    variable.prevEMA = candle.close
}

And the calculation of EMA with a function (it is worth noticing the function is declared at the end of the code snippet in Superalgos) :

variable.ema = calculateEMA(P, candle.close, variable.prevEMA)
//EMA calculation
function calculateEMA(periods, price, previousEMA) {
    let k = 2 / (periods + 1)
    return price * k + previousEMA * (1 - k)
}

The rate of change is calculated by first storing the right amount of close price values and proceeding to the calculation by dividing the current close price by the first member of the close price array:

variable.allClose.push(candle.close)
if (variable.allClose.length > len) {
    variable.allClose.splice(0, 1)
}
if (variable.allClose.length === len) {
    variable.roc = candle.close / variable.allClose[0]
} else {
    variable.roc = 1
}

Finally, we get energy with a single line:

variable.E = 1 / 2 * len * variable.roc + 1 / 2 * P * candle.close / variable.ema

The Z calculation reuses code from Z-Normalization-based indicators:

variable.allE.push(variable.E)
if (variable.allE.length > T) {
    variable.allE.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allE.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allE[i]
    }
    variable.MA = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allE[i] - variable.MA, 2)
    }
    variable.sigma = Math.sqrt(variable.SQ / T)
variable.Z = (variable.E - variable.MA) / variable.sigma
} else {
    variable.Z = 0
}
variable.allZ.push(variable.Z)
if (variable.allZ.length > T) {
    variable.allZ.splice(0, 1)
}
variable.sum = 0
variable.SQ = 0
if (variable.allZ.length === T) {
    for (var i = 0; i < T; i++) {
        variable.sum += variable.allZ[i]
    }
    variable.MAZ = variable.sum / T
for (var i = 0; i < T; i++) {
        variable.SQ += Math.pow(variable.allZ[i] - variable.MAZ, 2)
    }
    variable.sigZ = Math.sqrt(variable.SQ / T)
} else {
    variable.MAZ = variable.Z
    variable.sigZ = variable.MAZ * 0.02
}
variable.upper = variable.MAZ + up * variable.sigZ
variable.lower = variable.MAZ - low * variable.sigZ

We also update the EMA value.

variable.prevEMA = variable.EMA

Conclusion

We showed how to build a detrended oscillator using simple harmonic oscillator theory. Kinetic detrender's main line oscillates between 2 fixed levels framing 95% of the values and 2 dynamic levels, leading to auto-adaptive mean reversion zones.

Superalgos' Normalized Momentum data mine has the Kinetic detrender indication.

All the material here can be reused and integrated freely by linking to this article and Superalgos.

This post is informative and not financial advice. Seek expert counsel before trading. Risk using this material.

The Lex Fridman podcast host has interviewed Elon Musk.

Lex is a minimalist YouTuber. His videos are sloppy. Suits are his trademark.

In a video, he shares a typical day. I've smashed my 6-month goals using its ideas.

Here's his schedule.

Morning Mantra

Not woo-woo. Lex's mantra reflects his practicality.

Four parts.

Rulebook

"I remember the game's rules," he says.

Among them:

• Sleeping 6–8 hours nightly

• 1–3 times a day, he checks social media.

• Every day, despite pain, he exercises. "I exercise uninjured body parts."

Visualize

He imagines his day. "Like Sims..."

He says three things he's grateful for and contemplates death.

"Today may be my last"

Objectives

Then he visualizes his goals. He starts big. Five-year goals.

Short-term goals follow. Lex says they're year-end goals.

Near but out of reach.

Principles

He lists his principles. Assertions. His goals.

He acknowledges his cliche beliefs. Compassion, empathy, and strength are key.

Here's my mantra routine:

Four-Hour Deep Work

Lex begins a four-hour deep work session after his mantra routine. Today's toughest.

AI is Lex's specialty. His video doesn't explain what he does.

Clearly, he works hard.

Before starting, he has water, coffee, and a bathroom break.

"During deep work sessions, I minimize breaks."

He's distraction-free. Phoneless. Silence. Nothing. Any loose ideas are typed into a Google doc for later. He wants to work.

"Just get the job done. Don’t think about it too much and feel good once it’s complete." — Lex Fridman

30-Minute Social Media & Music

After his first deep work session, Lex rewards himself.

10 minutes on social media, 20 on music. Upload content and respond to comments in 10 minutes. 20 minutes for guitar or piano.

"In the real world, I’m currently single, but in the music world, I’m in an open relationship with this beautiful guitar. Open relationship because sometimes I cheat on her with the acoustic." — Lex Fridman

Two-hour exercise

Then exercise for two hours.

Daily runs six miles. Then he chooses how far to go. Run time is an hour.

He does bodyweight exercises. Every minute for 15 minutes, do five pull-ups and ten push-ups. It's David Goggins-inspired. He aims for an hour a day.

He's hungry. Before running, he takes a salt pill for electrolytes.

He'll then take a one-minute cold shower while listening to cheesy songs. Afterward, he might eat.

Four-Hour Deep Work

Lex's second work session.

He works 8 hours a day.

Again, zero distractions.

Eating

The video's meal doesn't look appetizing, but it's healthy.

It's ground beef with vegetables. Cauliflower is his "ground-floor" veggie. "Carrots are my go-to party food."

Lex's keto diet includes 1800–2000 calories.

He drinks a "nutrient-packed" Atheltic Greens shake and takes tablets. It's:

• One daily tablet of sodium.

• Magnesium glycinate tablets stopped his keto headaches.

• Potassium — "For electrolytes"

• Fish oil: healthy joints

“So much of nutrition science is barely a science… I like to listen to my own body and do a one-person, one-subject scientific experiment to feel good.” — Lex Fridman

Four-hour shallow session

This work isn't as mentally taxing.

Lex planned to:

• Finish last session's deep work (about an hour)

• Adobe Premiere podcasting (about two hours).

• Email-check (about an hour). Three times a day max. First, check for emergencies.

If he's sick, he may watch Netflix or YouTube documentaries or visit friends.

“The possibilities of chaos are wide open, so I can do whatever the hell I want.” — Lex Fridman

Two-hour evening reading

Nonstop work.

Lex ends the day reading academic papers for an hour. "Today I'm skimming two machine learning and neuroscience papers"

This helps him "think beyond the paper."

He reads for an hour.

“When I have a lot of energy, I just chill on the bed and read… When I’m feeling tired, I jump to the desk…” — Lex Fridman

Takeaways

Lex's day-in-the-life video is inspiring.

He has positive energy and works hard every day.

Schedule:

• Mantra Routine includes rules, visualizing, goals, and principles.

• Deep Work Session #1: Four hours of focus.

• 10 minutes social media, 20 minutes guitar or piano. "Music brings me joy"

• Six-mile run, then bodyweight workout. Two hours total.

• Deep Work #2: Four hours with no distractions. Google Docs stores random thoughts.

• Lex supplements his keto diet.

• This four-hour session is "open to chaos."

• Evening reading: academic papers followed by fiction.

"I value some things in life. Work is one. The other is loving others. With those two things, life is great." — Lex Fridman