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Average vs compounded return in a backtest

October 17, 2026 · 8 min readbacktestingreturnstesting-method

Average return and compounded return answer different questions. An arithmetic average describes the typical period or event in a backtest. A compounded return describes what happened to one continuing pool of hypothetical capital as gains and losses accumulated. Use the first to study a signal's outcomes. Use the second to read a portfolio path.

Confusing them can make a weak result look tolerable. A rebound earns its percentage on the smaller base left after a loss, so equal-looking moves in opposite directions don't cancel in wealth. A backtest report needs both views, each attached to the thing it actually measured.

What is the difference between average and compounded return?

The arithmetic mean return adds a set of returns and divides by the number of observations:

arithmetic_mean = sum(period_returns) / period_count

It treats each observation as one row in a distribution. That makes it useful for questions such as: what was the average benchmark-relative outcome after a fresh qualification? No imaginary dollar has to travel from the first event into the next one.

The compounded return links each period's growth factor to the next:

wealth_multiplier = product(1 + period_return)
total_return = wealth_multiplier - 1

If the periods span several years, the annualized compounded return, also called the geometric annual return, is the constant yearly rate that would connect the same starting and ending values:

annualized_return = wealth_multiplier^(1 / years) - 1

That last number is a translation of the full path into one annual rate. It isn't the arithmetic average of the annual rows. The SEC's Form N-1A performance instructions use this same ending-value logic for standardized average annual total return: solve for the constant rate that turns a starting payment into the ending redeemable value over the measurement period.

None of these measures is the universal "real return." They summarize different objects. Trouble starts when a table labels all of them average return and leaves the reader to guess.

Why do losses make the two measures diverge?

Percentages apply to the capital available at that moment. After a loss, the next gain works on a smaller amount. The arithmetic mean ignores that changing base because its job is to describe the rows, while compounding can't ignore it because its job is to describe wealth.

A public market example makes the gap concrete. NYU Stern's S&P 500 return history, including dividends, records a 36.55% loss in 2008 and a 25.94% gain in 2009. The arithmetic average of those annual returns is a 5.31% loss. Link the returns, though, and $100 becomes about $79.91 across the two years, a cumulative loss of 20.09% and an annualized compounded loss of about 10.61%.

Both summaries are arithmetically correct. Only the compounded pair reconciles the starting value with the ending value. The average tells you where the two yearly observations were centered.

The gap between arithmetic and geometric returns is sometimes called volatility drag. The name can invite a bad mental model, as if a separate fee were deducted. Nothing extra was charged in the example. Multiplication did the work. Wider swings generally create a wider gap because losses reduce the base on which later gains compound.

That also means you shouldn't repair the gap by averaging more finely sampled returns. A mean of monthly rows and a mean of annual rows are different summaries. To move from one frequency to another, link the growth factors first, then annualize the result over the elapsed time.

Which return belongs in an event study?

An event study asks what happened after each fresh signal. In Quantery, a go event begins when a company newly passes the thesis gate. Each measurable event contributes a benchmark-relative outcome at a stated forward horizon.

Those outcomes are a cross-sectional sample. They aren't consecutive deposits into one account. Several can begin on the same date, overlap for much of their forward window, or belong to the same company after it qualifies again. Multiplying all event returns together would invent a portfolio that the study never held.

Use the arithmetic mean to describe the average event, then keep it beside the median and hit rate. The median shows the middle event. The hit rate shows how often events beat the benchmark. A large gap between mean and median warns that a few outcomes may be carrying the average. Testing dependence on one big winner takes that diagnosis further.

The mean still doesn't tell you how much independent evidence exists. Same-date events can share a sector shock, and overlapping windows can reuse the same market move. Read the event dates and company recurrence before treating the row count as repeated confirmation. The guide to clustered backtest signals explains why a crowded cohort can contain many rows but little new calendar history.

Benchmark-relative event returns need matching intervals too. Subtract the benchmark's return over the same start and end dates for each event. Don't compare a company's forward return with a calendar-year index average. That changes the market path underneath the comparison.

Which return belongs in the portfolio result?

A portfolio backtest follows one pool of hypothetical capital through a sequence of holding periods. Its subperiod returns must compound. The ending value, total return, and annualized compounded return should all reconcile through the wealth multiplier.

Quantery's naive portfolio is this kind of policy test. Qualifying companies become equal-weight positions under the saved entry and exit rules, and the resulting interval returns form one path. The walkthrough for reading a backtest report keeps that curve separate from the event study for exactly this reason.

Annualization is useful when runs cover different lengths, but it can also make a short and unusual stretch sound durable. State the effective start and end dates beside it. If coverage begins later than the requested start, annualize the covered path rather than the empty calendar requested in the form.

Compare the portfolio with a benchmark calculated on the same basis. If the strategy return includes distributions as cash while the benchmark assumes reinvestment, their gap mixes the thesis with a return-convention mismatch. The same goes for stock splits, delisting returns, and the treatment of idle cash. Auditing dividend treatment in a backtest shows why total return still needs a definition.

Backtested returns are hypothetical and exclude trading costs. Compounding gross interval returns doesn't make those missing frictions disappear. A high-turnover policy can show a sound gross calculation and still leave the implementation question unanswered.

Does the order of returns matter?

For a fixed set of periodic returns, with no deposits or withdrawals, multiplication gives the same terminal value in any order. The path can still look completely different. Put the losses early and the drawdown arrives early. Put them late and the curve can surrender years of apparent progress near the end. Maximum drawdown and the experience of following the rule depend on that order.

A real stock-selection backtest doesn't get to rearrange periods anyway. The sequence determines which filings are available, which companies qualify, how many positions share the portfolio, and whether an exit happens before the next shock. Calendar order is part of the policy.

External cash flows add another distinction. A personal account receiving contributions or funding withdrawals can have an investor return that differs from the portfolio's time-linked return because more money was present during some periods than others. Quantery's naive portfolio doesn't reconstruct those personal cash flows. Use it to compare a frozen research policy. Its annualized rate isn't a forecast for an account with its own funding schedule.

How should you audit the reported return?

Start with a small reconciliation. Take the saved interval returns, convert each to a growth factor, multiply them, and confirm that the product reaches the reported ending value. Then annualize from that same ending value and the actual elapsed dates. If either result misses, don't explain the performance yet. Find the calculation or boundary mismatch.

Then work through the labels:

• Is an "average" calculated across events, calendar periods, holdings, or rolling windows?
• Is an "annual" number one observed year or a multi-year result converted to an annual rate?
• Do strategy and benchmark use the same dates and return convention?
• Are missing forward outcomes excluded consistently at every event horizon?
• Does the event mean sit beside its median, hit rate, and event anatomy?

Keep precision proportional to the inputs. A return printed to many decimal places can still rest on reconstructed universe membership, sparse early coverage, or one crowded cohort. Extra digits solve none of those problems.

What should you test when the measures disagree?

A strong average event return beside a weak compounded portfolio isn't a contradiction. It says the signal outcomes and the holding policy behaved differently. Check whether signals overlapped, whether the exit rule cut off later gains, whether a large cohort crowded the portfolio, and whether idle cash appeared when few companies qualified.

The reverse disagreement deserves more suspicion. A healthy portfolio curve beside a weak median event may owe much of its path to one long-held winner or one period with heavy exposure. Run a contribution check, remove the leading contributor under a declared rule, and compare equal weighting with the nearest plausible alternative. The recent guide to position weighting in a backtest treats that as a controlled policy test.

Don't choose whichever summary flatters the thesis. Preserve the event distribution and the compounded path, because together they tell you whether the selection rule worked broadly and whether a specific portfolio policy captured it. Change one rule, rerun both views, and keep the labels exact. The arithmetic is simple. Knowing which question each number answered is the real work.

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