# Holding period and the chance of a loss: stocks vs a 60/40

Canonical URL: https://marketheist.io/portfolio/learn/time-horizon
By Jeffrey Lin · Published 2026-11-07 · Updated 2026-11-07 · Data through Sep 2026
Category: Risk

## Key takeaways

- Over one year, a stock index and a stocks-and-bonds mix have ended with a gain in a similar share of rolling windows; in the US record shown here the difference appears over three to ten years, where the mix lost money less often.
- The share of rolling windows with a gain rises with the holding period because an annualized return averages more years; a 20-year record without a losing window is a description of one history, not a rule.
- Rolling windows overlap: consecutive 20-year windows share all but one month, and a 40-year history holds only two 20-year periods that do not overlap. The counts carry far less evidence than their number suggests.
- A falling chance of a loss is not falling risk. The size of the worst possible shortfall in dollars grows with the period, which is why Samuelson (1963) and Bodie (1995) argued that stocks do not become safer simply by holding them longer.
- MarketHeist counts a window as a gain when its annualized total return is zero or above, using monthly data with dividends reinvested, before inflation and taxes.

## Definition

The chance of a loss over a holding period is the share of all past periods of that length, starting in any month, that ended below where they began. For stock markets it has fallen as the holding period lengthens, but the periods overlap, the record covers few independent decades, and a lower chance of a loss is not a smaller possible loss.

Also known as: time horizon risk, probability of loss over time, time diversification, do stocks always go up in the long run, stocks for the long run, chance of losing money over 10 years.

## How it works

Take every holding period of a given length in a history, one starting in each month, and check whether it ended above or below where it began. The share that ended with a gain is the usual answer to the question of how often stocks have lost money over five, ten or twenty years. The rolling returns guide explains how the windows are built; here the question is what their share of gains does and does not show.

The share rises with the period for a simple reason. A long holding period's annualized return is an average of its years, and an average of many years swings less than one year does, so it crosses below zero less often. If yearly returns were independent draws with a positive average, the chance of a loss would keep falling with the square root of the number of years.

The evidence is thinner than the window counts suggest. Two 20-year windows a month apart share 239 of their 240 months; they are not two observations. A history of about 40 years holds two non-overlapping 20-year periods, and 100% of rolling 20-year windows with a gain means, statistically, that two or so independent stretches both ended up. One bad stretch in a different country or century is enough to break the pattern: Japanese stocks, measured by price, were still below their 1989 peak more than three decades later.

Holding longer to avoid a loss is like taking a longer route to avoid traffic lights: there are fewer stops, but when the road is blocked, the detour is longer. A long holding period rarely ends below its start, and when it does, many years of returns are lost with it.

This is the argument economists make against "time diversification". Samuelson (1963) showed that repeating a bet many times does not make it safer for an investor whose attitude to risk does not change with wealth; Bodie (1995) showed that the cost of insuring a stock portfolio against ending below a safe investment rises with the horizon. A lower chance of a loss and a smaller loss are different things, and a stocks-and-bonds mix lowers both, at the price of a lower typical return.

## Formula

**Share of N-year windows with a gain**

```
P_N = \frac{#{t:V_t \ge V_{t - 12 N}}}{W_N}, K_N = ⌊\frac{T}{12 N}⌋
```

where:

- P_N: share of rolling N-year windows that ended at or above their starting value
- Vₜ: growth of 1 at the end of month t, dividends reinvested
- W_N: number of rolling N-year windows (one ending in each month after the first full window)
- K_N: number of N-year periods that fit in the history without overlapping
- T: length of the history in months
- ⌊·⌋: round down to a whole number

P_N is computed from W_N windows, but it carries roughly the information of K_N independent periods.

**The textbook model behind the falling chance of a loss (not used by MarketHeist)**

```
Pr (loss over N years) = \Phi ( - \frac{\mu}{\sigma} \sqrt{N})
```

where:

- μ: average yearly log return (continuously compounded growth rate)
- σ: standard deviation of yearly log returns
- Φ: the standard normal cumulative distribution function
- N: holding period in years

It assumes independent, normally distributed yearly log returns with a known, constant μ and σ. Real returns have fat tails, regimes and an uncertain μ, and the uncertainty about μ itself grows with the horizon, so the true chance of a long-horizon loss is higher than this formula gives.

## Worked example

The S&P 500 alone (SPY) and the classic stocks-and-bonds portfolio (60% SPY, 40% BND, rebalanced every December), every rolling window from Jan 1987 to Sep 2026, about 40 years of monthly total returns.

Over one-year windows the two were almost indistinguishable by this measure: the S&P 500 ended with a gain in 81.9% of windows and the 60/40 portfolio in 83.4%. Bonds did not make a year in the red much rarer; they made it shallower.

The gap opened over longer periods. The S&P 500 gained in 88.2% of 5-year windows and 93.3% of 10-year windows; the 60/40 portfolio in 99.3% and 100.0%. Its worst 10-year window still earned 0.8% a year, while the S&P 500's worst returned -3.4% a year, over a decade that took in both the 2000 to 2002 decline and the 2008 crash.

Every 20-year window of both ended with a gain. Stocks' typical 20-year result was higher, a median of 8.6% a year against 7.8%, but their worst 20-year window, 4.7% a year, earned less than the 60/40 portfolio's worst, 5.3%.

These counts come from 237 overlapping 20-year windows in about 40 years of data, which hold at most two 20-year periods that do not share a month. "Every 20-year window had a gain" is an accurate description of this history and a weak basis for a promise about the next 20 years.

Data through Sep 2026. Reproduce id: 24f2b6fdb453c0cf (this guide, its lab setup and the data month).

## How MarketHeist computes it

- **Data**: Monthly total returns (dividends reinvested). Funds younger than the period shown are extended backward with older funds, spliced on returns, not prices.
- **Window**: The worked example and the lab use the common window of the two portfolios compared, Jan 1987 to Sep 2026 (477 months), ending at the data month of this page; a holding period is every window of that many years that fits inside it.
- **Portfolio streams**: A fund is its proxy-extended monthly return stream. A built-in portfolio is read as the MarketHeist MCP reads it: its composed stream with its own rebalancing rule and overlay. A custom mix is rebalanced yearly.
- **Holding periods**: From the monthly value path rebased to 1: for every month-end that has N years of history before it, the annualized return is (value now over value N years earlier) to the power 1/N, minus 1 (for one year, the plain return). The highest, lowest and median are over those windows; a window with a gain is one at or above 0. Overlapping windows share months, so the count of windows is not a count of independent periods.
- **Gain**: A window counts as a gain when its annualized total return is zero or above. Returns include reinvested dividends and are not adjusted for inflation, taxes or fees beyond the funds' own expense ratios. (`rollingStats` in packages/portfolio/engine/windows.ts)
- **Windows**: One window of 12N months ending in every month of the common window of both picks, once 12N months of history are available. Windows overlap; no adjustment is made for that. (`rollingCagr` in packages/portfolio/engine/windows.ts)
- **Portfolios**: A template's monthly returns are its simulated returns with its own rebalancing rule (the 60/40 resets to its targets every December), the same series the portfolio app and the MCP use. (`simulatePortfolio` in packages/portfolio/engine/portfolio.ts)
- **No probability model**: The share of windows is counted, not modelled. MarketHeist does not fit the normal-distribution formula above; the bootstrap lab in the Monte Carlo guide simulates paths from the same monthly returns instead.
- **Engine functions**: `rollingStats` (packages/portfolio/engine/windows.ts), `rollingCagr` (packages/portfolio/engine/windows.ts), `equityCurve` (packages/portfolio/engine/metrics.ts)

## Holding period and the chance of a loss compared with its neighbours

Ways to judge the risk of a long holding period

| Measure | What it counts | Grows or shrinks with the period | Main weakness |
| --- | --- | --- | --- |
| Share of rolling windows with a loss | How often a period ended below its start | Shrinks | Overlapping windows; one history |
| Worst rolling return | The deepest annualized result of any period | Shrinks in annualized terms | Set by one or two episodes |
| Shortfall in dollars | How far the ending value fell below a safe alternative | Grows | Needs a chosen safe alternative |
| Maximum drawdown | The deepest fall from a peak along the way | Grows or stays | Says nothing about recovery time on its own |
| Bootstrap simulation | Share of simulated paths ending below the start | Shrinks, usually more slowly | Assumes the past months are a fair sample |

## Limitations

- The windows overlap, so the share of windows with a gain is not a probability estimated from independent trials. Over long holding periods it rests on one or two distinct stretches of history.
- It is one country's record over one era. US stocks had one of the strongest records of any market; studies of many developed markets find long-horizon losses, especially after inflation, much more common than US history alone suggests.
- Returns here are nominal. After inflation, the share of long windows with a gain is lower, and in decades of high inflation bonds lost real value over long periods too.
- The measure ignores the path. A 10-year window that ended slightly up may have spent years far below its start, which is what makes investors sell; the drawdown and Ulcer index guides measure that.
- Long histories are extended backward with older funds or indexes where a fund is younger than the window, so early windows approximate the fund rather than reproduce it.

## Frequently asked questions

**Have US stocks ever lost money over 20 years?**

In the monthly total-return data used here, no 20-year window of the S&P 500 ended below its start, and Siegel's two-century US record found none with a loss after inflation, though several earned little more than inflation. Other markets have had 20-year losses, Japan's among them. The absence of a loss in one market's history is not a rule.

**Does holding stocks longer make them less risky?**

It makes an annualized loss less frequent in the historical record, but not the outcome less uncertain in dollars: the range of ending wealth widens with time. Economists call the belief that long horizons cancel risk the time diversification fallacy; whether it applies to an investor depends on whether the money has a fixed date and amount it has to reach.

**Why did the 60/40 portfolio lose money less often?**

Bonds rose or held up in several of the years stocks fell, and they earned interest throughout, so the mix's annual results were less spread out. A narrower spread around a positive average crosses below zero less often over any period, at the cost of a lower typical return.

**What holding period is safe for stocks?**

None is safe in the sense of a promise. Past data show the share of losing periods falling as the period lengthens, but the evidence for long periods rests on few independent episodes. Money needed by a fixed date is usually matched to assets whose value at that date is more certain, such as bonds that mature then.

## References

1. Samuelson, P. A. (1963) Risk and Uncertainty: A Fallacy of Large Numbers. Scientia 98. Why repeating a gamble does not make it safer.
2. Bodie, Z. (1995) On the Risk of Stocks in the Long Run. Financial Analysts Journal 51(3). The cost of insuring against a shortfall rises with the horizon.
3. Siegel, J. J. (1994) Stocks for the Long Run. McGraw-Hill. The case for long holding periods from two centuries of US data.
4. Fama, E. F. and French, K. R. (2018) Long-Horizon Returns. Review of Asset Pricing Studies 8(2). Bootstrap evidence on how often stocks trail bills over long horizons.
5. Anarkulova, A., Cederburg, S. and O'Doherty, M. S. (2022) Stocks for the Long Run? Evidence from a Broad Sample of Developed Markets. Journal of Financial Economics 143(1). Long-horizon losses after inflation across many countries.

## Try it

App: https://marketheist.io/portfolio/p/classic-60-40

MCP prompt (MarketHeist MCP server, https://marketheist.io/mcp):

```
Using MarketHeist.io, in what share of rolling 1-, 5-, 10- and 20-year periods did the S&P 500 and a 60% SPY / 40% BND portfolio end with a gain, and what were the worst periods of each?
```

Historical simulation, not advice.