At a cursory glance, Broadcom (NASDAQ: AVGO) doesn’t seem particularly attractive for long-side debit options traders. Down more than 13% in the trailing month, AVGO’s equity loss alone is painful. Factor in the leverage of derivative contracts, and absorbing such red ink becomes even more ghastly. Still, if the ticker’s history is any indicator, the current malaise may translate into a contrarian opportunity.
It comes down to the commonly accepted concept of mean reversion. Basically, when a top-tier security like AVGO stock stumbles, the assumption is that the corrective pressure will eventually die down. Once enough weak hands are flushed out of the system, the bulls may move in, thus driving the ticker higher to at least the previously established baseline — perhaps even beyond.
However, much of this reasoning in the financial publication sector often comes down to author intuition or vibes. Don’t get me wrong — vibes can occasionally produce “correct” answers. But such a broadly subjective worldview lacks discriminatory power. If the author was always going to declare a bullish sentiment no matter what, this methodology doesn’t distinguish from when the opportunity might be bearish.
No, I prefer an empirical approach. While I don’t deny the presupposition of mean reversion, I want the claim to be grounded in reality rather than emotion. One way we can better infer a future outcome for Broadcom stock is to deploy Markov chains. But before we go there, we need to understand what the game of probabilities is all about.
AVGO Stock and the Random Walk Theory
As a basic standard, the probabilistic implications of where an optionable public security could finish at expiration is derived by the Black-Scholes family of calculations. Undergirding this model is the presupposition that the target ticker — Broadcom stock in this case — will undergo a random walk between now and the selected expiration date.
Further, the volatility input (meaning the implied volatility or IV, which is generated from actual orders) is integrated into the framework and stays constant throughout the journey to the expiration date. As such, Black-Scholes assumes a random, risk-neutral environment.
To get a basic understanding of the likelihood of AVGO stock hitting a particular terminal price at expiration, you may consult OptionCharts.io, which is a free resource that is incredibly useful for retail traders. Perhaps most notably, the resource’s Probability Distribution screener lays the basic groundwork for projected expectations.
It’s an intuitive image. The center of the distribution represents the region the model considers most plausible. As you move farther into either tail, the modeled outcomes become progressively less probable.
This is all basic stuff, and you probably assumed the implications by instinct. From the long side, the further away the target price is from the current spot price, the more incrementally difficult it will be to hit by the selected expiration date.
However, this projected trend presupposes that distance to spot is the core driver of market probabilities. Further, because Black-Scholes assumes stochasticity in its formula, whatever inputs that are plugged in at the onset will always visually lead to the same graphical structure (i.e., a standard bell curve). That necessarily means that under this construct, the future is independent of the past.
In other words, it doesn’t matter if AVGO stock incurred…
- five consecutive up weeks,
- a 20% collapse followed by a recovery,
- unusually strong momentum,
- a volatility shock,
- some specific sequence of returns.
Black-Scholes will always spit out a bell-curve-shaped probability distribution. Personally, I don’t find this presupposition convincing, which is why I turn to Markov chains.
Under the probabilistic axiom of Russian scientist and mathematician Andrey Markov, the future state of a system depends on the current state. The defining feature of the Markov axiom is that the next link in the series of sequences depends only on the current state, not the entire earlier chain.
There is a key distinction, though, that often confuses newcomers. Markov does not necessarily mean “ignores the past.” It means “whatever past information matters has been compressed into the present state.”
From this axiom, we arrive at the key conclusion that makes Markov chains — and simulations based on this principle — tick: the future is dependent on the relative past.
That matters for AVGO stock because we’re not just trying to calculate its probabilistic trajectory “as is” like Black-Scholes is effectively doing. Instead, to better infer where it might go over the next several weeks, we need to understand what happened to AVGO in the previous several weeks.
Specifically, for the last 10 weekly candlesticks, six of them were in the red, leading to a downward slope across the period. Said differently, 60% of the defined time period resulted in bearish trades. Moving forward, the assumption is that Broadcom stock may mean-revert if a good portion of the weak hands have been flushed out.
But how do we know that this flushing has occurred? That’s where we run a Markov simulation. We know that since its public market debut, AVGO stock flashed this 4-6-D sequence a total of 96 times. On the fifth week following the signal (which corresponds with the Oct. 16 expiration date), AVGO has hit the equivalent of the $380 price point 52 times or a success ratio of 54.2%.
Now, it’s time to do some comparative calculations.
Identifying an Intriguing Vertical Spread
One idea to potentially take advantage of this upward trend in Broadcom stock is the 370/380 bull call spread expiring Oct. 16. For a net debit of $440, traders will be hoping that AVGO triggers the $380 second-leg strike price at expiration. If it does, the maximum profit would be $560, a payout of over 127%.
While this trade sounds enticing on paper, bear in mind that Wall Street assigns a probability of 37.6% to trigger the breakeven threshold of $374.40 at expiration. To hit $380 proper on Oct. 16, the odds slip to a very modest 31.25%.
Just to reiterate, my Markov simulation provides a probability of full profitability of 54.2%. To break even, the odds improve to 61.5%. That means out of 96 times that the 4-6-D signal flashed, AVGO stock hit the threshold 59 times.
Now, the question is, who’s right? It’s here that we all have to be honest with ourselves. Anytime we make a forecast about the unknown future, we have to start with a presupposition. I’m presupposing nonrandom behavior following an extended bearish streak. Wall Street is presupposing a random walk.
As a final defense, most of us generally believe that the equities market is nonrandom — otherwise, what would be the point of reading financial articles looking for an edge? All I’m really saying is this: if you believe in nonrandom price discovery, why would you depend on a random model?
