What’s the premise behind my bullishness for PBR stock and the oil market in general? It’s not simply that the Iran crisis is back on the geopolitical frontline. Sure, that is a fundamental factor but it’s also a well-known, well-digested news item. Reading yesterday’s article from Reuters is not going to provide you a trading edge today.

Instead, the premise is market structure; specifically, how certain structures signal a probability of an upcoming transition. Philosophically, I rely heavily on Markov chains. The question is as follows: given a particular market structure (or behavioral state), what is the probability of it transitioning to another, different structure?

Again, I don’t really care about the fundamentals or the technical — they provide some descriptive context of how a ticker like PBR stock ended up where it is. But I don’t believe that such knowledge inherently provides alpha. Frankly, it’s more like delusions of grandeur. Think about it: why would reading yesterday’s news or drawing arbitrary lines on a chart consistently lead to exploitable mispricings?

Instead, my philosophy revolves around the concept that future market returns represent an independent variable. What’s my evidence? Well, consider the opposite argument. The assumption that asset returns are completely Independent and Identically Distributed (I.I.D.) — or a pure, memoryless random walk — is fundamentally refuted by theoretical econometrics and empirical market data.

In other words, what happens tomorrow depends on what happens today. That’s the core Markovian philosophy when applied to the financial markets. It’s here that I’m in full agreement, actually, with fundamental and technical analysts.

But the difference is that I use an algorithm to measure the outcomes of these dependent variables. Enticingly, my algorithm points to a potential bullish opportunity in Petrobras stock.

A Market Footprint Opens the Door for PBR Stock

In earlier StockEarnings.com articles, I made specific trading ideas for Exxon Mobil and Petrobras. For the former, I discussed the opportunity present in the 138/141 bull call spread expiring July 31, while for the latter, I focused on the 17.50/18 bull spread expiring July 31.

Unless the floor decides to drop out, those trades are well on their way to full profitability. What’s compelling is that I used the exact same model to formulate those options strategies. This doesn’t mean that my model is the absolute truth because that’s not true — I get things wrong all the time. However, what you see is what you get with me. Whatever the trading idea, it’s going to come from the same methodology.

Indeed, the main reason why I’m interested in Petrobras stock at this hour is that the security just flashed an exploitable trading signal. In the last 10 weeks, the number of up weeks and down weeks was split 50/50. However, the overall slope was negative across the 10-week period, which represents a unique situation.

Since January 2019, there have been 375 rolling 10-week sequences. Of this figure, 63 comprised of the above 5-5-D quantitative signal. Here’s where the fun part comes in. If we were to look at where PBR stock may end up over the next 10 weeks using an aggregate of all quant sequences, the expected forward distribution would land between $18.95 and $19.30 (assuming a starting price of $19).

With probability density only peaking at $19.08 or thereabouts, the expected performance when buying PBR stock randomly offers practically no advantage. When you factor in transaction costs, you would risk a negative expectancy over time.

However, when you buy PBR stock after it flashes the 5-5-D sequence, you may expect a forward 10-week distribution between $18.50 and $20.40, with probability density peaking at $19.48. That’s not much better than the aggregate baseline but keep in mind that the positive variance isn’t orderly and linear.

Specifically, on the fourth week following the flashing of the above signal, the median endpoint is a move up of approximately 4.74%. That would put PBR stock at the equivalent of around the $19.90 price point at the Aug. 21 expiration date.

Putting Two and Two Together

So, assuming you believe the above inductive model, there’s an enticing argument to consider buying the 19.50/20 bull call spread expiring Aug. 21. Attractively, the net debit per spread is only $20 so you can penny-pinch your exposure to this trade. Should Petrobras stock rise through the second-leg strike ($20) at expiration, the maximum payout is 150%.

What does that mean? You pay $20 for the bull spread and if PBR stock hits $20 on Aug. 21, you collect $30 of profit.

That may sound too good to be true, and this is where Wall Street comes into play. Currently, this spread’s breakeven price is $19.70, which is considered a low-probability affair. In fact, the market assigns a probability of profit of only 36.6%. It’s here that many, if not most, conservative traders ignore the deal.

Nevertheless, the core mathematical tension is that this probability stems from the Black-Scholes model, which assumes that future stock outcomes are independent variables. I’m not convinced by this assumption because the overwhelming evidence (in my opinion) points to future returns being dependent variables; that is, the future outcome depends on or is heavily influenced by immediate prior outcomes.

As a quick example, if a security falls 10% in a day, it’s most likely going to react differently than if said security jumped 10% instead. Black-Scholes, as a risk-neutral, lognormal environment, structurally treats both circumstances the same, thereby exposing options priced using this model to potential distortions.

That’s actually my argument, that the options pricing for PBR stock is distorted in your favor. Of the 63 times that the 5-5-D signal has flashed, the ticker has exceeded the $19.70 breakeven price a total of 32 times. Therefore, the conditional, observed probability of profit could be 50.8%. If true, you’re getting over 1,400 basis points of free odds.

A Brazilian majority state-owned multinational corporation, Petrobras has suffered a downward slide between the end of April and the beginning of July. However, with the renewed hostilities in Iran, circumstances have cynically moved positively for PBR stock. Over the past five sessions, for example, the security has gained more than 7% of value.

To be fair, the afterhours session on Friday has demonstrated a sideways consolidation. However, with the latest geopolitical spark that was reported on Saturday evening by the New York Times, it’s quite likely that PBR stock and the broader fossil-fuel energy market will rise.

Of course, that’s an obvious inference as a renewed conflict would again impose an inflationary crisis on the global economy, not to mention the catastrophic energy supply chain disruption. Because there’s so much at stake, there’s a non-zero probability that the Trump administration will back down. From just a political angle, the war is deeply unpopular. Plus, it wouldn’t be the first time the White House walked back its previously tough stance.

With that in mind, I’m looking for a near-expiry debit-based options trade. By this, I believe that an argument could be made for a directional trade. Under this framework, I want to pay a debit (start from a cash outflow position) to bet on a particular outcome materializing. Essentially, a debit spread on PBR stock is a low-probability, high-reward wager.

However, it’s more than possible that the way the “low probability” is measured by the market is flawed, opening a door to astute retail traders.

How the World Cup Provides a Lesson on Petrobras Stock

For sports fans everywhere, this year is particularly magical because of the World Cup. Even casual observers have tuned into the soccer tournament as they cheer on the globe’s best players. But what’s fascinating about the beautiful game is how the structure changes as soon as one team scores.

Typically, following the initial kickoff, both teams are cagey — feeling each other out while making sure not to make an early mistake. But as the game drags on and a team eventually makes a breakthrough, the nature of the competition changes. Suddenly, the team with the lead has an incentive to be more defensive-minded, while the team that was scored on must chase the game.

At half-time, each manager could make strategic and personnel changes — all in response to one goal. Now, the question for PBR stock or any other publicly traded security is this: if a soccer team changes how it operates based on shifting conditions in the game, why would the equities market be any different?

Here’s a clear, quantitative example. In the last 10 weeks, PBR stock printed only three up weeks, leading to a downward slope. Before I get into the forward 10-week distribution conditioned for this 3-7-D sequence, ask yourself this: would Petrobras stock respond differently if it had printed only three down weeks, thereby leading to an upward slope?

My theory is yes, the market would almost certainly act differently. Why? Because nowadays, the dominant forces in the equities sector use algorithmic or rules-based trading. When the algos of advanced hedge funds notice that PBR stock flashes a 3-7-D sequence, it may interpret that as a temporary discounted opportunity. Even better, the data puts inductive weight on the theory.

Conditioned for the 3-7-D sequence (which has flashed 24 times on a rolling basis since January 2019), the expected 10-week forward distribution of PBR stock would likely stand between $16 and $22, with probability density peaking around $18.20. That’s assuming a starting price of $17.32, Friday’s close.

Why is this observation significant? Because as a random baseline, the expected forward distribution of PBR stock would be between $17.25 and $17.60, with probability density peaking near $17.41. On average across the spectrum, you’re looking at a 4.54% positive variance.

Playing the Inductive Card Shrewdly for Petrobras Stock

Although the forward distribution of Petrobras stock under 3-7-D conditions statistically has a better expected performance outcome than the random baseline, the trajectory may not be linear. From an inductive viewpoint, PBR has a tendency of rising through the first four weeks before taking a conspicuous dip on week 5.

Obviously, there’s no guarantee of the uniformity of nature, meaning that anything could happen this time around. However, if we were to play the numbers, the 17.50/18 bull call spread expiring July 31 could be interesting. Over the next three weeks, PBR stock would be expected to rise through the $18 level, which should trigger the second-leg strike. Doing so at expiration would result in a 150% maximum payout.

What’s really eye-catching here is the net debit, which is only $20 per spread. It’s a tantalizing opportunity but the reason is that the market only assigns a probability of 38% that PBR stock will rise to $17.70, the breakeven point for the above spread.

While 38% sounds dangerously low, this figure is calculated largely by the distance (in standard deviations) the spot price is from the target threshold, assuming a risk-neutral, log-normal distribution. However, as I just explained with the World Cup example, a distribution of outcomes is likely to change based on shifting conditions.

In this case, we shouldn’t calculate the probability of PBR stock assuming risk neutrality. Instead, we must calculate it based on its current sentiment state, which is negative. Observationally, because of the extended negativity, there’s a greater chance of positive mean reversion.

Fundamentally, I dispute the market’s low probability of profit (reaching breakeven). Indeed, the odds that Petrobras stock rises above $17.32 by the end of week 3 is 70.8% (or 17 occurrences over 24 times). I wouldn’t be surprised, then, if the chance of PBR hitting $17.70 is between 58% to 60%, not 38%.