2025-10-01 10:51 Tags:Mentol Models

Mean Reversion

What is Mean Reversion?

Mean reversion is a theory implying that asset prices and historical returns gradually move towards the long-term mean, which can be based on the economy, industry, or average return within a set of data.

Trading with Mean Reversion

Applying that knowledge, investors are capable of measuring and determining when to buy under the mean and sell above it. Mean reversion is also used in options pricing to better determine how an asset’s volatility fluctuates along with its long-term average.

Investors employ mean reversion strategies to capitalize on asset prices that have deviated significantly from their historical mean.

I would say significantly is the heighlight.

How Catalysts Affect Mean Reversion

It is important to recognize that unexpected highs or lows can ultimately imply a shift in the nature of the stock, caused by events such as positive or negative news.

Generally, returns of normal patterns are not always guaranteed, but it is indeed still possible for assets to experience mean reversion in the most extreme circumstances. Nonetheless, much like any event, it is difficult to fully determine how market activity for securities will be affected by the news.

Random Walk

Instead of reverting back to the mean, stock prices may lead to a random walk post-shock. A random walk is a process when prices do not return to previous levels, nor do they gradually move towards the mean. For example, an increase in the momentum of the stock may lead to a greater deviation from the mean.

Musings on Markets

Mean Reversion: Basis and Push Back

The notion of mean reversion is widely held and deeply adhered to not just in many disciplines but in every day life. In sports, whether it be baseball, basketball, football or soccer, we use mean reversion to explain why hot (and cold) streaks end. In investments, it is an even stronger force explaining why funds and investors that fly high come back to earth and why strategies that deliver above-average returns are  unable to sustain that momentum.

At the risk of over generalization, much of market timing is built on time series mean reversion, whereas the bulk of stock selection is on the basis of cross sectional mean reversion. While both may draw their inspiration from the same intuition, they do make different underlying assumptions and may pose different dangers for investors.

🕰️ 1. Time-series mean reversion (Market Timing)

• What it means: Looking at how one variable (say, the market P/E ratio, or interest rates) moves over time, and betting it will go back to its historical average.

• Example:

  • If the S&P 500 CAPE ratio is way above its long-term mean, you might predict a correction.

  • If inflation spikes unusually high, you expect it to come down toward its historical level.

• Underlying assumption: The past average is a “true anchor,” and forces (policy, competition, investor psychology) will pull the series back.

• Danger: Sometimes the world changes structurally. For example, tech companies really did earn higher margins after the internet scaled — waiting for “mean reversion” could leave you out of decades of growth.

👉 This is what people try when they “time the market” by saying: “The market is too high, it must fall soon.”

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📊 2. Cross-sectional mean reversion (Stock Selection)

• What it means: Looking at differences across companies at one point in time, assuming extremes won’t last.

• Example:

  • A company with unusually high profit margins vs peers → assume competition will erode those margins.

  • A company with unusually poor returns → assume survival pressure or recovery will push it closer to peer averages.

• Underlying assumption: Industries are competitive, and competitive advantages erode; no company stays extreme forever.

• Danger: Some companies do have durable moats (Apple, Coca-Cola, McDonald’s). Their high returns persist for decades, and waiting for mean reversion makes you underestimate them.

👉 This is what many “value investors” try when they say: “This stock is too cheap compared to peers; eventually it will revert.”

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这个真的需要辩证看待 首先Cross-sectional mean reversion我就觉得不行 均值回归很难在长牛市场实现 但是你又怎么知道这是长牛市场呢？

The Fundamental Critique

The first is aging, with the argument easiest to make with individual companies and more difficult with entire markets. As companies move through the life cycle, you will generally see the numbers for the company reflect that aging, rather moving to historic norms. That is especially true for growth rates, with growth rates decreasing as a company scales up and becomes more mature, but it is also true of both other operating numbers (margins, costs of capital) as well as pricing metrics (price earnings ratios and EV multiples). While markets, composed of portfolios of companies, are less susceptible to aging, you could argue that aging equity markets (the US, Japan and Europe) will exhibit different characteristics than they did when were younger and more vibrant.

• The second is technology and industry structure, shaking up both the product market structure and creating challenges for accountants. This is true clearly at the company level, as is the case with retailing, where Amazon’s entry and subsequent growth has laid waste to historic norms for this sector, bringing down operating margins and changing reinvestment patterns. It is also true at the market level, where an increasing proportion of the equity market (say, the S&P 500) are service and technology stocks and the accounting for expenses in these sectors (with many capital expenses being treated as operating expenses) creating questions about whether the E in the PE for the S&P 500 is even comparable over time.

• The third is changes in consumer and investor preferences, with the first affecting the numbers in product markets and the latter in financial markets. For instance, there is an argument to be made that the surge in index funds has altered how stocks are priced today, as opposed to two or three decades ago.

Looking at this data, at least, the evidence seems strong that a high CAPE today goes with lower stock returns in future periods, with the mean reversion becoming stronger for longer time periods. In fact, if you are one of those who lives and dies by statistics, using today’s CAPE of 27.27 in this regression will yield a predicted annualized return of 4.30% on stocks for the next 10 years:

Expected annualized return in next 10 years = 16.24% - 0.0044 (27.27) = 4.30% 16年的文章 但其实一直在长牛 如果空仓那错过了多少

The CAPE’s timing payoff is greater when it is used as a buying metric than as a selling metric. In fact, you make a positive payoff from using a low CAPE as a buying indicator over the entire period but using it is a signal of over priced markets costs you money in both time period. 有意思哈

Conclusion

Both in academia and in practice, I see more and more use of statistical significance as proof that you can beat markets and my reason devising and testing out market timing strategies with CAPE were not meant to be an assault on CAPE but more a cautionary note that statistical correlation is not cash in the bank. This may also explain why there are so many ways to beat the market, on paper, and so few seem to be able to deliver those magical excess returns, in practice.

反正我觉得不适合只用这一种工具 但可以参考 尤其在市场恐慌时 我觉得是可以利用它大量买入但卖出确实很难去选择

What Mean Reversion Is, and How to Invest Using It

Famed value investor Jeremy Grantham argues that “profit margins are probably the most mean-reverting series in finance, and if profit margins don’t mean revert, then something has gone badly wrong with capitalism. If high profits don’t attract competition, there’s something wrong with the system.”

Buffett agrees, and in 1999, he stated, “you must be wildly optimistic to believe profits can remain high for any sustained period.”

I agree

WHAT CAUSES MEAN REVERSION?

At an industry level, competition is the primary reason why mean reversion occurs, as fast-growing or highly-profitable industries attract new challengers.

MEAN REVERSION HAS TWO CRITICAL IMPLICATIONS FOR INVESTORS

Highly-profitable companies growing faster than the average tend to slow down and become less profitable over time.

Companies that were once profitable but now have declining profits, slowing growth, and are cheaply priced, may actually perform better over time.

A simple mistake that investors make is overpaying for fast-growing profits at present by extrapolating that growth unrealistically into the future.

Consequently, you might think that a company growing so fast would warrant paying almost any price to own it. However, your return depends not only on the company’s growth rate, but also the multiple, or price, you paid for that growth.

我们好像太过于高估高增长公司给我们带来的回报 不值得花过高的价格去买？

The Calculus of Value

Value

Investment assets – things such as stocks, bonds, companies, and buildings – have a value, which is sometimes referred to as their “intrinsic value”: what the asset is “worth” at a point in time. This value is subjective. It can’t definitively be found anywhere – not even by AI, as far as I know – and opinions will differ as to what it is.

In my parlance, the value of an asset is derived from its “fundamentals.” The fundamentals of a company, for example, encompass a great many things. These include its current earnings, its earning power in the future, the steadiness or variability of its future earnings, the market value of its component assets, the skill of management, its potential to develop new products, the competitive landscape, the strength of its balance sheet, and the myriad additional factors that will influence the company’s future. Ultimately, the totality of an asset’s fundamentals constitute its earning power, which in turn is the source of its value.

A company may own land, buildings, machinery, vehicles, and natural resources such as mineral deposits or forests, and even facilities that allow it to derive electricity from river water or sunshine (which it obviously doesn’t own). These are tangible assets, and there’s often a market for them and a realizable price. But a company may also have assets that are intangible, such as patents, trade secrets, knowhow, research capability, reputation and image, human talent, management skill, and culture. Some of these may be transferable and salable, but others are not.

All the assets mentioned above have earning power individually, and in combination they create a company’s overall earning power. A company’s earning power almost always exceeds the sum of the earning power of each of its individual assets taken in isolation. Combining individual assets to maximize a company’s overall earning power is the top job of management. When successful, the result is synergy: the benefit gained from skillfully combining things.

But not all assets have earning power (as I define it), and thus not all have calculable investment value. I describe earning power as the money you can make by owning and operating an asset – that is, I omit from “earnings” the possible gains from simply holding an asset and ultimately selling it. A diamond ring, painting, or classic car doesn’t produce earnings for its owner (short of renting it out or charging people to look at it). For this reason, its economic potential comes exclusively from the possibility of selling it at a profit. And the person who buys it is likely to be doing so in the hope of selling it to someone else at a still-higher price … despite the fact that it won’t produce earnings in the interim. I think of assets that don’t produce operating cash flow or have the potential to do so in the future as not having earning power, and that makes them impossible to value objectively, analytically, or intrinsically

Assets can be tangible or intangible, and an asset’s earning power can produce earnings today and also in the future in amounts that might be higher or lower than today. Together, an asset’s current earnings, plus its power to produce earnings in the future, constitute its key fundamentals. Some investors emphasize paying a reasonable price for today’s earning power, and others are willing to bet on what they see as potential growth in earning power. Regardless, I think prudent investing has to be based on judgments regarding an asset’s present and future earning power. Once an investor has determined an asset’s intrinsic value in this way, he will have a basis for establishing a “right” price that will allow for good returns in the future.

Price

While value can seem theoretical and ephemeral, price is concrete. It’s the amount you pay to obtain something. Ultimately, as indicated above, doing a good job of investing comes down to estimating value appropriately and purchasing that value at a reasonable price.

So that’s what an asset’s price is: the consensus view of investors regarding its underlying fundamental value.

When the majority of investors are optimistic, they cause price to rise and potentially exceed value. And when the pessimists reign, they cause price to decline and potentially fall short of value. Thus, a preponderance of investor psychology on one side or the other – in lieu of the rationality and objectivity on which the Efficient Market Hypothesis is predicated – can create the bargains or over-pricings the hypothesis says can’t exist. Investors should be on the lookout for them.

The price of an asset means nothing in isolation. You can’t tell whether a car is good buy at $40,000 unless you know about the things that determine its market value: its make, model, age, mileage and condition. It’s the same in investing; what matters is the relationship between an asset’s price and its value. Investors call that relationship the asset’s “valuation.”

The Interaction of Price and Value

In the long term, the success of an investment will hinge primarily on whether the buyer was right about the asset’s earning power. However, an asset’s current earning power and opinions regarding its future earning power usually don’t change much from month to month or even year to year. Thus, short-term investment performance is likely to stem mostly from changes in the price investors are willing to pay for the asset. That makes price the dominant consideration for anyone whose principal concern is the short run.

Value should be thought of as exerting a “magnetic” influence on price. If price is above value, future price movements are more likely to be downward than upward. And if price is below value, future price movements are more likely to be upward than downward. However, in the short run, price can move in just about any direction relative to value. This is so because an asset’s price at any given point in time is mostly determined by investor psychology, which can be irrational and unpredictable. Thus, while the current relationship of price to underlying value should move in the expected direction, it can only be counted on to do so in the long run at best.

“More likely to be” is the key phrase in the above paragraph. An undervalued asset can remain cheap – or even get cheaper – for a long time, just as an overvalued asset can become more overvalued, and then extremely overvalued, and then crazily overvalued. It’s the ability of price to go to crazy extremes that causes bubbles and crashes. If price always stopped going up when it began to exceed value, we wouldn’t have extended bull markets and bubbles (and the ensuing crashes), and vice versa.

People who bet heavily that price will move in the direction of value – which we call “converging” – can be carried out if they don’t have sufficient staying power. That’s why John Maynard Keynes said, “The market can remain irrational longer than you can remain solvent.” It’s intellectually sound to expect price to move toward value rather than diverge further from it, and even to bet that it will happen, but it’s unwise and potentially dangerous to bet heavily that it’ll happen soon.

As Benjamin Graham said, in the short run the market functions like a voting machine, reflecting assets’ popularity. But in the long run, it’s a weighing machine, assessing assets’ value. Thus, we can think in terms of a “calculus of value” that I find entirely logical and almost mathematical … except for the fact that it’s applied by people who aren’t:

• Value is what you get when you make an investment, and price is what you pay for it.

• A good investment is one in which the price is right for what the value turns out to be.

• Due to the volatile nature of investor psychology, asset prices fluctuate much more than fundamental value.

• Thus, most price changes reflect changes in investor psychology rather than changes in fundamental value.

• Because of the key role psychology plays in setting asset prices, in order to have a sense for where price stands relative to value, investors should try to gauge prevailing psychology, not just quantitative valuation parameters.

• The relationship of price to value should be expected to strongly influence investment performance, with high valuations presaging low subsequent returns, and vice versa.

• But that relationship must not be counted on to have the expected impact in anything but a long-term sense.

Getting Up to Date

An aside regarding the valuation of the S&P 500: A bit over half of its jaw-dropping 58% two-year total return in 2023-24 was attributable to the spectacular performance of just seven stocks, those of the so-called “Magnificent Seven” – Apple, Microsoft, Alphabet (parent company of Google), Amazon, Meta Platforms (parent company of Facebook), Nvidia, and Tesla. These are great companies – some are the best companies ever – and these seven stocks have grown to represent a startling one-third of the total market value of the 500-stock index. (Please bear in mind that I don’t claim to be an expert on stocks in general or tech stocks in particular.)

Because of these companies’ greatness, their stocks are highly valued, and there’s a popular perception that their elevated valuations are responsible for the S&P 500’s unusually high average p/e ratio. The fact is their p/e ratios average out to roughly 33. This is certainly an above average figure, but I don’t find it unreasonable when viewed against what I believe to be the companies’ exceptional products, significant market shares, high incremental profit margins, and strong competitive moats. (A lot of the Nifty-Fifty stocks First National City Bank owned when I got there in 1969 were selling at p/e ratios between 60 and 90. Now that’s high!) Rather, I think it’s the average p/e ratio of 22 on the 493 non-Magnificent companies in the index – well above the mid-teens average historical p/e for the S&P 500 – that renders the index’s overall valuation so high and possibly worrisome. 他觉得另外剩余的公司估值过高才是问题 而不是巨头估值过高

Here’s my explanation:

• Investors are by nature optimistic. You must be an optimist to hand over your money to someone else in the hope of getting more back later. This is especially true of equity investors, and I think their optimism dies hard.

• When they’re in an optimistic mood, investors have the ability to interpret ambiguous developments positively and overlook negatives.

• The last sustained market correction ended in early 2009, meaning it’s been over 16 years since risk bearing was seriously punished and “buying the dips” wasn’t rewarded. That means no one under 35 or so – professional and amateur investors alike – has ever experienced a prolonged bear market. Older investors have experienced one or more, but, with the passage of such a long time, some may have been lulled into a false sense of security.

• Although the U.S. probably continues to offer the best investment fundamentals in the world, some investors may not appreciate the possibility that it’s a little “less best.”

• Rationalizations often emerge to keep bull markets going. One these days is “TACO,” which stands for “Trump Always Chickens Out.” The suggestion is that his strongest threats – and some of investors’ worst resulting fears – won’t be realized.

• Given the long skein of good years in the markets, it seems today’s investors are motivated more by FOMO than by concern about the chance the market is high and likely to produce poor returns or even losses.

• Finally, of course, the consensus of investors responsible for today’s asset prices probably view the fundamental outlook as more positive than I do.

What’s the bottom line of the calculus? Fundamentals appear to me to be less good overall than they were seven months ago, but at the same time, asset prices are high relative to earnings, higher than they were at the end of 2024, and at high valuations relative to history. Most bull markets are built through the addition of a “constellation of positives” on top of a well-functioning economy. Today I see elements that include the following:

• the positive psychology and “wealth effect” resulting from recent gains in markets, high-end real estate, and crypto,

• the belief that, for most investors, there really is no alternative to the U.S. markets, and

• the excitement surrounding today’s new, new thing: AI.

These are the kinds of things that have the ability to fire investor imaginations and contribute to bull markets, and they certainly seem to be doing so now.

In every strongly rising market, there has to be a justification for the extended valuations: the “bull case.” If it didn’t exist, asset prices couldn’t be where they are. It’s usually some variation on “it’s different this time.” Here’s how it goes today: 这次不一样哈哈哈哈哈🤣 但我觉得这次很可能是一样的 估值过高是的 但200刀一周定投 我依旧觉得是合理的

A p/e ratio is basically the result of applying a discounted cash flow calculation to a stream of earnings, as described above. The main inputs for performing such a calculation and assigning a valuation are assumptions regarding the earnings’ growth rate, durability, and return on invested capital. Compared to the past, today’s S&P 500 is increasingly made up of companies that (a) grow faster, (b) are less cyclical, (c) require less incremental capital to grow, enabling them to generate more free cash flow, and (d) have much stronger competitive positions or “moats.” Thus, they deserve above average p/e ratios.

This explanation makes complete sense. It cites factors that really might be different. And per Sir John Templeton, the first person that I know talked about the trap of “it’s different this time,” 20 percent of the time things really are; today I’d bet it’s more than 20 percent.

So, on one hand, “it’s different this time” is a recurring bull-market cliche that always bears scrutiny and on the other hand, failing to recognize when things actually are different is something that stands between the average investor and superiority. I just have no idea which of those two concerns is more valid today. But investors should bear three things in mind:

• the enormous likelihood that AI and related developments will change the world,

• the possibility that it is “different” for some companies – those that truly embody the factors listed above and will demonstrate the “persistence” I described in On Bubble Watch, but also

• the fact that in most “new, new things,” investors tend to treat far too many companies – and often the wrong ones – as likely to succeed.

The existence of overvaluation can never be proved, and there’s no reason to think the conditions discussed above imply there’ll be a correction anytime soon. But, taken together, they tell me the stock market has moved from “elevated” to “worrisome.”

But I have no problem thinking it’s time for Stop buying and Reduce aggressive holdings and increase defensive holdings

Regression Toward the Mean: An Introduction with Examples

Stats is so interesting!!!!!!

This is one of the reasons it’s dangerous to extrapolate from small sample sizes, as the data might not be representative of the distribution. It’s also why James March argues that the longer someone stays in their job, “the less the probable difference between the observed record of performance and actual ability.”

In reality, the science of performance is complex, situation dependent and often much of what we think is within our control is truly random.

Kahneman observed a general rule: Whenever the correlation between two scores is imperfect, there will be regression to the mean.

This at first might seem confusing and not very intuitive, but the degree of regression to the mean is directly related to the degree of correlation of the variables. This effect can be illustrated with a simple example.

Assume you are at a party and ask why it is that highly intelligent women tend to marry men who are less intelligent than they are. Most people, even those with some training in statistics, will quickly jump in with a variety of causal explanations ranging from avoidance of competition to the fears of loneliness that these females face. A topic of such controversy is likely to stir up a great debate.

Now, what if we asked why the correlation between the intelligence scores of spouses is less than perfect? This question is hardly as interesting and there is little to guess – we all know this to be true. The paradox lies in the fact that the two questions happen to be algebraically equivalent. Kahneman explains:

If the correlation between the intelligence of spouses is less than perfect (and if men and women on average do not differ in intelligence), then it is a mathematical inevitability that highly intelligent women will be married to husbands who are on average less intelligent than they are (and vice versa, of course). The observed regression to the mean cannot be more interesting or more explainable than the imperfect correlation.

This is so interesting!! That’s why some people always make us wonder how they found such a man! lol

We often mistakenly attribute a specific policy or treatment as the cause of an effect, when the change in the extreme groups would have happened anyway. This presents a fundamental problem: how can we know if the effects are real or simply due to variability?

Luckily there is a way to tell between a real improvement and regression to the mean. That is the introduction of the so-called control group, which is expected to improve by regression alone.

If there is anything to be learned from the regression to the mean it is the importance of track records rather than relying on one-time success stories.

所以说 爆款是不可持续的 And no one can be NO.1 always and no country either