OT: How do we know when the party's over

Investment Analysis Clubs Saul’s Investing Discussions
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Recently there was a very long thread on this board regarding what kind of drawdowns we might expect while pursuing a high growth strategy. As the discussion evolved, there was an exploration of how to better understand sell signals in that Saul’s methodology inherently leads to selling at a time significantly after a stock has peaked. In other words, the criteria employed to select stocks appears to be less effective when it comes to divesting a company. @innerpeace123 contributed an AI assisted longitudinal analysis of Saul’s past performance that clearly demonstrated that his incredible performance would have been considerably better if he had a better understanding of when to sell.

A couple of days ago the linked Substack article showed up in inbox. This article sets forth mathematical criteria for recognizing when the top of certain investment vehicles have peaked with respect to business performance, even as the value of ownership may continue to rise. But, inevitably, the price will falter and when it does it tends to be a more or less sudden event.

It is the author’s argument that the AI boom is not at all similar to the dot com implosion, rather, it shares the most important factors that led to the GFC in 2008.

It is more complicated than I can be adequately summarize, but in an effort to abbreviate a fairly lengthy article it boils down to tracking the 2nd derivative of revenue and other significant fundamentals. In case you don’t know how to calculate the second derivative, I will provide an example using revenue.

Take revenue is the fundamental worthy of attention, then % change of revenue over a given time period is the first derivative and % change of of the percentage change in revenue, or the rate of change in revenue over the same period of time is the second derivative. When the rate of change, the 2nd derivative starts to decline over a series of time periods the author argues the business has already peaked, the value of holding an ownership position is destined to decline in the not too distant future - but exactly when that might occur remains illusive. Much of the argument makes sense to me, but I would appreciate comments from others (if this post survives a monitor review).

Here’s the link:

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This is an excellent article, thanks for posting. It might be off (or above) topic, but to bring this towards a more on-topic and directly actionable place, there are a number of takeaways I have beyond the value of second level thinking and second order derivatives…

  1. This is consistent with almost every other evaluation I have read about the nature of the potential AI bubble that we face - that this should be characterised as a credit/debt bubble (a la the GFC) than a technology adoption bubble as per the Dotcom situation

  2. There are very clear potentially higher vs lower risk plays involving OpenAI and its ecosystem (higher risk) vs Anthropic and its ecosystem (lower risk) in terms of offerings/positionings, finances and value chain counter parties/associates.

  3. The higher risk Open AI allied cohort includes CoreWeave and Oracle as the most exposed. But effectively many neoclouds and much of the value chain and counter parties also face risk.

  4. Some counter parties amongst the hyperscalers are better placed than others to survive/prosper in the face of any fall out

  5. The article highlights capital raising funding rounds as the potential trigger points, although I thought it missed out the continued cuts in opex (mass layoffs) that hyperscalers are continuing to make (even just this week) in order to continue funding Capex spend

  6. What wasn’t addressed was the potential for disproportionate demand scaling with advances in token efficiencies that could be secured that extend uses cases and demand in an exponential way

A good read and thanks for sharing.
Ant

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If the case is to be made that the second derivative growth, or the rate of growth is the most important, there are plenty of businesses this board is following that show massive steps up in the rate of growth.

A good example is Micron where the rate 2nd derivative rate of growth recently skyrocketed during the period when revenue went from,

11.3B → 13.6 → 23.9

The growth rate from 11.3 to 13.6 is 21%, and the growth rate of going 13.6B to 23.9B is 75%. This means that the 2nd derivative growth went from 21 to 75, or 54 percentage points of growth. Just using this one period as an example, obviously the acceleration rate is not going to be a perfect curve.

Not really sure on that case about the fund raising or valuation leveling off makes a real issue for OpenAI? I’d expect a business that is growing rapidly, to have a larger rate of growth in the early seed rounds. As they are progressing to an IPO, I would expect the valuation to have a slowing down growth rate. For example, if a business raised at a valuation of 100B, and the next round was at 300B, I would not expect this company to be 3x’ing+ on subsequent rounds.

Maybe OpenAI will fail because of their business model is not working. The same could happen with Anthropic. But it is likely they are failing because another company built a superior system or model. It is just with this current cycle of innovation, it is happening so blindly fast, the boom/bust cycle is likely to be accelerated as well. Either way, even if I thought there was a good chance of a cascading effect for the economy, I would continue to invest. This is because there will be plenty of companies that continue to grow through those conditions, whether in AI or not.

I’m finding it hard to make sense of parts of the article. For example, this quote here makes no sense to me,

The capex arms race is a Nash equilibrium, but a conditional one: it holds only while the market rewards the next dollar of spending as a call option on growth.

I’m not sure what the CapEx arms race being at Nash Equilibrium would mean, in that each actor can’t make a mistake, or each move is equal to another. Also I don’t know what is meant by a “call option on growth”. My honest take is here a good portion of the article is written by AI or AI-assisted at a minimum. There’s a lot of parts like that which kind of sound like they should make sense, but even if you re-read them it does not make any more sense.

Maybe the point is accurate about the 2nd rate of growth. That is something this board has discussed over the years about looking for companies where the quarter or quarter jumps are increasing.

I would make the case the market is offering more of these large accelerations in the rate of growth than ever before. Micron is a relevant example, I believe because it so clearly meets the criteria the board looks for.

If we look back at the Zoom example on this board, there was hardly anyone saying it didn’t make sense to invest because it is only growing because of covid. At the time it was up in the air how long work from home would last. Similar to now, nobody knows how long the demand will exceed supply for memory. Still if the memory companies can continue to grow strongly even for a minimum of a few more years, the returns in the stocks are likely to be phenomenal.

I’m surprised to see so many investors talk about pulling out of the market, or trying to figure their way out. From my perspective this market is offering so many compelling opportunities right now, I’m finding the biggest challenge is how to narrow down to which companies may over perform the most.

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@wpr101 as usual, you have terrific insights. However, I wish to point out that author did not suggest that 2nd derivative analysis was a necessary or sufficient indicator of a market downturn for every equity investment. He was quite explicit in suggesting that it was appropriate for investments that appeared to resemble the credit crunch that brought on the GFC in 2008. To the best of my recollection, he was moot on other types on investments.

So, looking at Micron as either support or a counter-argument may or may not be valid. In fact, just before I read your comments I was attempting to reason through this fundamental difference. Needless to say, I have not come to any conclusions - I thought back testing studies my help resolve the issue, but the time and labor to do so seems intimidating.

Possibly, Claude could be of assistance, but I don’t have a subscription and the cost of subscribing simply to perform this study (which may well be inconclusive) gives me pause.

Separately, but related, there are a large number of indications that the AI investment boom may be curtailed sooner than generally anticipated. In that this entire thread is somewhat off topic, I won’t dwell on it, but here are just a few examples of potential inhibitions to further growth. Communities are rejecting AI factory build outs. The recent occurrence of a META data center polluting the municipal water supply for the city of Cheyanne, WY with heavy metals and superbug bacteria is just one instance. The grid stress, water consumption, noise, water and air pollution and general disregard for the communities in which these monstrous campuses supporting AI is resulting in a lot of pushback. The overwhelming pushback against sensible regulations for AI with respect to both project citing and general use of AI is being met with opposition by a growing contingency of congresscritters. Grok’s display of lifelike, explicit and compromising images along with the targeting of a girl’s school in Iran are examples. A large segment of college aged populations here and abroad may impede adoption. The utter insensitivity and arrogance with which the human resource at many of these AI competitors is appalling. I’ve read of engineers hoping to be fired in order to collect the severance package. I could go on, but these factors and several others are worthy of bear case consideration when trying to assess the duration of related AI investments.

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This whole thread was a bit dubious on Saul’s board to start with but this last post has really jumped the shark. We all have opinions on many subjects in life but this is not the appropriate place for standing on a soapbox for OT subjects.

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@Buffjan2 I am responsible for the “last post.” The one that “jumped the shark” (some still remembers Happy Days) correctly asserts the entire thread is dubious as it does not discuss a specific company. I said so at the outset and labeled the original post as such.

Nevertheless, I did address facts, not opinions, actual bona fide, documented facts that are directly related to the investment thesis that underlay a large number of the companies that we do discuss on this forum and which are often neglected. These facts, are IMO relevant to investments which we make with our real dollars. I personally am invested in several companies that have remarkable growth almost entirely due to their relationship to the AI build out.

Understanding negative factors that play an important role in the future of one’s investments is generally considered a good practice. Ignoring important factual bear case information because you don’t like it (or any other reason) is akin to burying one’s head in the sand.

If you disagree with the facts I have cited please provide countervailing evidence that would bring those facts into dispute. If you feel these facts are irrelevant or unimportant, that’s your prerogative. But to simply assert that facts are opinions is disingenuous at best.

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It is common political rhetoric to cloth opinion as fact. It does not convert opinion to fact, it just remains opinion. Anger clouds one’s ability to see the difference.

Nonetheless, there is plenty of room for opinions in discussing a company on this board when it stays within the proper lane.

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I would like to take this offline, as it feels like it’s getting personal. But there’s no way to reply to you directly. Let me refer you to the linked YouTube channel focused on AI. The host, El is a data scientist. I encourage you to watch a number of her videos.

El is an AI advocate. In addition to her job as a data scientist, she is also a technologist, researcher and commentator. Most of her commentary is in regard to what she perceives as problems with AI engaged businesses and some of the documented executive decisions and actions. Her opinions are based on observed facts, some of which I have cited. I think she’s knowledgeable, intelligent and analytical. I agree with some of her opinions and disagree with others. Nevertheless, I have not expressed her or my opinions. I have cited what I believe to be facts. As I said before, if you have evidence to the contrary, please provide it. So far, you have not done so. You have simply reasserted that I have voiced my opinions.

I will admit that I coined the word “congresscritter.” That’s not an opinion, it’s an abbreviation for Senators and congressional representatives.

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Fair clarification on the second-derivative framework being specific to credit-bubble-style investments rather than general equity analysis.
I don’t share the view that the environmental, regulatory, and cultural concerns raised materially affect the investment thesis for AI infrastructure. Different read.
More fundamentally, drawdown is part of investing. Growth investing carries drawdown risk as a structural feature, if you can’t sit through 50-80% drawdowns without capitulating, this style will destroy your returns and mental health. Choose a different strategy that matches your actual risk tolerance.
The way to handle it is to have living expenses covered separately like Saul, then the portfolio drawdown is uncomfortable but not existential.

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I agree. I do have separate funds for living expenses and I have a separate portfolio for income production. I remain invested in growth stocks, many of them related to the AI buildout. I do not see that as a good reason to completely ignore realistic exogenous threats to the thesis. They are real. Make of them what you will.

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Back on topic here: Saul does write about when to sell a stock. It’s

  1. Don’t get a stock get over 20% of your portfolio

  2. Reinvest proportionally to your confidence in the stock.

Essentially, if the your holding is not already oversized, sell based on your assessment of future performance of the company.

I’d warn against mechanical investing style methods like 2nd derivative of revenue curve or something similar. Or to be more precise, it might be valid, but it’s not Saul’s method.

Instead, read the call transcripts and understand what is being said. With smaller companies there might be sharper swings in the revenue curve that are completely warranted and do not indicate a faltering business. They go both ways. The CEO may warn you that the big revenue jump is due to one time regulatory change or due to an aquisition. These have a sharp upturn and then a sudden flattening effect which your 2nd derivative may pick up but fail to interpret properly.

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I appreciate your well reasoned and unemotional reply. I don’t disagree with you. I have not adopted 2nd derivative analysis as a technique for evaluating investments - but I thought it was an interesting observation and wondered if it could be extended beyond credit bubble situations. I was halted due to the labor involved in back testing to determine if there was an historical basis to dive deeper.

I was surprised (maybe I should have expected) that some commentors seemed angry in their replies. Especially, when the conversation was broadened when I cited the growing objections from young people, communities that were or likely will be adversely impacted and even some politicians. IMO, these are factors worth considering. It’s OK to disagree, but to assert that mentioning them demonstrates that I am clouded with anger . . . ? And to be clear, these are observations. I’ve not made investment decisions based on these facts, but I am looking at my allocations. I am looking at the level of diversity in my companies (frankly, a lot of AI infrastructure/tech concentration).

And I am really puzzled about why we should just tolerate 50% or more drawdown in the value of our portfolios if there might be a fairly reliable way to actually sell high and buy low. I think it’s worth exploring extensions to Saul’s method that might help with a better understanding of sell signals irrespective of whether the analysis rests on quarterly reports or external factors or both.

I will not post any further on this thread.

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Having read the article I can kind of understand how people here could react emotionally to it. Its verbiage is very flowery, one might say even pompous and its tone sounds overly dismissive.

When we look at companies here on these boards, we always talk about YoY growth. That’s the first derivative, the rate of change. What we also do is line up the YoY growth from 8 consecutive quarters next to each other and remark that YoY growth has been declining. In that case we are talking about the second derivative, the rate of change of the rate of change.

In fact, everybody in growth investment is talking about the second derivative all the time. If a company had a YoY growth of 25% in Q1 and now in Q2 the YoY growth is 15%, everyone will expect the CEO to explain the decline in the growth rate. The typical answer is that revenue is seasonal so it’s not a big deal. It’s more notable when when 2025 Q1 YoY growth was 25% and 2026 Q1 YoY growth was 15%, because that is not seasonal. The explanation can be that the company is simply not growing as fast, but it also might be that there was an aquisition in 2025 that had distorted the revenue growth in that year but in fact the actual growth is accelerating now. One needs to read the transcripts…

But anyway, when the article says “nobody is talking about the second derivative” it sounds condescending to finance folks because they do talk about it, they just don’t use that fancy name for it.

Look at the black graphic in chapter II. in the article. It points a big arrow to the place where the red line (second derivative) crosses 0 and says “growth stops accelerating here”. But gee, isn’t it already obvious from looking at the yellow line? Isn’t everyobody already pointing out when growth rate starts dropping without actually calculating the 2nd derivative as being below 0?

The second thing I would remark on the article is that I think it is wrong. From the article:

And the entire financing architecture erected over the past twenty-four months is a bet on S″ - on the acceleration of demand continuing - dressed up as a bet on the level.

This is wrong. The contention in AI is not how much the demand is going to grow but rather that the costs are going to grow at the same rate as revenue. This was the same contention in the dot com bubble. Analysts would look at Amazon and say that the same physical constraints that make the company burn $5-10 per package shipped are going to be in place regardless of how many packages Amazon will process and that people will not pay that markup. Or that the backend infrastructure of broadcast.com will have to grow proportionally to demand and it will not be able to compete with traditional broadcasters.

They were wrong in principle. Amazon could scale the costs down and even though broadcast.com couldn’t, Youtube manged to do that a couple of years later.

I think we are in a similar situation to the dot com bubble. AI providers will be able to scale their services disproportionately to their costs and will be successful. We just don’t know which ones. It’s also notable that at the height of dot com companies were valued at 200 times revenue or more. Anthropic is expected to IPO at around 40 times trailing sales.

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One last remark. Think a closely at what the article is saying in chapter II. Look again at the black chart:

It’s saying that analysts look at the peak of the yellow line (YoY growth is highest it’s ever been) and say the stock is in excelent shape. The author on the other hand looks at the second derivative being 0 and says this is the beginning of decline.

What the author is doing there is impossible to calculate in reality. Let’s consider a realistic example:

It’s march 2026 and you are looking at the following trailing results of YoY growth:

25Q2: 15%

25Q3: 19%

25Q4: 25%

26Q1: 29%

At this point the news would be quite excstatic about the results. But unbeknownst to everybody, in June the company is going to report 26Q2 growth as 25%. And past that it will be clear that 26Q1 was the apex of growth and the company was going to decline.

But how will you know that in March 2026? How will you calculate the 2nd derivative being zero without knowing the future results?

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