祝融说。

In the first two parts, we systematically elaborated on how to build a core investment portfolio with high certainty, centered around the nation's "hard consensus" and the enterprise's "hard reality." However, a complete investment system should not only guard the steady returns brought by certainty but also possess the ability to capture excess returns amidst uncertainty. This chapter enters the domain of speculation and strategic interplay, exploring how to price and trade "possibility" on top of a core position, thereby achieving non-linear wealth growth while keeping risk under control. Taking resource stocks as an example, we will establish a systematic framework for trading on expectation gaps. Its core is to harvest the premium of value reassessment during the process of "possibility" collapsing into "reality."

Section 1: The "Schrodinger State" of Resource Stocks: The Theoretical Foundation for Pricing "Possibility"

1.1 Theoretical Deepening: From "Schrodinger's Cat" to Behavioral Finance

In Part Two, we focused on enterprises whose value is rooted in "hard reality"—those with stable operations, reliable cash flow, and solid balance sheets. Valuing them is, as Graham said, "weighing." However, there is another fascinating class of assets in the capital market whose current value is not based on already existing "reality," but points to an unfulfilled "possibility." Exploration-stage resource stocks, R&D-stage pharmaceutical companies, and startups whose business models have not yet been validated all fall into this category. Their core asset is often just a "mine on paper," a "molecule in a lab," or a "slick business plan."

Will this "blueprint" become a rich gold mine, or will it ultimately be proven a worthless piece of land? Before the outcome is fully confirmed, the value of such a company exists in a superposition state of "both yes and no." This is highly similar to the famous thought experiment in quantum mechanics—"Schrodinger's Cat." Before the black box is opened, the cat is simultaneously in a superposition of "alive" and "dead" states. Similarly, before the "possibility" of these companies is "observed" and "verified" by a series of key events, their value also exists in a superposition of "extremely high" and "extremely low."

The characteristics of this type of asset precisely hit the "weakness" of the market, especially the market dominated by institutional investors pursuing short-term certainty and relative rankings. Behind this lie deep behavioral finance roots.

• "Ambiguity Aversion": This concept, introduced by Daniel Ellsberg, profoundly reveals a characteristic of the human mind: we not only dislike risk (i.e., a known probability of a bad outcome) but even more so dislike "ambiguity" (where even the probability itself is unknown). A jar with 50 red balls and 50 black balls, where drawing a red ball wins CNY 100, is a "risk" problem. Another jar with 100 balls of unknown red-black proportion, where drawing a red ball wins CNY 100, is an "ambiguity" problem. Most people choose to bet on the first jar. For a mining project that requires 5-10 years to see final results, its success probability is inherently full of "ambiguity." It cannot be calculated precisely like rolling dice. Faced with this "ambiguity," the vast majority of market participants—especially fund managers under short-term performance pressure—instinctively choose to avoid it. To compensate for this psychological discomfort, they demand an extremely high "ambiguity discount." This is the first source of profit for "probability investing": through deep research, we transform "ambiguous" assets into "risky" assets with a rough probability range, thereby earning the excessive discount the market pays for "ambiguity."
• "Certainty Effect": Proposed by Kahneman and Tversky in Prospect Theory, it indicates that people overweight certain outcomes in decision-making and relatively underweight outcomes that are merely highly probable. For example, the perceived loss in value from reducing a 100% certain win to a 99% chance of winning is much greater than reducing a 50% chance to 49%. This psychological bias causes the market to exhibit a non-linear response to the evolution of the "progress bar." A project advancing from 0% to 10% (e.g., just obtaining a prospecting permit) makes the market feel "it's pretty much the same as nothing," a relatively sluggish reaction. But when a project advances from 90% to 100% (e.g., officially announcing commercial production), the market, due to the ultimate achievement of "certainty," gives an excessive emotional premium. This creates a second source of profit for "probability investors": intervening in the early, low-certainty stages and enjoying the valuation premium brought by the market's "certainty effect" during the process from "high probability" to "certainty."
• Disciplinary Positioning of "Probability Investing": Based on the above analysis, we can clearly define "probability investing" as an independent investment discipline. It runs parallel to traditional value investing based on "hard reality," but follows a fundamentally different evaluation system and decision-making logic.
  • Value investing is "weighing": It seeks "hard realities" whose value is underestimated, believing that price will eventually return to value, earning money from "mean reversion."
  • Probability investing is "betting": It seeks assets whose "possibility" is mispriced by the market. Through calculating "win rate" and "odds," it bets on the side with positive mathematical expectation, earning money from "probability realization."

1.2 Rethinking the Valuation Framework: A Thinking Tool for Quantifying Odds

To elevate "betting" from emotional "gambling" to rational "investing," we need a thinking framework that can quantify odds and win rates. Although precise calculation is nearly impossible in reality, a simplified probability valuation model can greatly aid our logical reasoning:

Expected Value (EV) = (Success Value (Vs) * Success Probability (Ps)) - (Failure Value (Vf) * Failure Probability (Pf))

(Note: For simplicity, this assumes failure value is negative, i.e., the capital loss. A more rigorous model should consider residual value.)

The focus of this model is not on pursuing a precise number, but on forcing us to answer three key questions, thereby constructing a complete decision-making loop.

How to Estimate "Success Value" (Vs)? — Define Your Trophy

"Success Value" refers to the intrinsic value increment that the project can bring to the company upon full success. This is the "trophy" of our hunt, and its size determines how great our "odds" are. Estimating Vs typically involves two methods:

1. "Comparable Transaction/Company Method" (Market Cap per Ton of Mineral): In the resource field, the market usually gives a relatively fair "market cap per ton of mineral" for proven, extractable resources. For example, the market generally believes that for a phosphorus mine with excellent grade and good mining conditions, each ton of proven reserves is worth about CNY 100-150. If a project has proven 1 billion tons of reserves, its long-term value is around CNY 100-150 billion. This method is simple and intuitive but rough.
2. "Discounted Free Cash Flow After Project Completion": This is a more refined method. Based on the project's feasibility study report, we need to forecast its annual output, sales price, and unit costs after production, thereby estimating its average annual free cash flow, then discount it to the present using an appropriate discount rate. This is essentially a DCF model, but its application scenario is much more reliable than valuing the entire company, as the project's variables are fewer and clearer.

Whichever method we use, we are not pursuing a precise number, but a value range of "fuzzy correctness." This range defines our potential return ceiling.

How to Judge "Success Probability" (Ps)? — Measure Your Chances

This is the core, most difficult, and most research-intensive part of the entire framework. Judging Ps is not a matter of gut feeling like "I feel it's 80% likely to succeed," but a structured assessment process based on evidence, dynamic and continuous. This process is the "Progress Bar Method" we will detail in the next section. Judging Ps comes from a deep understanding and weight assignment of each key node on the "progress bar."

How to Define "Failure Value" (Vf)? — Calculate Your Cards

"Failure Value" refers to the company's residual value after the project completely fails. This is the last line of defense for our safety margin. It may include:

1. Value of the company's other businesses: If the company has other mature, stable cash-generating businesses besides this new project, the value of these businesses constitutes the most solid "hand."
2. Residual value of the project: Even if the project fails, some initial investments, such as land, infrastructure, and some general-purpose equipment, may still have some residual value.
3. Shell value: In the specific ecology of the A-share market, the "shell" of a listed company itself also has some value.

A clear definition of Vf helps us estimate the maximum possible loss in the worst-case scenario, allowing for a more rational assessment of this "bet's" risk-reward ratio.

Through this structured thinking framework, we transform a vague investment impulse into a clear probability problem. It forces us to quantify returns, assess chances, and guard the bottom line.

Section 2: The "Progress Bar Method": An Operable Manual for Harvesting "Possibility"

The "Progress Bar Method" is our core practical tool tailored for "probability investing." It deconstructs a project development process, which can span years and is full of uncertainty, into a clear set of observable, assessable milestone stages. By dynamically tracking the manual-style "progress bar," investors can clearly judge real-time changes in "Success Probability" (Ps) and position themselves before key "value discovery" nodes, systematically harvesting the huge value reassessment premium brought by the collapse of "possibility" into "reality."

2.1 Stage One: Exploration and First Signs (Progress 0% - 20%)

This is the prologue of the story, the germination stage of "possibility" going from 0 to 1. At this point, everything is shrouded in thick fog, requiring investors to possess strong foresight and the ability to discern information.

Key Nodes

• Obtaining a prospecting permit: The company acquires the right to conduct mineral exploration in a specific area from the government through bidding, auction, listing, or negotiated transfer. This is the starting point of the project's legality. The progress bar advances from 0% to 5%.
• Publishing preliminary exploration results: The company completes initial geological surveys, geophysical and geochemical work. Based on some scattered drill holes or surface indications, it publishes an announcement about "estimated" or "inferred" resource quantities. The progress bar advances to 10%-20%.

Interpretation Guide

The quality of announcements at this stage varies enormously and requires careful scrutiny.

• "Gold Content" of the Prospecting Permit: Research whether the area of the permit is located on a known mineralization belt. Are there large-scale mines already in production nearby? This determines the base probability of "striking gold."
• "Language Game" of Geological Exploration Reports: The geological exploration industry has a strict set of standards for resource/reserve classification (such as China's GB/T 17766-2020 standard, or the internationally recognized JORC Code). Investors must learn to distinguish several key terms:
  • "Inferred Resources": The lowest level of estimation, based on sparse engineering and geological data, with very low continuity and reliability. Think of it as "a bold conjecture."
  • "Indicated Resources": Based on denser and more reliable engineering and geological data, with medium continuity and reliability. Think of it as "a well-founded inference."
  • "Measured Resources": Based on dense, detailed, reliable engineering and geological data, with very high continuity and reliability. Think of it as "a basically confirmed fact." In Stage One, companies typically only announce "Inferred Resources," which carry extremely high uncertainty.

Market Reaction

At this point, the market typically reacts coldly, even with ridicule. The vast majority of investors view it as "pure pie-in-the-sky" or "storytelling." Stock price movements are primarily driven by a small number of well-informed hot money or highly forward-looking individual investors. Trading volume is usually low, though there may be impulsive unusual movements.

This stage has the highest risk but also the highest potential odds. It is only suitable for "explorer-type" investors with deep professional knowledge in specific fields (such as geology, pharmacy) and the ability to take on extremely high risk.

Example (YTKG)

(Note: YTKG and the "Niuzhaizhai" project below are composite cases; the people, company, and prices are scenario figures used to demonstrate the method, not a record of actual events.)

Suppose, many years ago, a company YTKG, mainly engaged in traditional chemical business, had its stock price hovering between CNY 6-7. One day, the company issued an inconspicuous announcement stating that it had obtained a prospecting permit for a phosphate mine in a southwestern region, and that preliminary exploration showed the area was "estimated" to have abundant phosphate resources. The market reacted mildly, and the stock price barely moved.

An investor named Mr. Li, with a background in geology and a long track record of tracking global phosphate resources, discovered through research that the area of the prospecting permit was closely connected with a world-class giant phosphate deposit belt. He made a bold judgment: this was likely a "golden child" being overlooked by the market. He began to build a 1% observation position, buying at CNY 6.5. His judgment at the time was: the success probability (Ps) was only 10%, but if successful, its value could be several times its current market cap. The odds were excellent.

2.2 Stage Two: Feasibility Study and Approval Strategic Interplay (Progress 20% - 60%)

If Stage One was "drawing the pie," Stage Two is "kneading the dough." At this stage, dreams begin to collide with reality, and the project's outline shifts from blurry to clear. This is also the biggest test of the investor's research ability, as a large amount of technical and economic detail surfaces.

Key Nodes

• Publishing a detailed exploration report: The company completes denser drilling, upgrading most "Inferred Resources" to "Indicated Resources" or even "Measured Resources." This is the first authoritative confirmation of the resource endowment. The progress bar advances to 30%.
• Publishing a detailed Feasibility Study Report: This is the core of this stage! The company commissions a professional design institute to conduct a comprehensive assessment of the project's technical plan, engineering design, investment estimate, financial evaluation, and risk analysis. The progress bar advances to 50%.
• Passing the Environmental Impact Assessment (EIA): The project passes the review of provincial or national environmental protection authorities and receives EIA approval. With increasingly stringent environmental regulations today, this is one of the most important "passes" for the project. The progress bar advances to 60%.
• Obtaining NDRC Project Approval: The project receives approval documents from the National Development and Reform Commission, meaning the project conforms to national industrial policies and overall planning and is permitted to proceed.

Interpretation Guide

The "Feasibility Study Report" is the "bible" for probability investors. A hundreds-page FS report might overwhelm ordinary people, but professional investors must dig out the gold from it. Core data include:

• Total Investment: How much money does the project need? For example, the "Niuzhaizhai" project has a total investment of CNY 8 billion. This determines the company's financing pressure.
• Construction Period: How long will it take to build? For example, 3 years. This determines the time cost of waiting for value realization.
• Product Plan and Capacity: What will the project ultimately produce? What is the annual output? For example, 5 million tons of phosphate rock raw ore per year.
• Unit Production Cost: This is the core of cost advantage. For example, due to high ore grade and shallow burial, the full cost per ton of ore is only CNY 200.
• Internal Rate of Return (IRR): This is a core indicator for measuring project profitability. For example, assuming a phosphate rock price of CNY 600/ton, the project's after-tax IRR is 18%. This number is very attractive.
• Sensitivity Analysis: At the end of the FS report, there is usually an analysis of how sensitive the IRR is to variables like product price, operating cost, and total investment. This is the key to calculating the project's "profit elasticity." For example, the report shows that for every CNY 100 increase in phosphate rock price, the project IRR increases by 3 percentage points.

The "EIA Approval" means the project has achieved a decisive victory in the environmental link, which is the easiest to be "vetoed." In some industries under heavy environmental pressure (such as heavy chemicals, mining), passing the EIA can be even more important than the FS report.

Market Reaction

With the publication of the FS report and the passing of key approvals, market disagreement begins to intensify. Some deep researchers and left-side traders, after understanding the FS report and confirming the project's economic feasibility, begin to enter heavily. They are the "awakeners" of the market.

However, the mainstream voice of the market remains skeptical. They say, "FS reports are fabricated by design institutes; the numbers can be tweaked at will." "So what if the EIA passed? There are so many approvals left; without the mining license, everything is for nothing." This divergence is the source of the expectation gap.

At this stage, the stock price typically leaves the bottom range and shows a slow, massively volatile upward trajectory. Each favorable approval announcement brings a wave of increase, followed by a pullback due to market doubts. This is the stage that most tests holding conviction.

Example (YTKG)

After a year of silence, YTKG released a detailed FS report for the "Niuzhaizhai" project. The report showed a total investment of CNY 8 billion, a 3-year construction period, annual output of 5 million tons of high-grade phosphate rock, and a full unit cost of CNY 200/ton. Against a phosphate rock market price of CNY 600/ton at the time, the project IRR was as high as 18%. Even more astonishing was the profit elasticity: if phosphate rock prices could return to the historical high of CNY 1,000/ton, the project's annual profit would exceed CNY 3 billion, while the company's total market cap at the time was only CNY 7 billion.

After carefully studying the FS report, Mr. Li believed the market's undervaluation was absurd. He increased his position from 1% to 5%. He believed that Ps had risen from the initial 10% to 40%, and the outline of Vs (success value) had become extremely clear and attractive due to the FS report. During this period, the stock price rose from CNY 7 to CNY 12, but the process was tortuous, with multiple pullbacks exceeding 20%. Many less determined investors were shaken out during this process.

Six months later, the company announced that the project had passed the EIA of the Ministry of Environmental Protection. This news greatly boosted confidence, as phosphate mining has extremely high environmental requirements. The stock price broke through its previous plateau and rose to CNY 15. The market began to see more sell-side analysts publish in-depth reports discussing the potential value of the "Niuzhaizhai" project. However, mainstream institutions remained on the sidelines. Their core argument was: "The mining license hasn't been obtained yet; everything is still a story."

2.3 Stage Three: Obtaining the "Birth Permit" and Construction Launch (Progress 60% - 90%)

This is the critical stage where the "probability wave" collapses. The nature of the asset undergoes a qualitative change from "resources on paper" to "legal assets." This is also the dividing point between "smart money" and "trend money."

Key Nodes

• Obtaining the Mining License! This is the most important and decisive milestone in the entire progress bar. It means that the state, in legal form, has confirmed the company's right to mine the mineral resource. This is the project's "birth permit." The progress bar jumps from 60% to 85%!
• Project Financing Secured: The company has secured all the funds required for project construction through bank loans, private placements, introduction of strategic investors, etc. This removes the financial uncertainty.
• EPC Contractor Confirmed: The company signs an Engineering, Procurement, and Construction (EPC) turnkey contract with a large engineering firm, locking in construction costs and timeline.
• Formal Construction Begins: The project holds a groundbreaking ceremony, driving the first pile. This marks the project's official transition from paper to reality. The progress bar steadily advances to 90%.

Interpretation Guide

When the "Mining License" is announced, investors only need to read the headline. The "gold content" of this document is incomparable to all previous announcements combined. Why? Because it causes a non-linear, dramatic increase in "Success Probability" (Ps).

Before obtaining the mining license, Ps might be at 60%. The market applies a discount factor of 0.6 to its valuation, and even this coefficient itself is hotly debated. After obtaining the mining license, Ps can be widely accepted by the market as 90% or higher. The remaining construction and commissioning stages, while still risky, are mostly technical and managerial, with uncertainty far below that of policy approvals.

This is like a startup that has been telling stories and making PPTs. Although the prospects were tempting, investors always had doubts. Until one day, it won formal purchase orders from Huawei or Tencent, and its business model was instantly validated. The mining license is the "Huawei order" for resource projects.

Market Reaction

Once the mining license announcement is made, market consensus begins to form rapidly. All the previously skeptical reasons ("can't get the license") have vanished. At this point, the large number of right-side traders, trend investors, and responsive institutional funds that were previously on the sidelines rush in like a tidal wave.

They no longer agonize over the project's details. Their buying logic is very simple: "Uncertainty is gone, buy!"

The stock price typically enters a main upswing via consecutive daily limit-up moves or sharp acceleration. Trading volume surges, and market attention peaks. This stage is the core phase for "probability investors" to enjoy the fruits of victory, but it is also when they need to start thinking about exiting.

Example (YTKG)

After another long wait, YTKG announced that it had obtained the mining license for the "Niuzhaizhai" phosphate mine from the Ministry of Natural Resources. On the first trading day after the announcement, the stock price hit the daily limit-up directly. Subsequently, within just one month, the stock price soared from CNY 15 to CNY 35.

At this point, all research reports in the market began to calculate, in a tone of certainty, how much profit the "Niuzhaizhai" project would bring after production. The valuation logic fundamentally shifted from "How big is this pie? How likely is it to be realized?" to "The company will have X billion in profit next year; give it Y times PE; target price Z yuan."

After the stock price reached CNY 30, Mr. Li began his first batch of phased selling. He sold one-third of his position, recovering all his initial capital. The remaining position became a "zero-cost" pure profit. His reasoning was: from CNY 15 to CNY 30, the stock price had already doubled, reflecting the market's revaluation of the mining license value. But from construction to production, it would take another 2-3 years. During this period, the stock price could suffer pullbacks due to market fluctuations, commodity price declines, etc. He chose to lock in part of his profits.

2.4 Stage Four: Production and Value Realization (Progress 90% - 100%)

This is the final chapter and the ultimate realization of value. All "possibilities" have settled, transforming into concrete steel and concrete, machine roar, and numbers on financial statements.

Key Nodes

• Project Mechanical Completion: All construction work is finished and handed over to the owner.
• Commissioning and Trial Run: Raw materials are fed into the production line for linked trial operation, running through the entire production process.
• Official Announcement of Commercial Operation: The project successfully produces qualified products and begins stable operation.
• Achieving Design Capacity: Output gradually ramps up, ultimately reaching or exceeding designed capacity, with all cost and consumption indicators meeting design requirements. The progress bar reaches 100%.

Interpretation Guide

Entering this stage, uncertainty is essentially eliminated. The company's valuation system will completely shift from "probability pricing" to "entity pricing." The focus of analysts and investors is no longer "can it succeed?" but "how much money can it make?" The core evaluation tools revert to the familiar ones: PE, PB, EV/EBITDA, and DCF.

At this point, the analysis of the company returns to traditional fundamental research: tracking product price fluctuations, analyzing cost control ability, and forecasting future profit growth.

Market Reaction

Driven by the positive news of project production, the stock price may experience a final wave of increase, and market sentiment may peak. Due to the "certainty effect," the market gives an additional premium for this final "shoe dropping." Some of the most conservative funds, which had previously hesitated due to concerns about construction risk, will choose to buy at this time.

However, for "probability investors," this is often the best time to cash out in batches. Why? Because our core source of profit—the expectation gap—has been completely filled. When a story that once no one cared about as a "possibility" becomes a "certainty" known to everyone, its odds are no longer attractive. At this point, the company has transformed from an "odds" target into a "value" target. Continued holding requires a completely new set of "value investing" logic to assess whether it is still undervalued.

"Sell on good news"—this ancient market adage finds its most perfect expression at the endpoint of the "Progress Bar Method."

Example (YTKG)

After two years of construction, YTKG announced that the first phase of the "Niuzhaizhai" project had successfully completed commissioning and was about to enter commercial operation. At this time, phosphate rock prices, driven by global inflation and supply-demand imbalance, had risen to CNY 900/ton. Driven by these dual positive factors, the company's stock price further rose from CNY 35 to CNY 50.

At this point, the company's market cap had reached CNY 40 billion. Sell-side reports generally predicted that after full production, the project would generate annual profits of CNY 3 billion, and with 15x PE, saw a target price of CNY 55.

Mr. Li liquidated all remaining positions when the stock price reached CNY 50. His logic was:

1. The expectation gap had been fully realized. From a purchase price of CNY 6.5, he had achieved nearly 8x returns.
2. The company's valuation logic had already shifted. The market was now pricing a cyclical resource stock at 15x PE, a valuation level that was no longer cheap and did not have enough safety margin.
3. Future stock prices would depend more on phosphate rock price fluctuations, a macro variable he could not predict. His initial investment thesis—"collapsing the probability wave"—had been executed to completion.

Ultimately, YTKG's stock price, after reaching a peak of CNY 58, began a long value regression as phosphate rock prices fell. Mr. Li, however, had long since taken his substantial profits to look for the next "probability wave" in a "Schrodinger state."

This is the entire process of the "Progress Bar Method." It is a multi-year hunt centered around "expectation gaps." It requires the investor to possess the prudence of a geologist, the calculation of a financial analyst, and the patience of a hunter. Through this manual, we can transform the vague art of "possibility" into a rigorous, reproducible investment science.

Section 3: Risk Management: Dancing on the Blade of Uncertainty

The allure of "probability investing" lies in its astonishing potential returns. A successful project can multiply a company's value by 5x, 10x, or even more. However, behind high returns lies the ever-present shadow of high risk. The "probability wave" can collapse toward "success," but it can also equally collapse toward "failure." A disproven project can wipe out all capital invested in it.

Therefore, a "probability investing" system that does not address risk management is nothing more than a hopeless gamble. Dancing on the blade of uncertainty requires not courage, but extreme prudence and strict discipline. This section will delve into the three risk control pillars of probability investing: the quantitative application of safety margin, the science and art of position management, and the "checklist" management of logical falsification. This system is the only guarantee that we can survive long-term and ultimately prevail in this high-risk game.

3.1 Quantitative Application of Safety Margin: Deepening the "Binary Valuation"

"Safety margin" is the cornerstone of value investing, proposed by Benjamin Graham, meaning "buying a dollar's worth for forty cents." In "probability investing," we also need a safety margin, but its connotation and application have undergone a profound evolution. We concretize it into a "Binary Valuation" risk control strategy.

The core idea of "Binary Valuation" is to clearly split the company's value into two independent parts:

1. "Hard Reality" Value: This part comes from the company's existing, mature business that can generate stable cash flow. It is the "stock value" that does not depend on the success or failure of the new project. Its evaluation method follows traditional value investing principles, such as PE, PB, dividend yield, or DCF. This part is what we previously referred to as "Failure Value" (Vf).
2. "Possibility" Value: This part comes from the new project in the "Schrodinger state." It is an option whose value depends on the project's success probability (Ps) and its potential value upon success (Vs). Its evaluation method is the probability valuation model we constructed in Section One.

The application of "Binary Valuation" lies in the trigger condition for our buying decision. A strict probability investor's purchase price must satisfy the following condition: Price <= Vf

In other words, the price we pay must not exceed the value of its "hard reality" business.

Let us understand the power of this principle through a detailed example. Suppose we are analyzing YTKG:

• "Hard Reality" Value Analysis: Besides the "Niuzhaizhai" project, YTKG's traditional chemical business contributes a stable net profit of CNY 500 million annually. This is a mature cyclical industry, and the market typically gives 8-12x PE. Taking a conservative valuation of 10x PE, this part of the business is worth CNY 5 billion. The company has a total share capital of 1 billion shares, so its "hard reality" value corresponds to CNY 5/share. This is the safety margin bottom line we define.
• "Possibility" Value Analysis: Through our research on the "Niuzhaizhai" project, we estimate its potential value upon success (Vs) to be about CNY 30 billion. In the early stage of the project, we judge its success probability (Ps) to be 10%. Therefore, the expected value of its "possibility" is 30 billion * 10% = 3 billion, corresponding to CNY 3/share.
• Intrinsic Value Estimate: Adding the two together, YTKG's intrinsic value at this moment is approximately CNY 5/share + CNY 3/share = CNY 8/share.

According to the "Binary Valuation" risk control principle, our purchase price must be significantly below CNY 8/share, ideally at CNY 5/share or even lower.

What does this mean? It means we are paying for the company's "hard reality" business, while that CNY 30 billion phosphate mine project is a super option the market is "giving away" to us for free!

The benefits of this strategy are enormous:

• Downside Risk is Locked: If we buy at CNY 5/share, even if the "Niuzhaizhai" project ultimately proves to be a complete fraud or fails due to force majeure, our principal is relatively safe. Because the price we paid only reflects the value of its existing business. We may lose at most the time cost, but the risk of principal loss is minimal.
• Upside Return is Highly Attractive: Once the "Niuzhaizhai" project's "progress bar" begins to advance, and Ps increases from 10% to 30%, 50%, or even 90%, its "possibility" value will grow from CNY 3/share to CNY 9/share, CNY 15/share, or even CNY 27/share. And our purchase cost is only CNY 5. This extremely asymmetric risk-reward ratio is the core charm of probability investing.

The "Binary Valuation" method essentially uses the concepts of value investing to find a safety margin and the discipline of probability speculation to manage risk exposure. It builds an indestructible bunker for our "betting" behavior. In practice, finding a target that fully satisfies Price <= Vf is not easy, but this should be the gold standard we pursue. As a fallback, our purchase price should not be significantly higher than Vf plus a heavily discounted "possibility" value.

3.2 The Science and Art of Position Management: A Thought Experiment on the Kelly Criterion

Having determined the "safety margin" for buying, the next core question is: how much should I buy? Should this position be a 1% observation position, a 5% core satellite position, or even a 10% heavy position? Position management is the key to the long-term survival of an investment portfolio, especially in the high-volatility field of "probability investing."

The ultimate thinking tool for deciding position size is the Kelly Criterion. Originally proposed by John Kelly in 1956 to solve a problem in information theory, it was later applied by Edward Thorp and others to gambling and investing with great success. Its basic formula is:

f* = (bp - q) / b

Where:

• f* is the optimal betting proportion (i.e., our position size).
• b is the net odds received on the bet (i.e., if you win, CNY 1 wins CNY b).
• p is the probability of winning (our judged success probability Ps).
• q is the probability of losing (1 - p, our judged failure probability Pf).

We must emphasize that in the real investment world, we cannot precisely calculate all the variables required by the Kelly Criterion. We cannot know the exact odds and win rates as in a casino. Therefore, our purpose is not to derive a precise position number from this formula, but to understand its core insight and use it as a rational thinking framework.

The core insight of the Kelly Criterion tells us: the optimal position size should be proportional to the product of our judged "win rate" and "odds" (bp), and subtract the probability of loss (q).

Let us apply this core insight to the YTKG case in a thought experiment:

• Win Rate (p): Our judgment of the project's success probability (Ps). At the project's early stage, we judge Ps to be 10%.
• Odds (b): The calculation of odds is (Expected Gain) / (Expected Loss).
  • Expected Gain = Target price after success - Current purchase price = (CNY 5 hard reality + CNY 30 possibility) - CNY 5 purchase price = CNY 30
  • Expected Loss = Current purchase price - Value after failure = CNY 5 purchase price - CNY 5 hard reality = CNY 0 (this is the ideal case, assuming we can buy at Vf price, loss is 0). To make the calculation meaningful, assume the purchase price is CNY 6, slightly above Vf, so the expected loss is CNY 1.
  • Odds b = 30 / 1 = 30. This is an extremely high odds.
• Calculate f*: f* = (30 * 10% - 90%) / 30 = (3 - 0.9) / 30 = 2.1 / 30 = 7%.

This 7% number is not an instruction to immediately buy 7% of a position. It is a theoretical optimum. In practice, due to the uncertainty in our estimates of p and b (i.e., "ambiguity"), smart investors use a fractional Kelly strategy, such as betting only 1/2 or 1/3 of the Kelly formula's suggested position. A rational initial position might then be around 2%-3%.

The real value of this thinking framework is that it provides a basis for dynamically adjusting our position:

• When win rate (p) increases: As the "progress bar" advances, we judge Ps goes from 10% to 40%. At this point, the value of (bp - q) increases substantially, and the Kelly formula suggests a correspondingly larger position. This provides a theoretical basis for "adding to the position" after the project obtains key approvals.
• When odds (b) worsen: As the stock price rises, our purchase cost increases from CNY 6 to CNY 15. At this point, the expected gain decreases and the expected loss increases, so odds b decreases significantly. The Kelly formula would suggest reducing the position or stopping adding. This explains why we cannot chase prices at high levels.
• When certainty is extremely high (p approaches 1): f* approaches 100%. But this is never achievable in investing.
• When expected return is negative (bp - q < 0): f* is negative, and the Kelly formula suggests not betting at all, or even shorting.

Through the thought experiment of the Kelly Criterion, we upgrade position management from "gut feeling" to a rational decision process based on probability and odds. It tells us when to be bold and when to be conservative. It provides a scientific, albeit fuzzy, thinking framework for deciding whether a "satellite position" should be 1% or 5%.

3.3 "Checklist" Management of Logical Falsification

The essence of probability investing is holding a "hypothesis," namely, "we believe this project will succeed in the future." And the core of the scientific spirit is not to prove oneself right, but to constantly and rigorously seek evidence to refute one's own hypothesis. This is Karl Popper's idea of "falsification."

In investing, this means we cannot simply be a "bullish cheerleader," seeking positive news every day to reinforce our beliefs. We must simultaneously play the role of a ruthless "prosecutor," actively and systematically looking for "falsifying signals" that could cause our investment logic to "collapse in reverse."

The best method is to construct a "Falsifying Signal Checklist" specific to the project. At the time of purchase, we should list all the risk points we can think of that could lead to project failure. Then, throughout the holding period, regularly (e.g., weekly or monthly) review the checklist to check if any risk points are materializing.

Taking the "Niuzhaizhai" phosphate mine project as an example, our "Falsifying Signal Checklist" might include:

1. Technical Falsifying Signals:

   • During subsequent detailed exploration or mining, actual ore reserves or grade is found to be far below the FS report's expectations.
   • Discovery of significant, unforeseen hydrogeological or engineering geological difficulties, causing mining costs to skyrocket or making it technically infeasible.
   • Bottlenecks in beneficiation or processing technology, unable to effectively purify or handle associated harmful elements.

2. Economic Falsifying Signals:

   • The global phosphate rock or downstream phosphate fertilizer market falls into a long-term, structural oversupply, causing prices to remain depressed for an extended period, making the project unprofitable even after completion (IRR loses attractiveness).
   • The project's total investment severely overruns due to various reasons (inflation, design changes), far exceeding the original budget, leading to financing difficulties or diminished economics.
   • Emergence of a disruptive alternative technology (e.g., efficient phosphorus recovery from wastewater) that changes the supply-demand landscape of phosphorus resources in the long run.

3. Policy/Legal Falsifying Signals:

   • Irreversible rejection encountered during key approval processes such as EIA, safety assessment, land pre-approval, and water and soil conservation.
   • The national or local government introduces new, stricter environmental or safety production policies that pose a material obstacle to the project.
   • Property rights disputes over the land, forest land, etc., involved in the project, or deterioration of relations with the local community leading to mass incidents.
   • (For overseas projects) A dramatic change in the host country's political environment, with the new government announcing nationalization of mining policies or tearing up existing contracts.

4. Cooperation/Management Falsifying Signals:

   • Key strategic partners providing funding, technology, or sales channels for the project announce withdrawal.
   • Significant upheaval in company management, with core technical personnel or project leaders resigning.
   • The company is exposed to major financial fraud or legal disputes, affecting its financing ability and reputation.

5. Time Falsifying Signals:

   • Various approval milestones or construction progress of the project are repeatedly and indefinitely delayed, with the company unable to provide reasonable explanations. This usually indicates undisclosed major obstacles. Time is the greatest enemy; excessive delay in itself constitutes a failure.

This checklist is our "firewall." If any red light on the checklist turns on, we must immediately initiate a response plan: reassess the project's success probability (Ps), reduce the position if necessary, or even completely liquidate. This "checklist" management can maximally overcome our human tendency to "report only the good news and not the bad" and "selective blindness," forcing us to face risks in an objective, disciplined manner.

3.4 A Warning from Failure Cases: An Expensive Risk Education Lesson

The following composite case, reconstructed from risks commonly seen in public markets, tests the "progress bar" method: the overseas "gold mine dream" of a western mining company, called Company W. Because the text provides no sources sufficient to identify a listed company, announcement dates, or adjusted-price convention, it cannot remain anonymous while claiming that every number is historical fact. The company, country, tonnage, prices, and timeline below serve only to show evidential dependencies among exploration rights, resource confirmation, financing, and approval.

The Beginning of the Story (Progress Bar 0%-20%):

About a decade ago, Company W, whose main business was in trouble, suddenly announced that through its Hong Kong subsidiary, it had acquired the prospecting rights for a "world-class" gold mine at a very low price in a Central Asian country. The company's announcement painted an extremely tempting blueprint: preliminary exploration suggested that the deposit's gold resources "could exceed 1,000 tons," with a potential value of hundreds of billions. The news sent Company W's stock price from CNY 3 to CNY 15 in just a few months. Countless investors poured in, dreaming of a rags-to-riches miracle.

The Illusion of the "Progress Bar" and the Signals of "Reverse Collapse":

In the following years, Company W continuously issued "positive" announcements, seemingly showing the "progress bar" steadily advancing:

• "The company has signed a memorandum of cooperation with the local government."
• "Preliminary drilling results are encouraging."
• "The company plans to introduce an internationally renowned mining company as a strategic partner."

However, if any investor at the time had cross-referenced these with our "Falsifying Signal Checklist," they would have found countless fatal red lights already on:

• Policy/Legal Falsification: This Central Asian country had perennial political instability and was among the highest-risk regions for global mining investment. Its legal system was incomplete, and the risk of contract breach was extremely high. This was a huge "veto item" existing from the very beginning.
• Technical Falsification: The company never disclosed any resource assessment report prepared by an internationally recognized third-party institution (such as SRK, AMC) that complied with international standards like JORC. All of the "thousand-ton reserves" came from the company's own "estimates" and "inferences," with extremely low credibility.
• Cooperation/Management Falsification: The "internationally renowned mining company" that the company announced would be introduced never actually appeared. The company's financing plans also repeatedly failed to materialize, as no rigorous financial institution was willing to provide loans for a project lacking reliable data.
• Time Falsification: From the announcement of obtaining the prospecting permit, a full five years passed, and the project did not even release the most basic "Feasibility Study Report," let alone subsequent steps like EIA or mining license. The indefinite delay in time itself was the strongest failure signal.

The Final Outcome:

After several years of repeated hype and long waiting, the story's end was predictable. Political turmoil broke out in the Central Asian country. Company W's project site was occupied by local forces, and all previous investments were completely lost. The company eventually announced a massive asset impairment loss. The stock price also fell over 90% from its peak, back to the CNY 2-3 range. Countless investors' "gold mine dream" was utterly shattered.

Post-Mortem and Lessons:

Company W's case was a CNY 10 billion risk management lesson. It tells us:

1. "Probability investing" without a safety margin is gambling: Company W's main business was loss-making, so its "hard reality" value (Vf) was nearly zero or negative. Investors buying above CNY 3 were paying for a pure story, with no safety cushion whatsoever.
2. The quality of the "progress bar" matters more than its speed: The so-called "progress" announced by Company W consisted of "soft" milestones without substantive legal or technical force. None of the "hard" nodes that can truly increase Ps (authoritative reserve reports, FS, EIA, mining license) were ever achieved.
3. The "Falsification Checklist" is a lifeline: A rational investor, seeing the project located in a high-risk country, lacking an authoritative technical report, and facing indefinite delays, should have decisively liquidated and exited, rather than indulging in the fantasy of a "thousand-ton gold mine."

"Probability investing" is always a double-edged sword. It can create astonishing wealth but also bring devastating losses. We must be like a tightrope walker, one hand tightly holding the balancing pole of "high returns," the other hand always ready to grab the safety net of "risk management." Without rigorous, strict, disciplined risk management, even the most tempting "possibility" will ultimately lead to the abyss of total ruin.

Section 4: Conclusion: From "Weighing Machine" to "Odds Calculator"

Throughout this long journey, we have sailed from the solid continent of "hard reality" into the vast ocean of "possibility." We have dissected the market's systematic biases when facing uncertainty, constructed a valuation framework for pricing the "probability wave," and grounded this framework into an operable "Progress Bar Method." Finally, we spent an entire section weaving a safety net called "risk management" for this dance on the blade.

Now, it is time to return to the origin and re-examine the position of "probability investing" within our entire investment system. It is not a subversion of the value investing system centered on "certainty" that we built in the first two parts, but a crucial, high-level supplement and evolution.

Two Tools, Two Worldviews

We can compare these two investment paradigms to two tools, representing two fundamentally different worldviews:

• Value Investing: The World's "Weighing Machine"

  • Core Metaphor: Its soul is Graham's immortal adage: "In the short run, the market is a voting machine, but in the long run, it is a weighing machine." It believes that everything has its intrinsic value, which, like mass in the physical world, exists objectively and can be measured.
  • Core Tool: Its core tool is the "safety margin." Like an experienced merchant, before buying a sack of grain, he ensures the scale is accurate and the price paid is far below the market price of the grain.
  • Worldview: Its worldview is "mean reversion." It believes the tide of price will eventually recede, revealing the bedrock of value. All irrational noise will ultimately be pulled back to the value center by the gravity of economic law. The value investor's task is to stay rational and patient, weigh value amidst the noise, and wait for the return.

• Probability Investing: The World's "Odds Calculator"

  • Core Metaphor: Its core can be summarized as: "In the short run, the market is an emotion amplifier; in the long run, it is a probability realization machine." It acknowledges that in certain fields, the intrinsic value of things is not a fixed "weight" at a specific stage, but a "probability distribution" waiting to be "collapsed."
  • Core Tool: Its core tool is the "Kelly Criterion" style of odds thinking. It does not weigh like a merchant; more like an actuary or a professional poker player. He does not care about the certainty of winning or losing a single bet, but ensures he is on the side with positive mathematical expectation by precisely calculating "win rate" and "odds," and plays the game over the long term, repeatedly.
  • Worldview: Its worldview is "emergence and collapse." It believes the future is not predetermined but "emerges" from multiple possibilities. The development of a new drug, the discovery of a mineral deposit—these are non-linear mutations from 0 to 1. The task of the probability investor is to identify the "probability waves" mispriced by the market before the "collapse" occurs, and manage risk with strict discipline.

The Investor's Evolution: A Complete Toolbox

A novice investor might only have a hammer, seeing everything as a nail. He might be a fanatical technical analysis follower or a dogmatic value investing fundamentalist.

A mature, truly professional investor should have a complete toolbox in his garage. Faced with a complex machine that needs repair, he knows when to use a wrench, when to use a screwdriver, and when to use a multimeter.

Similarly, a mature investor should have both the "weighing machine" and the "odds calculator" in his thinking toolbox.

• He can, in the world of "hard reality," face a mature consumer goods company, and with great patience and rigor, "weigh" its free cash flow over the next 20 years like Buffett.
• He can also, in the world of "possibility," face a biotech company that has just announced the discovery of a new drug target, and with a cool head and actuarial discipline, "calculate" its odds of success and risk exposure like a venture capitalist.

He knows that these two tools are not contradictory. They are suitable for solving different types of problems and assessing assets with different attributes. He would not use a "weighing machine" to weigh a fog, nor use an "odds calculator" to bet on a coin flip.

The Ultimate Principle: The Fusion of Two Ways of Thinking

Throughout all the theories, methods, and risk management in this chapter runs one final, integrative principle, which is also the highest guiding principle for the art of managing "possibility":

"Use the concepts of value investing to find a safety margin; use the discipline of probability speculation to manage risk exposure."

The first half is our "shield." It requires us, even when chasing the most exciting "possibility," never to forget the "hard reality" under our feet. Our purchase price must be anchored to that value foundation where, even if the dream shatters, we remain safe. This is our guarantee against ruin.

The second half is our "spear." It requires us, when facing uncertainty, to use mathematical rigor and iron discipline to constrain human greed and fear. Position size, points for adding, and stop-loss standards should all be based on a dynamic assessment of probability and odds, not on momentary impulse. This is our compass towards victory.

Master the "weighing machine," and we can move steadily in the world of certainty. Master the "odds calculator," and we can discover wonders in the world of uncertainty. Integrate the two, and we can truly become an all-weather observer and practitioner who transcends bull and bear markets and masters cycles. With this, our exploration of "possibility" is complete.

Chapter Summary

This chapter delved into the advanced investment strategy of "expectation gap trading," defining it as an independent discipline of "probability investing," aimed at systematically pricing and harvesting the "possibility" of high-uncertainty assets (such as resource stocks, innovative drug companies). The core idea of the chapter is that the market, especially the market dominated by institutional investors pursuing short-term certainty, systematically undervalues assets with undetermined outcomes in a "Schrodinger state" due to behavioral finance biases such as "ambiguity aversion" and the "certainty effect." This creates a huge expectation gap and profit space for investors capable of precisely assessing "probability waves."

Theoretical Foundation and Valuation Framework: The chapter first established the theoretical foundation of probability investing and proposed a core probability valuation model: Expected Value = (Success Value * Success Probability) - (Failure Value * Failure Probability). The chapter detailed how to estimate the three core variables—"Success Value" (Vs), "Success Probability" (Ps), and "Failure Value" (Vf)—with "fuzzy correctness," emphasizing that the dynamic judgment of Ps is the essence of the entire framework.

Operable Methodology: The "Progress Bar Method": To put theory into practice, the chapter systematically constructed a "Progress Bar Method." This method deconstructs a project's lifecycle into four clearly identifiable and interpretable stages: from initial "Exploration and First Signs" (0%-20%), through "Feasibility Study and Approval Strategic Interplay" (20%-60%), to the decisive "Obtaining the 'Birth Permit' and Construction Launch" (60%-90%), and finally "Production and Value Realization" (90%-100%). Through a running case study, the chapter detailed how to interpret key milestones (such as the FS report, mining license) at each stage, how the market typically reacts, and the strategies investors should adopt accordingly.

Comprehensive Risk Management System: Given the high-risk nature of probability investing, the chapter devoted substantial space to constructing three risk control pillars. First, the "Binary Valuation" method, requiring the purchase price not to exceed the company's "hard reality" value, thereby obtaining the "possibility" option for free and locking in downside risk. Second, the Kelly Criterion thought experiment, providing a scientific decision-making framework for position management based on win rate and odds. Third, the "Checklist" management of logical falsification, overcoming human weaknesses and enabling disciplined decision-making by actively seeking and monitoring signals that could cause the investment logic to fail. The chapter also reviewed a real failure case, serving as a stark warning about the importance of risk management.

Intellectual Sublimation and Positioning: Finally, the chapter compared and positioned "probability investing" (odds calculator) with traditional value investing (weighing machine), arguing that a mature investor should master both tools to handle assets with different attributes and different market stages. It ultimately distilled the supreme principle of probability investing: "Use the concepts of value investing to find a safety margin; use the discipline of probability speculation to manage risk exposure." This is not only an investment strategy but also a complete worldview and action guide for achieving long-term success in a world full of uncertainty.