Monthly and yearly average

Also seen as: average monthly return, average annual return, Avg month

How are the monthly and yearly averages calculated?

Each is the arithmetic mean of its own return series.

where: $r_i$ is the return of month $i$ and $n$ is the number of months in the backtest period. The yearly average is the same calculation over the series of annual returns, with $n$ as the number of years.

Why is the yearly average not twelve times the monthly average?

Because each yearly return already compounds its own twelve months, while the monthly average only adds monthly figures up and divides. Compounding means a year's return is built by multiplying its months together, not by summing them, so the annual series carries growth-on-growth that the monthly series does not. Multiplying the monthly average by twelve therefore usually lands below the yearly average, and neither result is the strategy's compounded growth rate — that is CAGR, or AAGR when Reinvest profits is off.

What counts as a good value?

A positive monthly or yearly average means the typical period in the series gained rather than lost, but an arithmetic mean hides how spread out the figures were: two runs with the same monthly average can have completely different best and worst months. Comparing the yearly average with CAGR is the useful reading — a yearly average far above the run's CAGR points to returns that swung widely from year to year, because dispersion drags a compounded rate below an arithmetic one.

Defaults in Fincanva

• Both appear in the Averages group of the metrics table, labelled "Monthly average" and "Yearly average", as percentages to one decimal place and coloured by sign.
• The monthly returns view shows the same monthly figure as a KPI labelled "Avg month".
• Neither is annualized or compounded — the annualized slot on the metrics page holds CAGR or AAGR instead, depending on the Reinvest profits assumption.
• The monthly average is computed over the same month-by-month series the monthly returns heatmap displays; the yearly average uses the annual returns the by-year metrics table lists as "Annual return (%)".

Worked example

A five-year backtest has 60 monthly returns that add up to +41 percentage points, so its monthly average is 41 ÷ 60 ≈ +0.7% a month. The same run's five annual returns are +14%, −6%, +21%, +3% and +16%; they add up to +48, so the yearly average is 48 ÷ 5 = +9.6% a year. Twelve times the monthly average is about +8.2%, below the +9.6% yearly average, because each annual figure already compounds its own twelve months while the monthly average simply adds them up. Neither +0.7% nor +9.6% is the run's CAGR, which compounds the whole period into one rate.

Monthly and yearly averages describe what a strategy would have done on historical data, not what it will do. Fincanva provides no financial advice — see Is this financial advice?.