The Art of Being Approximately Right
Limits of Precision and the Illusion of Knowledge
Modern intellectual and financial life places enormous value on precision. Economic forecasts are expressed to decimal places, financial models project cash flows years into the future, analysts assign precise price targets to securities, and policymakers publish estimates of growth, inflation, employment, and fiscal balances as though the underlying economy were a system whose future could be measured with sufficient accuracy if only enough information were collected. Precision has consequently become associated with analytical rigour; numbers appear authoritative, models appear sophisticated, and detailed forecasts often command greater confidence than broader judgements even when the additional numerical detail is not supported by additional information.
The distinction between precision and accuracy, however, is fundamental. A forecast that predicts economic growth of 1.73 percent may appear more sophisticated than one that anticipates growth of approximately 2 percent, yet the additional decimal places do not necessarily contain additional information. If the uncertainty surrounding the forecast is substantial, specifying 1.73 rather than 2.0 can create an illusion of knowledge rather than an improvement in it, because the apparent exactness of the number may simply conceal the fact that the analyst cannot reliably distinguish between a range of nearby outcomes.
This problem becomes particularly acute when analysing complex systems because financial markets, economies, organisations, political institutions, and social systems are not mechanical objects governed by a small number of stable and perfectly observable relationships. They are adaptive environments in which participants respond to information, alter their behaviour, anticipate the actions of others, and consequently change the very systems that they are attempting to understand. Under such conditions, uncertainty is not merely a temporary deficiency in information that can eventually be eliminated through greater data collection; it is an intrinsic feature of the problem itself.
The art of being approximately right therefore begins with a deceptively simple recognition: the objective of analysis is not always to produce the most precise answer possible, but to produce the most useful conclusion that the available evidence can reasonably support. In many circumstances, that means accepting a degree of approximation precisely because pretending to know more than the evidence permits would constitute a deeper analytical error.
Approximation as an Intellectual Discipline
Approximation is sometimes treated as an admission of analytical weakness, particularly in environments where quantitative sophistication is highly valued and where the appearance of numerical precision can confer authority. In reality, knowing what can and cannot be estimated with precision is itself a form of analytical sophistication because it requires an understanding not only of the model being used but also of the uncertainty surrounding the model's assumptions.
Every model abstracts from reality; it necessarily excludes information, simplifies relationships, imposes assumptions, and defines a boundary around the problem being examined. The relevant question is therefore not whether a model is perfectly accurate, because no useful model can reproduce every feature of reality, but whether its simplifications preserve the relationships that matter for the decision at hand and whether the resulting uncertainty is represented honestly.
An approximate estimate can be extraordinarily valuable when it captures the correct order of magnitude, direction, range, or relationship, while a highly detailed estimate can be almost useless when its precision rests upon assumptions that are unstable, poorly measured, or fundamentally uncertain. A valuation model that estimates a company's intrinsic value at £47.32 per share may look more rigorous than a conclusion that the shares are worth somewhere between £40 and £55, yet the latter may be intellectually superior if the uncertainty surrounding long-term margins, discount rates, competitive dynamics, terminal value, and the broader economic environment makes the additional precision indefensible.
Approximation therefore requires judgement about the structure of uncertainty itself. The important question is not merely:
"What is the number?"
but rather:
"How much confidence should reasonably be placed in that number, and what range of outcomes would remain plausible if the underlying assumptions changed?"
Once that distinction is recognised, quantification becomes a tool for improving judgement rather than a mechanism for disguising uncertainty behind increasingly elaborate calculations.
The Difference Between Accuracy and Precision
The distinction between accuracy and precision is familiar in statistics and measurement science, but it has particularly important implications for economics and investment analysis because the objects being measured are often uncertain, dynamic, and only partially observable. Accuracy concerns the proximity of an estimate to the underlying reality, whereas precision concerns the degree of exactness with which that estimate is expressed; consequently, an estimate can be precise without being accurate, accurate without being highly precise, both precise and accurate, or neither.
Consider an investor attempting to estimate the future earnings of a company five years from now. A model may produce an estimate of £6.84 per share, supported by detailed assumptions regarding revenue growth, operating margins, taxation, capital expenditure, financing, and share count, and the arithmetic may be entirely correct. Nevertheless, the actual outcome could plausibly be £3 or £10 depending upon competitive developments, technological change, management decisions, economic conditions, regulation, and the evolution of the industry. The calculation itself may therefore be precise while the knowledge supporting it remains highly uncertain.
A more intellectually honest conclusion might be that long-term earnings are likely to fall within a broad range, with a central estimate around a particular level but substantial uncertainty surrounding it. Such a conclusion can appear less impressive because it acknowledges the limits of what can be known; analytically, however, it may be considerably stronger because the uncertainty in the conclusion corresponds more closely to the uncertainty in the underlying evidence.
This distinction is particularly important in investment because the decision-maker is rarely rewarded simply for producing a number. The value of analysis lies in its ability to improve a decision, and a less precise estimate that correctly represents uncertainty may therefore be substantially more useful than a highly precise estimate that encourages misplaced confidence.
Order of Magnitude Matters
One of the most powerful forms of approximation is the ability to determine the approximate scale of a phenomenon before becoming concerned with its exact measurement. Order-of-magnitude reasoning can often establish whether a proposition is plausible long before detailed modelling is required, thereby preventing considerable analytical effort from being devoted to refining a premise that is fundamentally incorrect.
If an investment opportunity requires £10 million of capital to produce an expected annual cash flow of £500,000, its broad economics can be understood immediately; similarly, if a proposed market is claimed to be worth £100 billion while the underlying customer base and average expenditure imply something closer to £1 billion, an elaborate financial model cannot rescue the original estimate because the problem lies at a much more fundamental level. This form of reasoning matters because many analytical errors are not small numerical errors but errors of scale. An assumption can be wrong by a factor of two, ten, or one hundred while still appearing superficially reasonable because the calculations built upon it remain internally consistent. A model can therefore be perfectly coherent in its internal arithmetic while being materially disconnected from the reality it is intended to describe.
The ability to identify such discrepancies quickly is consequently an important intellectual skill. Approximate reasoning provides a first line of defence against false precision because it establishes whether an answer is broadly plausible before analytical effort is invested in refining it. In many cases, knowing that something is approximately £10 billion rather than £100 billion is vastly more important than knowing whether the correct number is £9.7 billion or £10.3 billion.
This principle extends beyond finance because order-of-magnitude reasoning provides a way of separating economically meaningful differences from distinctions that are merely numerically visible. Good analysis begins by establishing what scale of phenomenon is actually being considered; only then does greater precision become worth pursuing.
The Economics of Uncertainty
Economics provides a particularly useful environment for understanding the value of approximation because economic variables are generated by human behaviour, institutional arrangements, technological change, expectations, and interactions between agents, none of which remain perfectly stable through time. Economic relationships are therefore neither completely observable nor mechanically fixed, and their future evolution cannot be inferred simply by extrapolating historical patterns.
An economic forecast does not merely involve calculating an unknown number from known inputs; it involves estimating an uncertain future from incomplete information while recognising that households, firms, investors, governments, and central banks may change their behaviour in response to the very conditions being forecast. A forecast can therefore influence expectations, expectations can influence behaviour, and behaviour can subsequently alter the economic outcome that was being forecast in the first place.
This creates a fundamental problem for excessive precision. A forecast for inflation over the next three years may be presented as a sequence of highly specific annual figures, yet the underlying distribution of possible outcomes may be considerably wider than the presentation implies. Small changes in assumptions regarding wages, energy prices, productivity, fiscal policy, monetary policy, exchange rates, or inflation expectations can materially alter the resulting trajectory, particularly when those variables interact rather than changing independently.
Approximate reasoning does not eliminate this uncertainty; instead, it provides a more appropriate language for communicating it. Rather than pretending that the future has a single measurable path, the analyst can identify plausible ranges, central tendencies, directional relationships, and conditions under which the outlook would materially change. The result is not less rigorous analysis but analysis whose level of confidence is more closely aligned with the structure of the underlying problem.
Financial Markets and the Limits of Exact Forecasting
Financial markets provide perhaps the clearest demonstration of the dangers associated with excessive precision because virtually every important variable that investors attempt to forecast is influenced by multiple interacting sources of uncertainty. Earnings, interest rates, exchange rates, commodity prices, market returns, volatility, liquidity, and asset valuations all depend upon relationships that can change as economic conditions and investor behaviour evolve.
A company's future earnings depend upon demand, pricing power, competition, costs, investment, financing conditions, management decisions, regulation, technological change, and the broader economic environment, while the valuation placed upon those earnings depends upon interest rates, risk premia, investor preferences, liquidity, and expectations regarding future growth. Even when each individual assumption appears reasonable, their interaction can produce a wide range of possible outcomes because small changes in several assumptions can compound into a substantial difference in the final result.
Investment analysis is therefore often more useful when expressed through scenarios, ranges, probabilities, and sensitivities rather than a single point estimate. A central estimate remains useful because decisions frequently require a reference case, but it should be understood as a conditional judgement rather than a statement of what will actually occur. The distinction matters because investors do not need to know the future with perfect precision to make rational decisions; they need to understand the distribution of plausible outcomes well enough to determine whether the expected reward is sufficient relative to the risks being assumed.
An investment can therefore be attractive even when its future value cannot be forecast precisely, provided that the range of plausible outcomes remains sufficiently favourable. Conversely, an apparently cheap asset can remain unattractive if the uncertainty surrounding its underlying economics is so large that the downside distribution overwhelms the apparent valuation opportunity. The purpose of analysis is consequently not to manufacture certainty where none exists, but to improve the quality of decisions made in its absence.
Why Ranges Can Be More Informative Than Points
Point estimates are psychologically attractive because they compress uncertainty into a single number, thereby providing a clear answer that can be compared easily with other estimates or with an observable market price. That convenience, however, can come at the cost of intellectual honesty because the central estimate may conceal the breadth of outcomes that remain genuinely plausible.
Suppose an analyst estimates that a company will generate £1 billion of free cash flow in five years. The estimate may be useful as a central case, but its informational value depends heavily upon the range surrounding it; if plausible outcomes extend from £400 million to £1.6 billion, then the central estimate communicates only part of the information relevant to an investment decision because the distribution of outcomes determines both the potential upside and the potential downside.
Ranges are therefore particularly valuable when uncertainty is material because they allow analysts to distinguish between situations in which a central estimate is relatively reliable and situations in which it represents merely one point within a broad spectrum of possible outcomes. A range can also reveal how sensitive a decision is to changing assumptions, which is often more informative than the central estimate itself. However, ranges can be abused just as easily as point estimates. An arbitrarily broad range provides little analytical value because it fails to distinguish plausible outcomes from remote possibilities, while a narrow range based upon unjustified assumptions merely recreates the illusion of precision in another form. The useful range is therefore neither the widest imaginable range nor the narrowest defensible interval, but the range that most honestly reflects the uncertainty inherent in the problem.
Approximation consequently requires discipline on both sides:
the analyst must avoid false precision without retreating into vagueness, because uncertainty becomes useful only when it is characterised sufficiently well to influence a decision
The Role of Heuristics
Human beings have always relied upon heuristics, or practical rules of thumb, to make decisions when information is incomplete and computational resources are limited. Although heuristics can generate systematic biases and should therefore be treated cautiously, they can also be highly effective when appropriately constructed and applied within environments that cannot be modelled completely.
A seasoned investor may recognise that a particular balance-sheet structure is becoming increasingly fragile without first calculating every conceivable stress scenario; an experienced trader may identify an unusual change in market behaviour before a formal model has incorporated the relevant information; and a business leader may recognise that a strategy is unlikely to work because its economics violate a basic principle of scale, incentives, or competitive positioning. Such judgements should not automatically be regarded as superior to quantitative analysis, but neither should they be dismissed merely because they lack the apparent precision of a formal model.
Heuristics can function as compression mechanisms, allowing experienced decision-makers to incorporate large amounts of accumulated information into relatively simple judgements. Their value, however, depends upon the quality of the underlying experience and the environment in which that experience was developed; a heuristic that worked reliably under one set of conditions may become misleading when the structure of the system changes. The important distinction therefore lies between informed approximation and careless intuition. A useful heuristic should be grounded in experience, evidence, or a coherent understanding of causal relationships, while remaining open to revision when evidence contradicts it. Approximation becomes dangerous when uncertainty is used as an excuse for arbitrary judgement rather than as a reason for disciplined judgement.
Knowing What Matters
One of the deepest benefits of approximate reasoning is that it forces the analyst to identify which variables actually matter. Complex models can contain hundreds or thousands of assumptions, yet only a relatively small subset may determine most of the variation in the final outcome; if an analyst spends enormous effort refining variables that have little influence on the decision while leaving major assumptions effectively unquestioned, the resulting model can become considerably more complicated without becoming meaningfully more informative.
Approximation encourages a different approach because it asks which distinctions are economically meaningful. If changing an assumption from 2.1 percent to 2.2 percent has almost no effect on the investment conclusion, the additional precision may be irrelevant, whereas a change in a major growth assumption from 3 percent to 8 percent may fundamentally alter the valuation and therefore deserves considerably greater analytical attention. The objective is consequently not maximum detail but maximum decision relevance; this distinction is especially important when analytical resources are limited because time spent understanding the variables that drive outcomes is generally more valuable than time spent making inconsequential assumptions increasingly precise.
Good analysis is selective because reality is too complex to model in its entirety. The analyst's task is not to capture every possible detail but to identify the relationships whose inclusion materially improves understanding and the assumptions whose uncertainty could materially change the decision.
Approximation and Model Risk
Every model carries model risk because every model represents a simplified interpretation of reality. The danger is not merely that an individual assumption may be wrong, but that the structure of the model may exclude a variable or relationship that becomes important under conditions different from those assumed when the model was constructed.
Financial history contains numerous examples of models performing well under ordinary conditions before failing dramatically when the environment changed. Relationships that appeared stable became unstable, correlations shifted, liquidity disappeared, and participants altered their behaviour in response to stress; the model had not necessarily been mathematically defective, but it had been applied beyond the conditions under which its assumptions remain useful.
Approximate reasoning can reduce this vulnerability by encouraging analysts to focus on structural relationships rather than becoming excessively attached to specific outputs. A model may suggest that an asset is attractively valued, for example, but the analyst should still ask which assumptions drive that conclusion, how sensitive the conclusion is to those assumptions, and what would happen if they proved substantially wrong.
The more uncertain the environment, the more important it becomes to understand the model's sensitivity rather than simply its central output. A model should therefore be treated as an instrument for reasoning rather than an oracle; its purpose is to organise information, clarify relationships, test scenarios, expose sensitivities, and improve judgement, rather than to become a substitute for judgement itself.
The Value of Being Approximately Right
Being approximately right is valuable because many decisions do not require exact knowledge of the future; instead, they require a sufficiently accurate understanding of direction, scale, probability, and consequence to distinguish between materially different courses of action.
An investor deciding whether an asset is materially undervalued does not necessarily need to know its precise fair value, just as a policymaker deciding whether an economy is entering a period of significant weakness does not need to know the exact level of GDP six quarters from now. Similarly, a business deciding whether an investment opportunity is commercially viable does not need to know its future revenue to the nearest pound if the economics of the opportunity remain attractive across a broad range of plausible outcomes.
In each case, the decision depends upon whether the available evidence is sufficient to distinguish materially different states of the world. Analytical quality should therefore be judged partly by the usefulness of the resulting distinction; if an analysis can reliably establish that an asset is worth considerably more than its current price under a broad range of reasonable assumptions, it may be more valuable than a model producing a highly precise valuation that depends upon a narrow set of fragile assumptions.
Approximate correctness is therefore not a lesser form of correctness. In uncertain environments, it can represent the highest level of correctness that the available information permits, particularly when the objective is not to describe the future perfectly but to determine whether the balance of probabilities and consequences is sufficiently favourable to justify action.
When Precision Does Matter
The argument for approximation should not be misunderstood as an argument against precision because there are many situations in which precision is both possible and essential. Engineering tolerances, accounting reconciliations, settlement systems, risk limits, legal obligations, scientific measurement, and operational processes may depend upon exact calculations because small deviations can have material consequences.
The key question is whether the underlying quantity is sufficiently observable and stable to justify precise measurement. There is little value in reporting an uncertain long-term economic forecast to several decimal places, but there is considerable value in calculating a transaction settlement accurately to the required unit because the underlying obligation is specific and the consequences of error are measurable. Precision is therefore most useful when measurement uncertainty is small relative to the decision being made and when the underlying relationships are sufficiently stable for the additional detail to matter. This distinction prevents approximate reasoning from becoming an excuse for sloppiness because the appropriate degree of precision should be determined by the structure of the problem rather than by a general preference for either numbers or intuition.
Good analysts are consequently capable of moving between exact calculation and approximate judgement, using each where it is most appropriate. The objective is not to choose between precision and approximation as competing philosophies, but to understand when each provides the greatest analytical value.
Approximation in a Complex Adaptive System
The challenge becomes even more profound when the object of analysis is a complex adaptive system because financial markets are not passive environments in which fixed laws operate independently of observation. Participants learn, adapt, imitate, compete, hedge, arbitrage, and change their behaviour in response to market conditions; their collective actions then alter the system being observed, creating feedback loops that can make exact prediction inherently difficult.
If investors become convinced that an asset is undervalued, for example, their purchases may cause its price to rise and thereby reduce the very undervaluation that attracted them. Conversely, if a market becomes perceived as fragile, participants may reduce their exposure, thereby creating some of the stress that they initially feared. Expectations can consequently become causes rather than merely reflections of future outcomes, while attempts to forecast the system can themselves influence the system.
Under such conditions, approximate reasoning becomes particularly valuable because it recognises that the system cannot be reduced to a static collection of relationships. The analyst must continually update beliefs as new evidence emerges and remain alert to changes in the environment that may invalidate previously useful assumptions; this requires a probabilistic rather than deterministic mindset in which attention is directed toward what appears increasingly likely, what remains uncertain, which assumptions carry the greatest weight, and what evidence would cause the conclusion to change.
The objective is therefore not to eliminate uncertainty but to become better at navigating it. Approximation provides a practical framework for doing so because it permits conclusions to remain useful without pretending that the underlying system is more stable, observable, or predictable than it actually is.
The Danger of False Precision
False precision is particularly dangerous because it can survive scrutiny more easily than obvious error. A clearly absurd forecast is likely to be rejected, whereas a detailed model containing reasonable assumptions, sophisticated mathematics, and precise outputs can create an impression of credibility even when its central premises are weak or its uncertainty is materially understated.
This is partly a psychological phenomenon because human beings often associate complexity with competence and precision with knowledge. A number expressed to four decimal places can appear more authoritative than a broad range even when the underlying evidence cannot justify distinguishing between the values contained within that range. Financial institutions are not immune to this tendency. Models can become institutionalised, outputs can become embedded within decision processes, and numerical estimates can acquire authority simply because they are generated systematically; over time, the distinction between a model's output and the reality it is intended to represent can become increasingly blurred.
The antidote is intellectual humility, which requires analysts to distinguish continually between what is observed, what is inferred, what is assumed, and what is genuinely unknown. It also requires recognition that uncertainty does not disappear merely because it has been expressed numerically; a probability estimate remains an estimate, and a model output remains conditional upon the assumptions and information that produced it.
Numbers are extraordinarily useful tools, but they do not become facts merely because they have been calculated. Their usefulness depends upon whether they represent the underlying uncertainty honestly enough to improve the decision for which they were produced.
From Approximation to Better Decisions
The ultimate purpose of approximate reasoning is not to make estimates less precise; it is to make decisions more robust. A robust decision is one that remains sensible across a range of plausible assumptions and future conditions, rather than one that succeeds only if a highly specific forecast happens to materialise.
If an investment only appears attractive under one narrow set of assumptions, its attractiveness is fragile regardless of how precise the underlying forecast may appear. If the investment remains attractive across a broad range of reasonable outcomes, by contrast, the decision may possess considerably greater resilience even though the future itself remains uncertain.
This shifts the analytical question from:
"What will happen?"
toward:
"What would need to be true for this decision to work?"
The first question encourages forecasting, while the second encourages understanding; more importantly, the second makes it possible to evaluate whether the investment thesis survives when individual assumptions are changed.
This distinction is especially important in investment because capital allocation is fundamentally a decision about asymmetric outcomes. Investors do not need to predict every future development if they can identify situations in which the downside is manageable, the upside is substantial, and the evidence supports a favourable distribution of outcomes. Approximation therefore becomes part of a broader discipline of probabilistic decision-making because it provides enough structure to distinguish attractive opportunities from unattractive ones without requiring the impossible task of forecasting every variable with precision.
The strongest decision is not necessarily the one based upon the most detailed forecast; it is often the one that remains defensible when the forecast is wrong within a reasonable range.
The MorMag Perspective
The art of being approximately right is ultimately an argument for intellectual honesty in an environment that frequently rewards the appearance of certainty. Financial markets, economies, and complex organisations contain too many interacting variables, feedback mechanisms, behavioural responses, and unobservable conditions to permit the degree of precision that many analytical outputs imply; the appropriate response is therefore not to abandon quantitative analysis, but to understand where its precision is meaningful and where it merely creates an impression of certainty that the evidence cannot support.
At MorMag, the distinction between precision and usefulness is particularly important because investment research should ultimately serve capital allocation rather than the production of impressive-looking numbers. A quantitative output has value when it improves understanding, clarifies uncertainty, identifies meaningful differences between opportunities, or changes the quality of a decision; it has considerably less value when its precision merely disguises the fragility of its assumptions. This means that approximately right can often be preferable to precisely wrong. An estimate that correctly identifies the direction of a relationship, the approximate magnitude of an opportunity, or the broad distribution of possible outcomes can provide more useful information than a highly precise forecast whose apparent certainty cannot be justified by the evidence. The distinction is not between quantitative analysis and judgement; rather, it concerns whether quantitative analysis is being used to strengthen judgement or to conceal the limits of what judgement can reasonably know.
The principle also reinforces the importance of ranges, probabilities, scenarios, sensitivities, and continuous updating. Rather than treating an analytical conclusion as a fixed answer, a robust research process should treat it as a conditional judgement that changes when the evidence changes. This is especially important in financial markets because the environment itself is adaptive; assumptions that were reasonable yesterday may become inappropriate tomorrow as liquidity, policy, expectations, behaviour, competitive conditions, and risk appetite evolve. Approximation therefore does not represent a retreat from quantitative sophistication. It represents a more mature use of it, in which models are expected to identify what matters, estimate what can reasonably be estimated, expose what remains uncertain, and reveal how conclusions change when assumptions change. Quantitative outputs inform judgement; they do not replace it, and the usefulness of a model should ultimately be measured by whether it improves the quality and resilience of the decisions that follow from it.
The deeper principle is that uncertainty should be managed rather than denied. An investor who understands the limits of knowledge can distinguish between a genuinely informative estimate and a number whose precision is largely cosmetic, while an investment process that explicitly recognises uncertainty is better positioned to adapt when the world departs from its central assumptions. In a world characterised by incomplete information and complex adaptive systems, the ability to know approximately what is true, while remaining conscious of what remains uncertain, may be one of the most important forms of analytical judgement available.
Conclusion
The art of being approximately right is not the art of being vague; it is the discipline of matching the precision of a conclusion to the quality of the information supporting it. Where the evidence is strong and the underlying relationships are stable, precision can be valuable because additional detail may materially improve the decision; where uncertainty is fundamental and the system is constantly changing, however, insisting upon precision can create an illusion of knowledge that is more dangerous than openly acknowledging uncertainty.
Approximation allows analysts to focus on order of magnitude, direction, probability, sensitivity, and consequence rather than becoming distracted by numerical detail that does not materially improve the decision. It encourages attention toward the assumptions that matter most and makes it easier to distinguish genuine analytical insight from false precision, while also requiring sufficient discipline to prevent uncertainty from becoming an excuse for unsupported judgement.
In financial markets, this distinction is particularly important because the future cannot be observed directly and the systems being analysed are adaptive, reflexive, and only partially observable. Investors therefore operate not by possessing certainty but by forming beliefs, testing assumptions, updating probabilities, and allocating capital according to the balance between potential reward and risk; the quality of the process depends less upon whether every forecast is correct than upon whether the process can distinguish meaningful information from noise and remain resilient when individual assumptions fail.
The strongest analysis is consequently not necessarily the analysis that produces the most precise number. It is the analysis that most accurately represents what can be known, what cannot be known, how uncertainty is distributed, which assumptions matter most, and how much the difference matters for the decision being made.
In summation, being approximately right (when the alternative is precisely wrong), is not a compromise with analytical rigour.; it is analytical rigour applied honestly to an uncertain world.
