Advanced Trading Statistics

Geometric mean daily return is the constant compounded return equivalent to the observed periodic returns.

Formula or calculation

Geometric mean of (1 + each eligible periodic return) − 1.

Why it is useful

Reflects compounding and is less misleading than an arithmetic average for multi-period growth.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Geometric mean monthly return is the constant compounded return equivalent to the observed periodic returns.

Formula or calculation

Geometric mean of (1 + each eligible periodic return) − 1.

Why it is useful

Reflects compounding and is less misleading than an arithmetic average for multi-period growth.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Daily return standard deviation summarizes shape, persistence, and extremes in canonical periodic returns for the selected account, period, and filters.

Formula or calculation

Calculated from eligible observations using the versioned TraderWaves analytics definition for this metric.

Why it is useful

Adds context when assessing shape, persistence, and extremes in canonical periodic returns.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Monthly return standard deviation summarizes shape, persistence, and extremes in canonical periodic returns for the selected account, period, and filters.

Formula or calculation

Calculated from eligible observations using the versioned TraderWaves analytics definition for this metric.

Why it is useful

Adds context when assessing shape, persistence, and extremes in canonical periodic returns.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Total positive periodic return relative to the magnitude of all negative periodic returns.

Formula or calculation

Sum of positive returns ÷ absolute sum of negative returns.

Why it is useful

Shows how much gain was produced for every unit of observed return pain.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Gain-to-loss ratio summarizes shape, persistence, and extremes in canonical periodic returns for the selected account, period, and filters.

Formula or calculation

Calculated from eligible observations using the versioned TraderWaves analytics definition for this metric.

Why it is useful

Adds context when assessing shape, persistence, and extremes in canonical periodic returns.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

A combined measure of daily return efficiency and return-tail asymmetry.

Formula or calculation

Daily return profit factor × daily return tail ratio, using the same canonical flow-adjusted return series.

Why it is useful

Rewards strategies that combine efficient aggregate gains with a favourable return distribution.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

A composite of profit factor, win rate, and payoff ratio.

Formula or calculation

Net trade profit factor × decisive-trade win rate (decimal) × net trade payoff ratio.

Why it is useful

Tests whether hit rate, payoff size, and aggregate profitability support one another.

Interpretation note

Calculated only from eligible imported observations in the selected account, period and filters; missing source data or an insufficient sample can make it unavailable.

Outlier win ratio describes unusually extreme returns beyond the approved distribution threshold.

Formula or calculation

Classify returns using the configured tail quantile, then count them or compare their mean with ordinary wins or losses.

Why it is useful

Shows whether a small number of exceptional outcomes dominate the strategy’s results.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Outlier loss ratio describes unusually extreme returns beyond the approved distribution threshold.

Formula or calculation

Classify returns using the configured tail quantile, then count them or compare their mean with ordinary wins or losses.

Why it is useful

Shows whether a small number of exceptional outcomes dominate the strategy’s results.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Positive return outliers describes unusually extreme returns beyond the approved distribution threshold.

Formula or calculation

Classify returns using the configured tail quantile, then count them or compare their mean with ordinary wins or losses.

Why it is useful

Shows whether a small number of exceptional outcomes dominate the strategy’s results.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Negative return outliers describes unusually extreme returns beyond the approved distribution threshold.

Formula or calculation

Classify returns using the configured tail quantile, then count them or compare their mean with ordinary wins or losses.

Why it is useful

Shows whether a small number of exceptional outcomes dominate the strategy’s results.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

The relationship between each periodic return and the return immediately before it.

Formula or calculation

Lag-one correlation of the canonical periodic return series.

Why it is useful

Reveals persistence or reversal patterns and warns when ordinary Sharpe assumptions may be optimistic.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Equity curve stability summarizes shape, persistence, and extremes in canonical periodic returns for the selected account, period, and filters.

Formula or calculation

Calculated from eligible observations using the versioned TraderWaves analytics definition for this metric.

Why it is useful

Adds context when assessing shape, persistence, and extremes in canonical periodic returns.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

How closely cumulative log equity follows a straight trend through time.

Formula or calculation

Coefficient of determination from the approved linear regression of cumulative log value on time.

Why it is useful

A higher value indicates smoother, more consistently trending account growth.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

The mean per-trade percentage return relative to variation between trade returns.

Formula or calculation

Mean per-trade percentage return ÷ sample deviation of per-trade percentage returns.

Why it is useful

Preserves the useful legacy trade-grain measure without mislabelling it as a conventional annualised Sharpe ratio.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

Autocorrelation-adjusted Sharpe ratio adjusts the ordinary Sharpe estimate for serial dependence in returns.

Formula or calculation

Canonical Sharpe ratio divided by the versioned autocorrelation penalty derived from return lags.

Why it is useful

Reduces overstatement when returns are clustered or not independent through time.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Autocorrelation-adjusted Sortino ratio adjusts the ordinary Sortino estimate for serial dependence in returns.

Formula or calculation

Canonical Sortino ratio divided by the versioned autocorrelation penalty derived from return lags.

Why it is useful

Provides a more conservative downside-efficiency estimate when returns are serially related.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

The estimated probability that the account’s true daily Sharpe ratio is greater than zero.

Formula or calculation

Normal CDF of the observed daily Sharpe adjusted for sample length, bias-corrected skewness, and bias-corrected kurtosis; minimum 30 daily returns.

Why it is useful

Distinguishes an apparently positive Sharpe from one supported by enough observations and realistic return-shape assumptions.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Annualised return relative to the combined magnitude of all equity drawdown episodes.

Formula or calculation

Annualised flow-adjusted return ÷ square root of the sum of squared maximum percentage depths for each drawdown episode.

Why it is useful

Penalises repeated drawdowns while giving deeper episodes greater weight.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Annualised return relative to the root-mean-square depth of equity drawdown episodes.

Formula or calculation

Annualised flow-adjusted return ÷ square root of the mean squared maximum percentage drawdown depths.

Why it is useful

Makes the Burke measure more comparable across samples of different lengths.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

The average depth of all percentage drawdowns through time.

Formula or calculation

Mean absolute percentage drawdown from the running peak.

Why it is useful

Captures the day-to-day burden of drawdowns rather than only the single deepest loss.

Interpretation note

Calculated only from eligible imported observations in the selected account, period and filters; missing source data or an insufficient sample can make it unavailable.

Annualised excess return relative to average drawdown depth.

Formula or calculation

Annualised excess return ÷ Pain Index.

Why it is useful

Shows how much return was earned for the typical drawdown pain experienced.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Annualised excess return relative to the Ulcer Index.

Formula or calculation

Annualised excess return ÷ Ulcer Index.

Why it is useful

Rewards return achieved with shallow and infrequent drawdowns; it is closely related to the Martin ratio.

Interpretation note

Calculated only from eligible imported observations in the selected account, period and filters; missing source data or an insufficient sample can make it unavailable.

Active return earned per unit of deviation from the selected benchmark.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: a governed benchmark or market-context data source has not been configured.

Excess return earned per unit of benchmark beta risk.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: a governed benchmark or market-context data source has not been configured.

Annualised variability of returns relative to the selected benchmark.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: a governed benchmark or market-context data source has not been configured.

The account return above or below the selected benchmark return.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: a governed benchmark or market-context data source has not been configured.

Win rate confidence interval gives an uncertainty range around the observed sample estimate.

Formula or calculation

Lower and upper percentiles from the approved bootstrap or statistical interval at the configured confidence level.

Why it is useful

Shows how much the metric could vary because the available trade or return sample is limited.

Interpretation note

The value can be unavailable when its denominator is zero or the eligible sample is too small. Compare the same account, period, timezone and filters.

Expectancy confidence interval gives an uncertainty range around the observed sample estimate.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the statistical interval convention has not yet been approved.

Profit factor confidence interval gives an uncertainty range around the observed sample estimate.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the statistical interval convention has not yet been approved.

Median trade return confidence interval gives an uncertainty range around the observed sample estimate.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the statistical interval convention has not yet been approved.

Return confidence interval gives an uncertainty range around the observed sample estimate.

Formula or calculation

Lower and upper percentiles from the approved bootstrap or statistical interval at the configured confidence level.

Why it is useful

Shows how much the metric could vary because the available trade or return sample is limited.

Interpretation note

Requires sufficient account equity or periodic-return history. Some equity metrics are unavailable for portfolio scope or when trade-level filters would make the result inconsistent.

The number of daily return observations required to support a Sharpe ratio above zero at 95% one-sided confidence.

Formula or calculation

1 + [1.64485 × square root of the Sharpe higher-moment sampling adjustment ÷ observed daily Sharpe]², rounded up.

Why it is useful

Shows whether the account has accumulated enough history for its observed risk-adjusted performance to be statistically persuasive.

Interpretation note

Calculated only from eligible imported observations in the selected account, period and filters; missing source data or an insufficient sample can make it unavailable.

The theoretical capital fraction that maximises long-run logarithmic growth under a simplified repeated-bet model.

Formula or calculation

Win rate − (1 − win rate) ÷ payoff ratio.

Why it is useful

Provides an educational upper-bound sizing reference; it is not an automatic sizing recommendation.

Interpretation note

Calculated only from eligible imported observations in the selected account, period and filters; missing source data or an insufficient sample can make it unavailable.

A deliberately reduced fraction of the theoretical Kelly sizing estimate.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the sizing or risk model has not yet been approved.

The modelled probability of breaching an explicitly selected ruin threshold.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the sizing or risk model has not yet been approved.

Monte Carlo probability of profit is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.

Monte Carlo median terminal return is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.

Monte Carlo 5th percentile terminal return is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.

Monte Carlo median maximum drawdown is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.

Monte Carlo 95th percentile maximum drawdown is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.

Monte Carlo median recovery time is a simulated outcome from many resampled paths of eligible historical returns.

Formula or calculation

Not currently calculated. The formula will be published after the required data and method are governed.

Why it is useful

Listed in Reports so the planned analysis area is visible without presenting an unavailable result as live.

Interpretation note

Coming Soon: the simulation and resampling policy has not yet been approved.