The metrics we use

Our collection of metrics fall into different categories and are designed to highlight the various aspects of an asset's performance.

To learn more about the time series data used as a basis for the metric calculation, read this article.

In the analysis and comparison advanced settings, the user has the option to choose whether the asset's close price or adjusted close price time series is used for the metrics calculations. Read this article for more information.

Metrics measuring different aspects of the return of an asset.

Returns time series

Time series of returns between each day and the first day.

The return on the first day of the time series is always zero, as the anchor to compare all other days to.

Code for returns time series calculation

Chart for returns time series

Mean return

Mean of (daily) returns, scaled to a given period, e.g. annualised.

Code for mean return calculation

Return between two dates.

Code for cumulative return calculation

Period return

Cumulative return but scaled to a given period, e.g. annualised.

For example, the annualised return or CAGR of an investment between two dates 10 years apart.

Code for period return calculation

Period yield

Difference between the return calculated with close prices vs. the return calculated with adjusted close prices, scaled to a given period, e.g. annualised.

Code for period yield calculation

Metrics measuring different aspects of the risk of an asset, specifically the mean risk and the tail risk.

Drawdowns time series

Time series of returns between each day and the preceding peak.

If a particular day is a new peak, the drawdown is zero. Otherwise, the drawdown is always negative.

Code for drawdowns time series calculation

Chart for drawdowns time series

Volatility

Standard deviation of (daily) returns, scaled to a given period, e.g. annualised.

Code for volatility calculation

Down volatility

Standard deviation of (daily) negative returns of a returns time series, scaled to a given period, e.g. annualised.

Code for down volatility calculation

Maximum drawdown

Standard measure of tail risk. The maximal percentage difference between a peak and a following trough in a given time series.

Code for maximum drawdown calculation

Value at risk

Hypothetical loss at a given confidence level assuming a normal distribution of (daily) returns, scaled to a given period, e.g. annualised.

For example, an annual value at risk of 10% at a 95% confidence level means a 95% probability of a loss of 10% or less in one year.

Code for value at risk calculation

Expected shortfall

Value at risk's sister metric, measuring the expected loss in the part of the distribution that was excluded in the value at risk calculation.

Consider this example with confidence level = 95% and period = annual:

• Value at risk = 10%: 95% probability of a loss of 10% or less in one year
• Expected shortfall = 15%: the average loss in the worst 5% of outcomes is 15% in one year

Code for expected shortfall calculation

Metrics measuring the return of an asset in relation to the risk of an asset.

Sharpe ratio

Standard measure of risk-adjusted returns, developed by Nobel Prize winner William F. Sharpe.

An investment with a higher return than risk has a Sharpe ratio greater than one. A loss-making investment has a Sharpe ratio below zero.

Code for Sharpe ratio calculation

Sortino ratio

Sharpe ratio but using down volatility instead of volatility as the risk measure.

Code for Sortino ratio calculation

Calmar ratio

Return per unit of maximum drawdown.

While the Sharpe and Sortino ratio use measures of mean risk in the denominator, the Calmar ratio uses a measure of tail risk.

Code for Calmar ratio calculation

Metrics measuring an asset's performance vs. a benchmark.

Correlation

Pearson correlation coefficient between the daily returns of an asset and a benchmark.

Code for correlation calculation

Beta

Measure of an asset's volatility relative to a benchmark and its correlation with the benchmark.

• Beta = 1: asset is perfectly correlated with the benchmark and has the same volatility as the benchmark
• Beta = 0: asset is perfectly uncorrelated with the benchmark
• Beta > 1: asset is correlated with the benchmark and has a higher volatility than the benchmark
• Beta between 1 and 0: asset is uncorrelated with the benchmark and/or has a lower volatility than the benchmark
• Beta < 0: asset is negatively correlated with the benchmark

Code for beta calculation

Alpha

Excess return of an asset vs. a benchmark adjusted to the same level of risk.

• Annual alpha = 0%: the asset and the benchmark generate the same return when adjusting for risk
• Annual alpha = +1%: the asset generates 1 percentage point more return than the benchmark when adjusting for risk‍
• Annual alpha = -1%: the asset generates 1 percentage point less return than the benchmark when adjusting for risk

Code for alpha calculation

Metrics measuring the characteristics of an asset's distribution of (daily) returns.

Skewness

The skewness of the distribution of (daily) returns is a measure of the symmetry of the distribution.

A normal distribution is symmetrical and has a skewness of zero. A distribution with positive skew is asymmetrical and shifted to the left with its tail on the right side.

Code for skewness calculation

Kurtosis

The kurtosis of the distribution of(daily) returns is a measure of the tailedness of the distribution, i.e. how much "weight" is in the tails vs. the centre.

We report excess kurtosis, so a normal distribution has a kurtosis of 0. A distribution with a kurtosis greater than 0 has more "weight" in the tails than a normal distribution, while a kurtosis below 0 has less.

Code for kurtosis calculation