VALYNOXSTRATEGY RESEARCH TECHNOLOGY
AlphaPrimeAlphaPrime
ACADEMY / Market views

Average stock market return: what it hides for systematic traders

The long-run average stock return is one number from one period, usually before inflation and only for markets that survived. Compare a strategy with buy-and-hold of the same market on the same data, and judge both on return and drawdown together.

By · Published · updated · Editorial policy

Contents
  1. What does "the average return on stocks" actually measure?
  2. What does the long-run average leave out?
  3. How much does the chosen period change the average?
  4. How does survivorship bias inflate the average?
  5. How do inflation and investor behaviour lower what people earned?
  6. What did buy-and-hold investors actually live through?
  7. How do you use buy-and-hold as a benchmark for a futures strategy?
  8. How do you compare return against drawdown in a performance report?
  9. Frequently asked questions
  10. References

The long-run average return on stocks is a single number. It depends on the start date, whether dividends and inflation are counted, and which markets survived. It says nothing about the drawdowns holders sat through. To judge a futures strategy, compare it with buy-and-hold of the same contract, on the same data, using return and drawdown together.

What does "the average return on stocks" actually measure?

The quoted average usually measures one index over one long period, often before inflation and with dividends reinvested, so you must check those three choices before you use the number. When you read "over time the average rate of return on stocks is…", ask three questions: from which year, with or without dividends, and before or after inflation. The rule-based alternative to holding is algo trading, which has to beat this baseline after costs.

  • Price or total return. The S&P 500 index level is a price index, so dividends are not in it. A total return series reinvests the dividends. Over decades, the gap between the two is large.
  • Nominal or real. A nominal return is the return in money as quoted. A real return is the return after inflation, so it measures what the money can buy.
  • Arithmetic or compound. An arithmetic average adds the yearly returns and divides by the number of years. A compound average is the single steady yearly rate that turns the starting value into the ending value. The compound average is the one your account actually experiences, and it is always lower when returns go up and down.

The compound annual growth rate (CAGR) is the steady yearly rate that links a starting value to an ending value:

CAGR = (E ÷ S)1/N − 1

Here E is the ending value, S is the starting value and N is the number of years. You take the total growth (E ÷ S), find the yearly rate that compounds to it over N years, and subtract 1 to turn the growth factor into a yearly rate (multiply by 100 for a percentage).

Hypothetical example

An index gains 50% in year one and loses 50% in year two. The arithmetic average is 0% a year. But $100 becomes $150 and then $75. The compound rate is about −13.4% a year. Same two years, two very different "averages".

Now inflation. Round numbers chosen only for the example: a source quotes 10% a year nominal, and inflation averaged 3% a year over the same period. The real return is about 1.10 ÷ 1.03 − 1, or roughly 6.8% a year.

What does the long-run average leave out?

The long-run average leaves out the luck of the chosen period, the effect of inflation on what you can buy and the markets and companies that did not survive. Each one makes the headline number look better than what a typical investor received.

How much does the chosen period change the average?

Results change with the start and end dates. A series that starts after a crash and ends at a market high shows a higher average than one that starts at a high. When two sources quote different figures for the "S&P 500 average return", the usual reason is that they cover different years.

How does survivorship bias inflate the average?

Survivorship bias is the error of measuring only what still exists and ignoring what disappeared. It works on two levels here:

  • Companies. An index removes shrinking companies and adds growing ones. The index return is not the return of the stocks that were in it at the start.
  • Countries. Long-run figures usually come from the US market, which did well over the last century. Some national markets did not. Russia's market was closed after 1917, and China's after 1949. An average built only from survivors describes the winners.

How do inflation and investor behaviour lower what people earned?

A nominal average can look strong in years when inflation was also high. In addition, the index return assumes you held every day and paid no costs or taxes. Many investors bought after rises and sold after falls, so they earned less than the index.

What did buy-and-hold investors actually live through?

Buy-and-hold investors lived through falls of about half their capital and waits of many years to recover, and the average return hides all of it. A drawdown is the fall from the highest account value so far to the lowest point before a new high. The recovery time is how long it takes to get back to that high.

Three S&P 500 price index episodes (index closing levels):

EpisodeDecline from peak (price index)What holders experienced
2000 to 2002About halfA buyer at the March 2000 high was below that level for most of the following thirteen years, in price terms.
2007 to 2009More than halfThe price index did not close above its 2007 high until 2013.
Early 2020About a thirdThe fall took roughly five weeks.

Dividends shorten these recovery times somewhat, but they do not change the size of the falls. A strategy that loses half its value would be stopped by most traders long before it recovered. Yet buy-and-hold has done this more than once, and the long-run average includes those years without showing them. You can measure the same thing on any equity series with the free drawdown calculator for maximum drawdown and recovery time.

The average hides the falls: an illustrative equity line rises along a smooth dashed average growth line, while the underwater view of the same line shows two deep drawdowns and the time each one took to recover to the previous high The average hides the falls Illustration, not market data Equity Average Drawdown Recovery Average shows the end, not the ride. So: judge return and drawdown together.
The average growth line (dashed) is smooth. The path holders actually lived through includes deep drawdowns and long recoveries. Illustrative shape, not market data.

How do you use buy-and-hold as a benchmark for a futures strategy?

Buy-and-hold is a benchmark that buys the market at the start of the test period and holds it to the end without trading. Use buy-and-hold of the same futures contract, on the same bars, over the same period, with the same costs, not a quoted stock market average. Only then does the comparison show what the strategy's rules added.

A quoted index return is the wrong yardstick for a futures strategy for two reasons. First, a long index futures position that is rolled each quarter earns roughly the index's total return minus a short-term interest rate. The futures price already accounts for dividends and financing, and the cash held as margin can earn interest separately. Second, a futures percentage return depends on how much account capital you assume per contract, as futures leverage and backtest drawdown explains. So compare in money per contract, or fix one account size for both.

Build the benchmark in this order:

  1. Use the same contract and data file as the strategy, for example the E-mini S&P 500 for an ES strategy. The guide to S&P 500 futures, ES vs MES covers the contract choice.
  2. Use a back-adjusted continuous series, so the jumps at each roll do not count as profit or loss. See roll gaps and continuous backtests.
  3. Hold one contract long from the first bar to the last bar of the test period.
  4. Charge roll costs: one round trip per roll, with the same commission and slippage you give the strategy. The article on trading costs in backtests shows how to set them.
  5. Record net result, maximum drawdown, longest recovery time and time in market for both.

Time in market is the share of bars on which the strategy holds a position. Buy-and-hold is always 100%. A strategy that holds a position 30% of the time and makes less money can still use its risk much better.

How do you compare return against drawdown in a performance report?

Put the strategy and buy-and-hold side by side on net result, maximum drawdown, the ratio between them and year-by-year results. A strategy with a smaller net result but a much smaller drawdown can be the better result, and a strategy that only wins in rising years may be buy-and-hold in disguise.

Hypothetical example

Same contract, same ten years, one contract, all costs included.

Buy-and-hold: net result +$120,000, maximum drawdown −$90,000, time in market 100%. Net result divided by maximum drawdown: about 1.3.

Strategy: net result +$80,000, maximum drawdown −$25,000, time in market 35%. Net result divided by maximum drawdown: 3.2.

The strategy made less money. But it earned more than twice as much per dollar of its worst fall, and it held no position for most of the period.

Hypothetical comparison on the same contract over ten years: buy-and-hold nets 120 thousand dollars with a 90 thousand dollar maximum drawdown, a ratio of 1.3; the strategy nets 80 thousand with a 25 thousand drawdown, a ratio of 3.2 Less profit, smaller falls Hypothetical · ratio = net ÷ drawdown Max drawdown Net result Ratio Buy-and-hold −$90k +$120k 1.3 Strategy −$25k +$80k 3.2 The strategy earns more per drawdown. So: judge the ratio, not net alone.
The hypothetical example: buy-and-hold wins on net result; the strategy wins on net result per unit of drawdown.

Read the comparison in this order:

CheckWhat a good sign looks likeWhat a weak sign looks like
Net result vs maximum drawdownClearly higher ratio than buy-and-holdLower ratio and lower net result
Year-by-year resultsSmall losses or gains in the years buy-and-hold fell hardLarge losses in the same years as buy-and-hold
Long and short resultsBoth sides contribute, or the short side helps in falling yearsAlmost all profit from long trades in a rising market
Recovery timeShorter than buy-and-hold's longest recoveryYears below the previous high
Number of tradesEnough trades for the ratio to mean somethingA handful of trades carrying the whole result

The long and short check matters most for stock index futures. Index futures rose over most long test periods. A long-only strategy that is in the market often will look good simply because the market rose. Its long trades then add little beyond what buy-and-hold already gave you.

A ratio measured over a short history has a wide margin of error, which applies to the Sharpe ratio as well (Lo, 2002). The Sharpe ratio is the average return above a short-term interest rate, such as a government bill rate, divided by how much the returns swing. And if you picked the strategy from many variants, its backtest result is biased upward and should be marked down before you compare it with any benchmark (Harvey & Liu, 2015). The free Sharpe ratio calculator annualises a list of daily, weekly or monthly returns, so you can run a short and a long stretch of the same strategy and compare the two ratios.

AlphaPrime (Valynox) shows these views in its Performance Report: equity, drawdown, trades, periodic performance, and long and short analysis.

What this means if you use AlphaPrime: build a buy-and-hold test of the same contract with the same data and costs as your strategy, and compare it with the strategy's results. Then use the Performance Report's drawdown, periodic performance and long and short views to see whether the rules add something beyond holding the market.

Frequently asked questions

What is the average return of the S&P 500?

The answer depends on the period and on whether dividends and inflation are included. Most long-run figures you see quoted are nominal, include reinvested dividends and start many decades ago. The real return after inflation is several percentage points lower. Always check the start year and the method before comparing figures from two sources.

Why is the arithmetic average return higher than the compound return?

Losses hurt more than gains of the same size help. A 50% gain followed by a 50% loss averages 0% arithmetically, but $100 ends at $75. The compound return reflects that, so it is the one that matches the money in your account.

Should a futures strategy beat buy-and-hold?

It should beat buy-and-hold of the same contract on return relative to drawdown, measured on the same data with the same costs. It does not need a higher net result. A strategy that makes less money but has a much smaller maximum drawdown and shorter recoveries can be the more usable result.

Is the long-term stock market average what investors actually earned?

Usually not. The index average assumes you held every day, reinvested every dividend and paid no costs or taxes. Many investors bought after rises and sold during drawdowns, so their own results were lower than the index.

References

  • Harvey, C. R., & Liu, Y. (2015). Backtesting. The Journal of Portfolio Management, 42(1), 13–28.
  • Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36–52.