The Mathematics of Estimation in Equity Investing

Stock selection is commonly perceived as a problem of identification—finding the right business at the right price.

However, in reality, stock selection is a problem of probabilistic estimation under uncertainty.

The process begins with analysis of financial statements, cash flows, balance-sheet strength, management quality, industry structure, and valuation. These variables form the observable and partially controllable inputs of the system. Based on them, an investor constructs an investment thesis—implicitly assigning probabilities to a range of future outcomes. 

However, once a stock is selected and capital is committed, the nature of the problem changes fundamentally. From that point on, the stock price is driven by forces far beyond any single model, forecast, or thesis. Once a stock enters your portfolio, certainty disappears. You never really know where the stock price will move next.

From that point onward, the investor is no longer solving for an outcome, but estimating the distribution of possible outcomes. The realised stock price becomes the result of numerous interacting variables—many of which remain beyond the investor’s control. 

Stock prices, therefore, are not the deterministic output of analysis. They are the emergent result of a complex system, influenced by macroeconomic forces, policy decisions, industry dynamics, capital flows, behavioural feedback loops, and exogenous shocks. Many of these variables are unobservable, time-varying, and mutually dependent. 

In this framework, stock selection is not prediction in the classical sense. It is an exercise in estimating probabilities across a high-dimensional system, where uncertainty is irreducible, and outcomes cannot be precisely forecast. The role of analysis is not to eliminate uncertainty, but to improve the expected value (EV) of decisions by working within the narrow domain of what can be reasonably assessed.

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The Investment Thesis: A Framework Built on Controllable Variables

Before capital is committed, investors necessarily restrict their analysis to a relatively small subset of variables—typically on the order of forty to fifty—that are observable, analysable, and reasonably stable at the time of decision-making. 

These variables form the basis of the investment thesis. They are not selected because they determine outcomes, but because they define the limited domain in which informed probabilistic estimation is possible. By working within this constrained set, the investor seeks to improve expected value while accepting that uncertainty cannot be eliminated.

The investment thesis is typically constructed using the following variables:

A. Business Model & Economics

1. Nature of the business

2. What the company does

3. How the company makes money

4. Revenue model and pricing power

5. Scalability of the business model

6. Sustainability and durability of demand

7. Competitive advantage / moat

8. Customer concentration risk

9. Supplier dependency

10. Geographic exposure

B. Financial Performance & Capital Structure

11. Revenue growth trajectory

12. Profit growth trajectory

13. Margin levels and sustainability

14. Operating leverage

15. Return on Equity (ROE)

16. Return on Capital Employed (ROCE)

17. Free cash-flow generation

18. Cash-flow consistency

19. Balance-sheet strength

20. Debt levels and leverage

21. Interest coverage

22. Working-capital discipline

C. Management Quality & Governance

23. Management integrity and ethics

24. Management competence

25. Capital allocation decisions

26. Reinvestment discipline

27. Track record of execution

28. Quality of communication and disclosures

29. Alignment with minority shareholders

30. Board quality and independence

31. Auditor quality

32. Related-party transaction risk

D. Industry Structure & External Constraints

33. Industry growth potential

34. Industry cyclicality

35. Competitive intensity

36. Barriers to entry

37. Regulatory environment

38. Sensitivity to policy changes

39. Technological disruption risk

E. Valuation & Downside Protection

40. Entry valuation

41. Valuation relative to history

42. Valuation relative to peers

43. Embedded growth expectations

44. Margin of safety

45. Downside risk under adverse scenarios

These variables help answer a narrow but critical question: Is this a business worth owning at this price?

This is the domain where analysis has meaning—where skill, experience, and disciplined effort can improve the expected value of a decision by working with observable information and eliminating weak candidates.

Importantly, this process does not eliminate uncertainty. It compresses it.

In probabilistic terms, stock selection is not about maximising certainty, but about tilting the odds—increasing the likelihood of favourable outcomes while limiting exposure to unfavourable ones.

And this is also where investor control largely ends.

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From Investment Thesis to Market Outcomes: The Domain of Uncontrollable Variables

Once an investment thesis is formed and capital is committed, the problem shifts from analysis to outcome realisation. The realised market outcome-the stock price-is no longer governed solely by the variables on which the original thesis was constructed. 

A stock price does not move because of a single cause. It moves because multiple inputs act together, non-linearly, with feedback loops, and frequently with time lags. Most of these inputs lie outside the investor’s control.

When these influences are carefully enumerated, one arrives at an uncomfortable realization: there are well over 130 identifiable variables that can affect the price of a stock.

In mathematical terms, this resembles a high-dimensional, non-linear, non-stationary dynamical system with over 130 interacting variables.

This system is characterised by:

• time-varying coefficients,

• interdependent state variables,

• non-linear relationships, and

• continuous exposure to exogenous shocks.

Such systems do not admit closed-form solutions. Even numerical methods struggle to solve them because small changes can lead to very different outcomes, feedback loops reinforce price movements, and human behaviour keeps the system in constant flux. From a systems-theory perspective, financial markets behave less like mechanical systems and more like complex adaptive systems. Agents learn and react. Rules evolve. Structure changes with scale. Past outcomes influence future behaviour.

This is why forecasting exact price paths is not merely difficult, but it is fundamentally non-solvable in a deterministic sense. Not because we lack data or computing power, but because the system itself is shaped by complexity, interaction, and constant change.

What follows is a structured mapping of these interacting forces. Seen together, they reveal why stock prices are better understood as probability distributions, not point estimates, and why humility, not precision, is the rational response to market complexity.

Understanding markets as complex adaptive systems is intellectually useful, but it can still feel abstract. To make this complexity tangible, it helps to break the system into its major components—not because they can be precisely modelled, but because they can be identified, respected, and contextualised.

The sections below map the key classes of variables that interact to determine stock prices.

Seen individually, each factor appears manageable. Seen collectively, they explain why stock prices move the way they do and why certainty in markets is an illusion.

Many of the variables listed below overlap with those used in the investment thesis; the distinction is not analytical relevance, but loss of control once capital is committed and the market takes over price discovery.

A. Macro & Global Factors

1. Global economic growth or slowdown

2. Global recession risk

3. Inflation trends

4. Interest-rate cycles

5. Central bank policies

6. Global liquidity conditions

7. Currency movements

8. Dollar strength/weakness

9. Commodity price cycles

10. Crude oil prices

11. Energy price volatility

12. Geopolitical tensions

13. Wars and conflicts

14. Trade wars and sanctions

15. Global risk-on / risk-off sentiment

B. Country, Political & Regulatory Factors

16. Government stability

17. Election outcomes

18. Fiscal deficit levels

19. Government borrowing

20. Taxation policy changes

21. Corporate tax rates

22. Import duties

23. Export incentives/restrictions

24. Industrial policy

25. Sector-specific regulations

26. Environmental regulations

27. Compliance requirements

28. Legal and judicial framework

29. Policy credibility

30. Sudden regulatory shocks

C. Industry / Sector Factors

31. Industry growth rate

32. Industry cyclicality

33. Demand–supply balance

34. Capacity utilisation (industry-wide)

35. Entry of new competitors

36. Exit/consolidation of competitors

37. Pricing power of the sector

38. Bargaining power of customers

39. Bargaining power of suppliers

40. Technological disruption

41. Substitute products

42. Input cost pressures

43. Regulatory intensity of the industry

D. Business Model & Operations (Micro)

44. Nature of the business

45. Revenue model

46. Pricing strategy

47. Product/service mix

48. Scalability of operations

49. Operating leverage

50. Cost structure

51. Execution capability

52. Project management quality

53. Customer concentration

54. Supplier concentration

55. Geographic exposure

56. Dependence on key contracts

E. Company Fundamentals (Micro)

57. Revenue growth

58. Profit growth

59. Margin sustainability

60. EBITDA margin volatility

61. Net profit margin stability

62. Return on equity (ROE)

63. Return on capital employed (ROCE)

64. Return on invested capital (ROIC)

65. Free cash-flow generation

66. Earnings quality

67. Earnings visibility

68. Earnings volatility

F. Balance Sheet & Working Capital (Micro)

69. Debt levels

70. Interest burden

71. Debt maturity profile

72. Leverage sustainability

73. Cash conversion cycle

74. Receivable days

75. Inventory days

76. Payable days

77. Working-capital discipline

78. Liquidity buffer

79. Funding availability

80. Refinancing risk

G. Management Quality (Micro)

81. Management integrity

82. Ethical standards

83. Capital allocation decisions

84. Track record of value creation

85. Strategic clarity

86. Long-term orientation

87. Risk appetite

88. Execution consistency

89. Ability to navigate cycles

90. Communication quality

91. Guidance credibility

H. Corporate Governance & Fraud Risk (Micro)

92. Board independence

93. Board competence

94. Auditor quality

95. Auditor independence

96. Related-party transactions

97. Transparency of disclosures

98. Accounting conservatism

99. Use of subsidiaries/complex structures

100. Promoter pledging

101. Governance failures

102. Fraud risk

103. Regulatory investigations

I. Valuation & Market Mechanics

104. Entry valuation

105. P/E multiple

106. P/B multiple

107. EV/EBITDA multiple

108. Relative valuation versus peers

109. Historical valuation bands

110. Multiple expansion

111. Multiple compression

112. Earnings surprises

J. Liquidity & Money Flows

113. Foreign institutional investor (FII) flows

114. Domestic institutional investor (DII) flows

115. Mutual fund positioning

116. ETF flows

117. Free-float availability

118. Trading liquidity

119. Block and bulk deals

120. Index inclusion or exclusion

K. Behavioural & Sentiment Factors

121. Investor psychology

122. Fear cycles

123. Greed cycles

124. Market narratives

125. Media influence

126. Social-media amplification

127. Herd behaviour

128. Recency bias

129. Expectation build-up

130. Expectation disappointment

From Estimation to Acceptance: Living With Uncertainty

After all the research, analysis, and effort, a central conclusion becomes unavoidable: most drivers of stock price movement remain uncontrollable.

This does not make analysis useless. It makes humility essential.

Equity investing is not a deterministic exercise. It is a probabilistic estimation.

The investor is not solving for certainty, but estimating outcomes under uncertainty—working with probability distributions rather than fixed answers.

Good investing, therefore, is not about prediction. It is about:

• Making the best possible decision with limited information

• Accepting variance and randomness

• Focusing on process rather than forecasts

• Managing downside risk instead of projecting upside

Once a stock is owned, the task is no longer to anticipate every price movement. The task is to remain disciplined when randomness dominates outcomes.

In the end, almost everything in markets is uncertain—except one variable: the price you pay. This is why the margin of safety becomes paramount.

Not as an expression of pessimism, but as a rational response to uncertainty—an acknowledgment of error, variance, and the limits of knowledge.

In markets, effort improves odds, discipline manages variance, and humility preserves capital.

In a system this complex, success belongs not to prediction, but to decisions built to endure uncertainty.

As Peter L. Bernstein wrote in Against the Gods:

“The essence of risk management lies in maximizing the areas where we have some control over the outcome, and minimizing the areas where we have absolutely no control.”

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-- Pady