Metrics glossary: return, risk and risk-adjusted return explained
The metrics Paperball uses to describe portfolios and securities — each with its definition, formula, how its values are read and its limits. Metrics describe the past: they are no reliable indicator of future results and no recommendation.
Return
How much a portfolio grew per year on average.
CAGR
CAGR is the compound annual growth rate: the constant return per year at which a starting value grows to the same end value.
Risk
How much the value fluctuated, how far it fell and how long it took to reach a new high.
Volatility
Volatility measures how much a portfolio’s value fluctuates: the annualised standard deviation of daily returns.
Maximum drawdown
Maximum drawdown is the largest loss from a previous high to the lowest point after it, as a percentage of that high.
Drawdown duration
Drawdown duration counts the trading days of the longest phase in which a portfolio stayed below its last high.
Ulcer Index
The Ulcer Index measures the depth and duration of losses below the last high: the square root of the mean of squared drawdowns.
Return per unit of risk
Return relative to a measure of risk — so portfolios with different levels of risk can be compared.
Sharpe ratio
The Sharpe ratio divides the return above the risk-free rate by volatility: it shows the return per unit of fluctuation.
Sortino ratio
The Sortino ratio divides the return above the risk-free rate by the fluctuation of losing days — gains do not count as risk.
Calmar ratio
The Calmar ratio divides the annual return (CAGR) by the largest loss from peak to trough (maximum drawdown).
Sterling ratio
The Sterling ratio divides the annual return by the average of each year’s largest loss plus 10 percentage points.
Martin ratio
The Martin ratio divides the annual return by the Ulcer Index, taking both the depth and the duration of losses into account.
Recovery ratio
The recovery ratio divides the annual return by the length of the longest losing phase in years — a measure of how quickly recovery came.
Guides
Questions that go beyond a single metric — calculated with the same simulation as in the app.
4% rule
Where the rule comes from and which withdrawal rates would have lasted 30 years and longer — recalculated in euros, with German tax and inflation.
How Paperball calculates the metrics
Every metric is calculated from a portfolio’s daily values. In the portfolio backtester you choose whether distributions are reinvested and which risk-free rate the Sharpe and Sortino ratios deduct. The Watchlist and the Community-Backtests always reinvest distributions; the Community-Backtests use a risk-free rate of 0%.
Working with the metrics
In the portfolio backtester you calculate every allocation of your securities in fixed steps and compare them by these metrics.
More about the portfolio backtesterIn the Watchlist, the same metrics appear for each individual security, over periods you choose.
More about the WatchlistMetrics describe the past. The Monte Carlo simulation builds 10,000 possible paths from real monthly returns for saving and withdrawing.
More about the Monte Carlo simulation
See the metrics of your own allocation
Pick your securities — Paperball calculates every allocation over the past and shows all the metrics in this glossary.