One of the most important lessons I have learned after more than a decade of studying businesses, valuation, financial markets, and investor behaviour is that precision and accuracy are not the same thing.

This lesson sounds obvious.

Yet in practice, investors repeatedly confuse the two.

The confusion often begins innocently enough. A discounted cash flow model produces an intrinsic value estimate of $142.37 per share. A Monte Carlo simulation generates an expected return of 31.46%. A spreadsheet calculates a weighted average cost of capital of 8.73%.

The numbers look scientific. The numbers look rigorous. Most importantly, the numbers look precise.

Unfortunately, none of these characteristics necessarily make them accurate.

Over time, I gradually stopped using two decimal points when assessing intrinsic value. Today, I still use them when reporting actual investment performance because realised returns are historical facts. However, I rarely use them when estimating future value because intrinsic value is not a fact. It is an estimate.

The distinction matters enormously.

Ironically, one of the people who helped shape this perspective was the individual often referred to as the “Dean of Valuation,” Aswath Damodaran.

Damodaran has spent decades teaching valuation at the Stern School of Business and has consistently emphasized that valuation is a combination of stories, assumptions, probabilities, and numbers rather than a purely mechanical spreadsheet exercise. He has repeatedly warned investors against becoming trapped in what he calls “spreadsheet nirvana” — the belief that increasingly detailed models automatically produce better valuations.

In my view, this lesson becomes especially important when examining the difference between 31% and 31.46%.

At first glance, the difference appears trivial.

In reality, it reveals an important truth about investing.

The Illusion of Precision

Suppose an analyst presents the following conclusion:

31% Expected annual return Communicates an estimate
31.46% Expected annual return Implies a calculation

Most people instinctively interpret these two numbers differently. The second estimate feels calculated. The first estimate feels approximate. The second implies knowledge. The first implies uncertainty. Yet both numbers may be based on exactly the same underlying assumptions.

The additional decimal places create an illusion of confidence.

This is one of the oldest problems in quantitative analysis. A model can produce outputs with extraordinary numerical precision while the inputs themselves remain highly uncertain.

Consider a simple intrinsic value model. You might forecast:

Each assumption contains uncertainty. None of these variables can be known with certainty. When these uncertain assumptions are combined, the resulting valuation estimate inherits their uncertainty.

A model that outputs $142.37 is therefore not necessarily more accurate than one that outputs $140. The extra $2.37 often reflects computational precision rather than economic reality.

This is precisely why Damodaran frequently emphasizes uncertainty in valuation and distinguishes between estimation uncertainty and economic uncertainty. While better analysis may reduce estimation errors, much of valuation uncertainty comes from the inherently unpredictable nature of the future.

The future is not a spreadsheet.

Intrinsic Value Is a Range, Not a Point Estimate

One of the most important shifts in my thinking occurred when I stopped viewing intrinsic value as a single number.

Instead, I began viewing intrinsic value as a range of plausible outcomes.

Imagine a company whose intrinsic value estimate is $100. What does that really mean? Does it mean the company is worth exactly $100.00? Of course not.

It might reasonably be worth:

The true economic value is not a precise point. It is a distribution.

Damodaran himself defines intrinsic value as value derived from an asset’s fundamentals — namely cash flows, growth, and risk. However, estimating those fundamentals necessarily requires assumptions about an uncertain future.

When viewed through this lens, the difference between $100.00 and $100.37 becomes largely irrelevant. The difference between $80 and $120 is what actually matters.

The investor who debates the final decimal point while ignoring the uncertainty surrounding long-term growth assumptions is focusing on the wrong variable.

Why Two Decimal Points Matter in Performance Reporting

Interestingly, I do not apply the same standard to performance reporting.

Here, two decimal points can be useful.

If a portfolio generated a return of 31.46%, that figure reflects a realised historical outcome. The portfolio either earned that return or it did not. The return is observable. The return is measurable. The return is factual.

Reporting 31.46%, therefore, serves a different purpose. It is not an estimate. It is a record.

This distinction is often overlooked.

These are fundamentally different concepts. One belongs to accounting. The other belongs to forecasting.

The Behavioural Danger of False Precision

Behavioural finance offers another reason to be cautious.

Human beings naturally equate precision with expertise. If one analyst says a stock is worth approximately $100 and another says it is worth $101.73, many investors instinctively view the second analyst as more knowledgeable. Yet there is no evidence that the second estimate is more accurate. The additional precision merely appears more sophisticated.

This behavioural bias has been observed repeatedly across disciplines. People often assign greater credibility to highly specific forecasts even when those forecasts possess no greater predictive power.

In investing, this creates a dangerous feedback loop:

The irony is that the increased confidence may have been entirely unjustified.

Damodaran has repeatedly argued that valuation requires balancing narrative and numbers. The numbers must be connected to a coherent business story, while the story must remain grounded in reality. Excessive focus on numerical detail can obscure rather than improve judgment.

Why Professional Investors Often Round

Many inexperienced investors believe institutional investing involves extraordinary numerical precision.

The reality is often quite different.

Experienced investors frequently round. Not because they lack analytical capability. Because they understand the limitations of forecasting.

A portfolio manager might estimate:

The word “roughly” appears frequently. The word “approximately” appears frequently.

This is not laziness. It is intellectual honesty.

When uncertainty is large, pretending otherwise does not improve the analysis. It merely disguises the uncertainty.

In fact, some of the world’s most successful investors deliberately simplify complex situations. They recognize that future outcomes are driven more by broad business economics than by tiny modelling refinements.

The key question is often not whether intrinsic value is $142.37 or $144.19. The key question is whether intrinsic value is closer to $80 or $180.

A Practical Example

Imagine two analysts examining the same business.

Analyst A

Intrinsic value

$142.37

Expected return

31.46%

Confidence level

High

Analyst B

Intrinsic value

$140–$160

Expected return

~30%

Confidence level

Moderate

Many investors would initially favour Analyst A.

I would increasingly favour Analyst B.

Because Analyst B acknowledges uncertainty. The range communicates the true nature of valuation. The estimate remains useful while avoiding the false implication of certainty. Analyst B understands that valuation is an exercise in probability rather than prediction.

The Real Meaning of 31% Versus 31.46%

This brings us back to the title of this essay.

Mathematically, the difference between 31% and 31.46% is only 0.46 percentage points.

Psychologically, however, the difference is much larger.

31% communicates: this is an estimate.
31.46% often communicates: this is a calculation.
Investors frequently treat the second statement as more reliable — yet both numbers may be based on identical assumptions.

The additional decimal places can create a false sense of certainty that exceeds the quality of the underlying information.

This is why I now reserve such precision for reporting realised outcomes rather than forecasting future value.

Final Thoughts

Perhaps the greatest lesson I have taken from years of studying valuation is that the goal is not to eliminate uncertainty.

The goal is to understand it.

No spreadsheet can remove uncertainty from investing. No model can eliminate economic unpredictability. No analyst can know the future with precision.

Damodaran has long argued that valuation is fundamentally about making judgments regarding cash flows, growth, and risk under uncertainty rather than discovering a single immutable truth.

As investors, we should strive to be approximately right rather than precisely wrong.

When estimating intrinsic value, I increasingly prefer rounded numbers, valuation ranges, scenario analysis, and margin-of-safety thinking. The decimal places have not disappeared because they lack mathematical validity. They have disappeared because they often imply a level of knowledge that does not exist.

A realised portfolio return of 31.46% deserves two decimal points because it actually happened.

An estimated future return of 31.46% deserves scepticism because it has not.

That is why, today, I still use two decimal points when reporting investment performance.

But when assessing intrinsic value, I usually stop at 31%.