How Statistics Can Help You Navigate Market Volatility

-----------------------------------------

Intro: A few words from Vincent

----------------------------------------

After talking with several of you and hearing your feedback following the launch of our DataHub, we got the message: our outdated Ebook might not be the most efficient way, in 2025, to help you ramp up on our signals — their variety and what fuels them. Our initial plan was to host a webinar on that topic. But we quickly realized that webinars are often a temporary solution, and tend to result in less efficient presentations. Give me Zoom time and a PowerPoint, and I immediately switch into my university professor innie — easily filling three hours with explanations. So, we decided to pivot toward well-scripted, animated videos. They’re more efficient, more evergreen, and better suited for future WealthUmbrella members. Of course, webinars have two components: the presentation, and the live Q&A. Our video capsules will only address the first part. That said, we still plan to host a webinar where we present the YouTube video, followed by an open discussion session. It’s something we can repeat over time as new members join.

Once we agreed on this plan, we geared up Zackary — who, we discovered, has a bit of a hidden Sir David Attenborough in him. Then came the big question: what should be the content of the first videos?

As boring as it might sound, no matter how we framed it, we realized that before we could explain how our signals work, we needed to make sure everyone was up to speed on statistics. Many of our indicators are built around key statistical concepts, so trying to explain them without that foundation would be difficult.

And so, here is our first video about Statistics 101. We’ve done our best to keep it simple and digestible — and honestly, we put in a real effort to avoid making it too dry. That said, while making the video, we realized just how time-consuming it is to produce something of quality (kudos to the YouTube legends like Veritasium — now we truly get it!). Given that our team is small, we quickly saw that continuing production on this video series would delay the release of our WU Advanced Signals as it was slowing us down significantly. So, we made the decision to pause the video capsule project until after we complete the launch of our extended DataHub — with advanced signals — targeted for the end of April. This turned out to be the right call, as it allowed us to use our new Buy the Dip indicators, which proved very helpful during the recent market correction — even in their incomplete form.

On that note: yes, we know the visual of the Buy the Dip indicators in our recent post looked... bad. On one, the blue signal is a strong, high-confidence signal; on the other, it’s a weaker one with lower predictive odds. That was our internal prototype not made for you to see. Don’t worry — the official version will be clean, clear, and easy to understand.

So, back to the videos: we’ll resume production in early May. But in the meantime, we decided to go ahead and release the Statistics 101 video. While it will help you better understand our work, we also believe these are key concepts that can help any investor level up their own approach. Plus, I often refer to these ideas in our market analysis posts — so having this shared foundation will be valuable for everyone.

We hope you enjoy Zack’s first steps as a Spielberg apprentice. It’s not perfect, but I promise you — we’ll learn, improve, and get better with each one. And if you have any comments/constructive criticism, do not hesitate to comment the video, this blog post or contact us at socials@thewealthumbrella.com. We are looking forward to hearing your feedback on this new venture.

-Vincent

----------------------------------------------------

How Statistics Can Help You Navigate Market Volatility

By Zackary Stephenson

You can click on the video above, but here is also a written version for those who prefer reading over listening.

At Wealth Umbrella, we believe that statistics and data analysis shouldn’t be tools reserved only for institutions. In fact, with a few key concepts, even individual investors can begin to navigate market volatility with much greater clarity and confidence.

In this article, we’ll introduce two foundational statistical tools that we use daily in our own risk management strategies. These tools have helped us read through noise, avoid costly missteps, and uncover valuable signals hidden within market data.

Let’s dive in.

Context: Why Distribution Curves Matter

The first concept we’ll explore is how distribution curves help us analyze data within context. This is especially important when adjusting thresholds for indicators in your strategy.

Imagine you’re using an indicator like our Phase Angle signal, which measures the divergence between a fast and slow EMA. Let’s say a threshold of 1.2 signals bullish momentum and -0.8 signals bearish.

These thresholds work well on a volatile stock like Tesla. But apply them to a low-volatility stock like Procter & Gamble (PG), and nothing gets triggered.

Why? Because the two stocks have completely different volatility profiles — reflected in their beta.

Tesla has a beta of 2.29, meaning it moves more than twice as much as the S&P 500. Procter & Gamble’s beta is just 0.41 — far more stable. Over the past two years, Tesla had 224 trading days with price swings of 2% or more. PG had just 17.

And even the same stock can require different thresholds over time. Volatility changes. The Phase Angle thresholds that worked on SPY in the 2022 bear market wouldn’t work in 2023’s low-volatility environment.

This is where distribution curves come into play.

Application: Using Distribution Curves to Normalize Indicators

A distribution curve shows how data points are spread around a mean. Take IQ scores, for example. The average is 100, and most people (68%) fall within one standard deviation (±15 points). Stretch that to two standard deviations and you cover 95% of the population.

This same logic applies to financial indicators. Instead of using fixed thresholds like 1.2 or -0.8, we can express values in terms of standard deviations from their recent mean. This allows us to compare data across assets or time periods on a normalized scale.

The formula is simple:

Using this, the Phase Angle signal becomes adaptive — able to detect “big” moves in both volatile and stable assets. A sharp move in PG might be small in absolute terms but large relative to its typical behavior.

Distribution curves also help detect outliers that are often synonym of abnormal market events. For example, our Dark Pool indicator (which tracks OTC volume) hit a 6.2 standard deviation peak just before the COVID crash in February 2020. That kind of spike is extremely rare — and meaningful.

Sample Size and the Danger of Anecdotal Thinking

Even if you normalize your indicators properly, the job isn’t done. You also need to evaluate whether a signal is statistically reliable. And this is where many investors go wrong — mistaking examples for evidence.

Context: Why Sample Size Matters

Let’s say someone claims (Like a Bitcoin youtuber I have seen recently) Bitcoin is unlikely to rise because institutional investors are short while retail traders are long — and that this pattern worked before the fall 2024 rally.

Sounds logical. Institutions are “smart money,” retail is “dumb money,” right?

But basing an investment thesis on a single example is dangerous. That’s not a sample — it’s an anecdote.

You could use a similar story about options positioning. In January 2023, our options model showed smart money started buying calls just days before the market rallied — and selling before the next downturn. A perfect narrative.

But then, in summer 2024, the market dropped before the options model reacted. The smart money seemed late that time.

So which story is true?

The truth is that long-term statistics show our options model leads the market in about 75% of cases. But that’s not always — and it certainly doesn’t mean one example proves a rule.

To evaluate reliability, you need to account for sample size. So maybe our Bitcoin YouTuber was right with his smart money/dumb money narrative — but it needs to be backed by a larger sample size than just one example.

Application: The Wilson Score and Confidence Intervals

That’s where the Wilson Score comes in. The Wilson Score is a statistical tool that adjusts for small sample sizes and estimates the confidence interval for a hit rate. It’s especially useful when working with smaller data sets — like signals that only happen a few times a year.

Take this fun example: my favorite soccer player, Cole Palmer, scored 9 out of 9 penalty kicks last season. That’s a 100% success rate — but would you really bet your life on him never missing one?

The Wilson Score tells us that with 95% confidence, his true conversion rate is somewhere between 70.1% and 100%. That’s far more realistic — and helpful.

We use the same approach in finance. Many of us have recently witnessed the Sahm Rule — an indicator with a supposed 100% success rate at predicting recessions — fail spectacularly right before our eyes the first time it was used in real time.

Just a quick reminder: the Sahm Rule triggers a recession alert when the three-month moving average of the U.S. unemployment rate increases by 0.5 percentage points or more from its lowest level in the past year.

It was presented as flawless, with 1963 as its starting point, but a closer look into history reveals a failed prediction in 1959. Despite this false alert, it still boasts an impressive 92% success rate over 13 instances. So why did this highly reliable signal let us down the first time it was used live? When we calculated the Wilson interval for these 13 cases, it indicated that the true accuracy could lie anywhere between 66.3% and 98.4% with 95% confidence.

This discrepancy highlights that even the Sahm Rule, while dependable, has a substantial margin for error due to the limited sample size it’s based on. Aware of this potential pitfall, last summer we proposed tweaking Claudia Sahm's original threshold from 0.5% to 0.61% — an option you can find in our related TradingView script. This minor adjustment now effectively gives the Sahm Rule a perfect track record. But let’s be real — if you’ve been following along, you know that even a 100% success rate doesn’t guarantee absolute certainty, especially when the sample size is small. Still, this adjustment improves the Wilson interval to a more robust 77.1%–100%, increasing the lower bound by roughly 11%.

As a result, our modified Sahm Rule with a 0.61% threshold has yet to fail, since the spike in the unemployment rate last fall (2024) — which crossed the regular Sahm threshold of 0.5% — reversed before ever reaching our revised 0.61% mark.

When assessing any strategy’s performance, always start by considering the sample size. If it looks small to you, it might be a good idea to use the Wilson Score to get a clearer picture of the real odds of success.

Final Thoughts

These two concepts — distribution curves and sample size awareness — can help you become a better and more confident investor.

They help you:

• Normalize your indicators across different market conditions

• Avoid misleading conclusions based on one-off examples

• Use small-sample statistics with proper context and caution

• 
  

At Wealth Umbrella, we apply these tools every day — building indicators for both the stock market and Bitcoin. If you want to explore them further, check out our website (linked below). And if you’re new to our approach, welcome — we’re glad you’re here. We hope this article helped you see that rigorous, thoughtful analysis isn’t just for institutions. It’s for anyone willing to learn.

-Zackary Stephenson