The 8% in Your Spreadsheet
Is a Guess, Not a Fact
Is a Guess, Not a Fact
Expected return, volatility, beta, correlation — every one of them is estimated from a slice of the past. Four properties decide how much weight any of those numbers can carry.
8%
The Estimate
25 yrs
Of Data Behind It
±8pp
How Wide It Really Is
📅 2026
⏱ 8 min read
📊 Interactive model
The Number Nobody Has Ever Seen
Ask what equities return over the long run and you will get a number. Eight percent, give or take. It gets typed into a retirement plan, a valuation model, an asset allocation, and from that moment it behaves like a fact.
It is not one. Nobody has ever observed the true expected return of the stock market. It is not recorded anywhere. What you were handed is somebody's average of a finite stretch of history — a sample, ending on a particular date, drawn from a particular market.
The same is true of every other input you will ever use. Volatility, correlation, beta, alpha, the return printed on a fund factsheet. Each one is a statistic computed from a limited window of the past and offered as a stand-in for something unobservable.
Which leaves exactly one question worth asking about any of them: how much is this number worth trusting?
There are broadly three answers you can get back, and telling them apart is the entire job. Each panel below shows where an estimate lands across many repeated samples, against the true value it is chasing.
Confidently Wrong
Tight, repeatable, and off-centre every single time. More data will not move it.
Honest But Vague
Right on average, but so spread out that it cannot settle a decision.
Worth Acting On
Centred on the truth and tight enough that the answer barely moves between samples.
Four Questions About Any Number
Four properties separate a number you can build a portfolio on from one you cannot. The technical name for each is worth knowing, and the rest of the article uses them — but the job each one does matters more than what it is called.
Does it lean?
Whether the method comes out systematically high or low. A method that does not is called unbiased.
Does it improve with more data?
Whether the answer closes in on the truth as the sample grows. That property is consistency.
Is it the sharpest available?
Whether another honest method could squeeze a tighter answer from the same data. That is efficiency.
How much would it move?
How far the number would shift with a different sample. That figure is the standard error.
The Investor
Nour has saved enough to start investing properly. She builds a spreadsheet, types 8% into the growth cell, and works out what her savings become in twenty years. Here is the gap between what she thinks she has and what she actually has:
What the cell implies
A known property of the market. Fixed, measured, the same for everyone who looks it up.
What it actually is
One average, from one sample, ending on one date. Redraw the sample and the number changes.
Nour is about to run into all four properties, in the order they tend to show up. Before that, two of them need separating carefully, because they are the pair most often blurred together.
Unbiased means the method does not lean. Run it on a hundred different samples and the answers scatter evenly around the true value, rather than sitting mostly above it or mostly below it. This holds at any sample size.
Consistent means the method improves. Give it more data and the answer closes in on the true value.
A method can do the second without the first. The sample standard deviation is the everyday example: with only a handful of observations it reads slightly below true volatility, so it is biased. But that lean fades as observations accumulate, and the estimate converges on the right answer. Biased today, right eventually.
Consistent means the method improves. Give it more data and the answer closes in on the true value.
A method can do the second without the first. The sample standard deviation is the everyday example: with only a handful of observations it reads slightly below true volatility, so it is biased. But that lean fades as observations accumulate, and the estimate converges on the right answer. Biased today, right eventually.
Each of the four questions gets a section below, and each section opens with a real decision. Two analysts, two numbers, both calculated correctly — and you pick the one you would act on before the explanation appears. Choosing first is the point: the reasoning lands differently once you have committed to an answer.
Does It Lean?
Decide first · then read on
What have emerging-market equity funds actually returned?
Two analysts search the same fund database and hand you an average annual return.
Analyst A
11.4%
average, 30 years of data
Uses every fund the database currently lists. Three decades of history behind the number.
Analyst B
8.2%
average, 10 years of data
Only a decade, but includes the funds that shut down or merged along the way.
B. Thirty years of the wrong sample is still the wrong sample.
● A — tight, and wrong every time● B — wider, but centred on the truth
The reasoning is in the section below.
Analyst A has three times the data and it does not help. Funds that perform badly get closed or merged away, and when they go they leave the database — so A is averaging the ones that survived.
Every year of that sample quietly excludes the failures, which means the number comes out high not by accident but systematically. This is survivorship bias, and it is why fund industry averages have historically flattered the industry.
Notice the shape of the failure. A leaning method does not give you a scattered answer. It gives you a confident one, in the wrong place, over and over. And extra observations cannot move it: more data cures noise, not a sample collected the wrong way.
| Where it shows up | What gets distorted | Which way it leans |
| Fund databases | Average returns, once the closed funds have dropped out | Too high |
| Hedge fund indices | Good early years added retrospectively when a fund joins | Too high |
| Property and private credit | Volatility and correlation, when prices are stale rather than traded | Too low |
That last row is the quietly dangerous one. Assets that trade rarely appear calmer and less correlated than they really are, which makes them look like better diversifiers than they are. The bias is not in the arithmetic. It is in the prices being fed into it.
Does It Improve With More Data?
Decide first · then read on
How volatile is this utility company?
A large, stable business. Same operations, same debt load, same market for years.
Analyst A
14.1%
from 12 months of returns
One year of daily data, calculated correctly.
Analyst B
17.6%
from 120 months of returns
Ten years of daily data, identical method.
B. As the sample grows, the estimate settles down.
● A — 12 months, scattered● B — 120 months, recentred and tight
The reasoning is in the section below.
Neither analyst did anything wrong here — this is not the survivorship case in disguise. Both used an honest method. The difference is only how much the answer has had a chance to settle.
And as the sample grows, two things happen at once. It is the pairing that matters:
It recentres
The estimate drifts toward the true value as observations arrive, and any small-sample lean shrinks away.
It tightens
The estimate stops swinging between samples. Two analysts running the same method start agreeing with each other.
Together those two are consistency. It is also why a slightly imperfect method can still be the right one to reach for — the sample standard deviation leans low in small samples, but the lean fades and the estimate converges. Unbiased means right on average. Consistent means right eventually.
Which invites the obvious conclusion: use as much history as you can find. That conclusion has a condition attached, and the next decision is where it breaks.
Decide first · then read on
What is this company's beta?
Three years ago the firm tripled its debt to fund a takeover. Its balance sheet today looks nothing like its past.
Analyst A
0.85
from 20 years of monthly returns
The longest history available. Two hundred and forty observations.
Analyst B
1.40
from 3 years since the deal
Only the period after the balance sheet changed. Thirty-six observations.
B. More data helps only while the company stays the same company.
● A — precise, about a company that no longer exists● B — noisier, about this company
The reasoning is in the section below.
Consistency assumes the process generating the data stands still. This one did not. A company carrying three times the debt is a riskier equity, full stop — and seventeen of Analyst A's twenty years describe a business that no longer exists.
So A's extra data is not extra evidence about the investment. It is evidence about a different, safer company that happens to share a name and a ticker.
The question is never only how much data do I have. It is how much of this data describes the asset I am buying today. A fund whose manager changed strategy, an economy in a new regime, a company after a transformative acquisition — in each case a long history quietly stops being an advantage.
Is It The Sharpest Available?
Decide first · then read on
Two ways to estimate the same beta.
Both analysts use the identical 60 months of returns. Both methods are honest: repeated over and over, each averages out to the true beta.
Analyst A
0.95 – 1.25
where the estimate lands across samples
Same data, tighter method. The answer barely moves.
Analyst B
0.70 – 1.55
where the estimate lands across samples
Same data, looser method. The answer swings.
A. Both are right on average. Only one is precise enough to use.
● A — same centre, far less scatter● B — honest, but vague
The reasoning is in the section below.
This is the first decision where neither number leans and neither would improve by waiting for more data. Both methods are unbiased. Both would converge. They differ only in how much they scatter, and the one that scatters less is the more efficient estimator.
So the choice is not between right and wrong. It is between precise and vague, from exactly the same information — which is the part that makes efficiency worth paying for. A wider answer costs you nothing in accuracy and everything in usefulness.
That matters here more than in most places, because beta does not stay in the spreadsheet where it was calculated:
Cost of equity = risk-free rate + beta × equity risk premium
Beta → Cost of equity → WACC → Discounted value of the shares
Beta → Cost of equity → WACC → Discounted value of the shares
Run Analyst B's range through that chain and the valuation it produces spans outcomes that would have you buying and selling the same share. The statistics are not a step before the valuation. They are the valuation.
How Much Would It Move?
Decide first · then read on
What return should you expect from this equity index?
Both analysts arrive at exactly the same answer: 8% a year. The index has a volatility of roughly 20%.
Analyst A
8%
from 4 years of data
Four annual observations behind the number.
Analyst B
8%
from 25 years of data
Twenty-five annual observations behind the number.
B — and even B is shakier than it looks.
● A — 4 years, standard error 10%● B — 25 years, standard error 4%
The reasoning is in the section below.
Identical answers, and one of them is worth far more than the other. What separates them is the standard error, which answers the question none of the previous three did: if you had drawn a different sample, how far would this number have moved?
If the true volatility is known: σ ÷ √n
If it is not — the normal case: s ÷ √n
If it is not — the normal case: s ÷ √n
For Analyst A that is 20% ÷ √4 = 10%. For Analyst B, 20% ÷ √25 = 4%. Same estimate, very different claim on your confidence.
And the square root carries a sting. To halve your uncertainty you do not need twice the data. You need four times the data.
Twenty-Five Years of Data, and Still Almost Nothing
Now take Nour's 8% seriously. It came from twenty-five years of annual returns on an index with a volatility of around 20% — Analyst B's number, the better of the two. This is how it went into her spreadsheet:
Expected return = 8.00% — treated as a fact, and it is not one
And this is what it actually says once the standard error is attached and taken out to a rough 95% range:
Standard error = 20% ÷ √25 = 4.00%
Range = 8% ± 1.96 × 4% = 8% ± 7.84%
True expected return sits somewhere between 0.16% and 15.84%
Range = 8% ± 1.96 × 4% = 8% ± 7.84%
True expected return sits somewhere between 0.16% and 15.84%
Twenty-five years of history, and the honest answer is somewhere between almost nothing and very good indeed.
That range is wide enough to justify two completely different portfolios. And to halve it, Nour would need a century of data — by which point the market she is measuring would be unrecognisable.
The 8% was never a fact. It was an estimate with an interval attached, and the interval was the more informative half.
That range is wide enough to justify two completely different portfolios. And to halve it, Nour would need a century of data — by which point the market she is measuring would be unrecognisable.
The 8% was never a fact. It was an estimate with an interval attached, and the interval was the more informative half.
A note on the arithmetic: this uses twenty-five annual observations, so n = 25 and the square root is 5. Using monthly data would raise n and shrink the standard error, but it buys less than it appears to — the volatility scales too, and the years of history are what actually constrain the answer.
What Professional Investors Do Instead
None of this makes history useless. It makes a raw historical average an unfinished piece of work — which is why capital market expectations at serious institutions are rarely just a long-run mean.
Longer histories, selectively
Use more data where the underlying process really has been stable. Discard history that no longer applies.
Building blocks
Assemble expected returns forward from a risk-free rate plus premiums, rather than reading one number off the past.
Shrinkage
Pull noisy estimates toward a sensible prior so one strange sample cannot dominate the allocation.
Blending
Combine several independent estimates instead of betting the portfolio on any single one.
Every one of those answers the same problem: the inputs are estimates, and estimates carry uncertainty that does not disappear because a spreadsheet displays the number to two decimal places.
The Four Questions, Side by Side
| The question | Its technical name | Where it bit in this article |
| Does it lean? | Unbiasedness | Survivorship bias in the fund database — three decades of data that could not help |
| Does it improve with more data? | Consistency | Volatility settling as the sample grew, then a beta that a long history made worse |
| Is it the sharpest available? | Efficiency | Two honest betas, one usable, feeding cost of equity and valuation |
| How much would it move? | Standard error | 8% turning into a range from 0.16% to 15.84% |
Check Your Understanding
Click each question to reveal the answer.
1. Thirty years of fund returns should beat ten. Why does the longer sample give the worse answer?
Because the problem is in how the sample was collected, not how large it is. Closed funds have already been removed from the database, so every one of the thirty years shows survivors only. More observations of a distorted process give you a more precise version of the wrong number. Extra data narrows scatter; it does not shift a systematic lean.
2. If an estimator is biased, why would anyone still use it?
Because bias and consistency are separate properties. The sample standard deviation reads slightly below true volatility in a small sample, yet as observations accumulate both its lean and its scatter shrink toward zero and it converges on the right answer. Unbiased means right on average at any sample size. Consistent means right eventually. An estimator can be the second without being the first.
3. Two analysts produce betas of 0.85 and 1.40 for the same company. The first used twenty years of data. Why is it the weaker estimate?
Because consistency only delivers while the thing being measured stays the same. The company tripled its debt three years ago, so seventeen of those twenty years describe a materially safer business. The longer sample is precise about a company that no longer exists. Relevance of the data beats quantity of it.
4. Twenty-five years of returns give an expected return of 8%. Why is that not enough to build an allocation on?
Because the standard error is 20% ÷ √25 = 4%, putting a rough 95% range at roughly 0.16% to 15.84%. The point estimate is fine; the interval around it spans outcomes calling for entirely different portfolios. And since precision improves only with the square root of the sample, closing that range meaningfully would take a century of additional data.
RUQQI KEY TAKEAWAYS — PROPERTIES OF ESTIMATORS
- Expected return, volatility, beta and correlation are estimates from a finite sample, never observed facts.
- Bias is a flaw in how the sample was collected, so more data cannot remove it.
- Consistency means the estimate both recentres on the truth and tightens as the sample grows.
- Unbiased and consistent are different promises. The sample standard deviation keeps the second without the first.
- A long history only helps while the asset stays the same asset. Relevance beats length.
- Between two honest methods, the efficient one gives a tighter answer from identical data — and beta flows straight into valuation.
- The standard error falls with the square root of the sample, so halving uncertainty takes four times the data.