Over a hundred years of S&P 500 gains — and the years that were not so great.

The pitch we all know.

For years the script has been the same. Time in the market beats timing the market. Ignore the naysayers. Dollar-cost average. Buy the dips. Set it and forget it. Markets are efficient in the long run, so investors with a long time horizon (especially the young) can absorb the losses and make them back.

Wait. There are losses?

Yes. And some of them are large enough to change a plan. Why? Because we’re humans and as humans we panic. But before anyone hides cash under a mattress — or loads the whole book into an index fund because “the average is 8%” — look at the record. Prices go up, down, and sideways. What an astute investor who manages risk actually asks is not “did the market go up on average?” It is “how wide is the miss around that average, and can this household live through it?”

That should be the primary task of any investor willing to put precious capital to work. Before discussing portfolio weights. And before rendering a verdict on buy-and-hold.   That’s the job and this post should help. Let’s look at the data, the raw object: one hundred and one years of annual price changes in the S&P market index (even before it became 500).

What we are measuring.

The working file is beginning-of-year levels of the S&P market index from 1 January 1925 through 1 January 2026. That produces 101 annual price returns (1 January 1925→1926 through 1 January 2025→2026). That is the sample.

These are price returns, not total returns. Dividends were paid along the way. We are not reinvesting them here. Admittedly, that understates the compounded wealth effect. Historically they have been a large part of the total paycheck — on the order of four points a year against a 6.7% price-only compounded rate. We set them aside for now for one reason only: the industry’s working definition of market risk is the volatility of price changes, and that volatility is almost the same with or without the dividends. Wealth later. Risk first.

Why rates of change at all? Because price levels at different time periods and different economic regimes aren’t meaningful.  A price of 10.58 in the beginning of 1925 has little in common with the current trading price in 2026. It’s apples and oranges, they’re not comparable. What remains relevant are the rates of change across prices. Those stay consistent irrespective of time and it conveys investor behavior through different economic regimes. Convert each year to a percentage change and every regime speaks the same language — Depression, postwar boom, stagflation, GFC, whatever comes next.

The grade-school formula is the whole engine:

E(r) is the calendar-year price return. $P_{t}$ is this beginning-of-year index level. $P_{t−1}$ is last year’s. price level. Subract 1 to get the rate change and multiply by 100 to convert the whole value into percentage terms. That’s it! That’s the math. Keep this in mind as there’s a nifty trick in excel that will make this calculation even simpler.

Four numbers, four insights

Arithmetic mean. 8.43% a year.

Add the 101 returns and divide by 101. That is the expected one-year price return if next year is drawn from this history. It is not the growth rate of a dollar left alone. It is a year-over-year rate of change. Useful but not complete.

Geometric mean. 6.70% a year.

Alternatively:

A dollar at the 1925 close became about 655 price-index dollars by the 2025 close. The gap between 8.43% and 6.70% is variance doing its work: a bad year shrinks the base that a good year later multiplies. Mix the two means and a slide deck turns a volatile asset into a bond. One looks noisy (8.43%) while the other looks like a smoother ride (6.70%). Pay attention here as this is what sell-side marketers are really good at.

Sample standard deviation. 18.58%. Variance 0.0345.

In English: the typical year’s miss from the 8.43% mean is on the order of nineteen percentage points. A one-sigma year is roughly −10% or +27%. About two-thirds of the history landed inside that band. We use n−1, not n, because these 101 years are a sample from a process, not the entire future of the market. Calculate it manually to really understand what it meansExcel: STDEV.S.

Excess over cash. About 4.63 percentage points.

The working cash stand-in is 3.8% (three-month Treasury bill, not fed funds). Subtract 3.8% from 8.43% and you have the premium the equity book has historically asked a household to underwrite. The premium is the compensation. The 18.58% is the invoice. That premium is also called the equity risk premium — here measured on price returns, so it is a conservative cousin of the textbook total-return premium.

The median year was +10.87% — better than the mean — because the left tail is longer than the right (skew about −0.40). Most years are fine. A handful of deep corrections sit far enough left to drag the average below the typical year. That is negative skew. It is not a coin flip around 8%.

The chart: over a hundred tickets, not a smooth 8%

Figure 1: Green bars are up years; red bars are down years. The solid line is the 8.43% arithmetic mean. Dashed lines are one standard deviation either side. The dotted line is the 3.8% cash stand-in.

Sixty-nine years were positive. Thirty-one were negative. Sounds about right. Statistically consistent. More than 2 out of 3 returns (~67%) is positive that’s why the market index has a positive drift. Twenty-seven years paid +20% or more on price alone. Six years took 20% or more. The worst single print in the file is 1931 at −48.1%. The best is 1933 at +48.7%. Clustering matters: the market regime between 1929 and 1932 cut the index by about 71%; 1973–74, 2000–02, and 2008 each took a bit more than a third. Pay careful attention here since these are times when accumulated wealth gets destroyed but it’s also a time when the greatest opportunities are found.

That is the statistical content of equity risk. It is not a feeling. It is a histogram with a long left-tail. A plan that needs the money on a fixed date cannot treat 8.43% as a coupon. It’s not a fixed payment, it changes. That’s why it’s an expectation not a promise.

Significant drawdowns can destroy your wealth. But with the right risk management approach it can also value good assets at great discounts. Again, focus on risk, wealth comes as a natural consequence of it.

How a risk manager reads the data

Expected return is the first moment. It answers: if I must put a number on next year’s price change, what is the center of that price history? Variance is a second moment. It answers: how wide is the cloud around that center? Risk-adjusted thinking starts when those two numbers sit in the same sentence.

An 8.43% mean with 18.58% volatility is a noisy paycheck. The ratio of mean to sigma is about 0.45 before cash. The ratio of excess return to sigma — the Sharpe ratio on this price series — is about 0.25. Neither ratio tells you how much of the market index to hold. They are diagnostics. They tell you the average year is not the typical year, and that cash at 3.8% buys a much tighter cloud at the cost of most of the premium.

Two more observations. First, arithmetic mean is the right input for a one-period expectation; geometric mean is the right description of a path that compounded. Second, over a hundred annual observations is long enough to see the shape and still short enough that the next crash is not required to look like 1931 or 2008. All it takes are consecutive years of losses and impact is the same. History sets the scale. It does not sign the next ticket. It doesn’t tell you with certainty what the return will be the following year or if a crash is coming. It doesn’t tell you if buy-and-hold is a good strategy. What it tells you is what the market expects and that it isn’t certain. It’s up to you to manage the risk.

What the averages are not

This is not a forecast that next year, or even the next decade, pays 8.43%. “Expected” is the operative word here. It’s a statement about the center of a noisy historical distribution, not a promise. It is not a claim that dividends do not matter. They do — just not in this context. It is not an indictment against the buy-and-hold strategy either. But it should be enough to question it. That question was brought up because everyone arrives with it. The data only get you as far as this: the paycheck is real but so is the risk associated with it.

So, the next time someone tells you to own the market because it pays well on average, look them in the eyes and ask the only follow-up that matters.

At what cost?