Risk-adjusted returns, explained for crypto traders
A return on its own says what a trader made and nothing about what they risked to make it. Two traders who both finished a quarter up 30% can have had very different quarters, and only one of them is likely to do it again. Risk-adjusted returns are the family of measures that put the two side by side.
Key takeaways
- A risk-adjusted return divides what a trader made by a measure of the risk they took to make it.
- The common measures differ in what counts as risk: all swings, only the falls, or the single worst fall.
- The yardstick matters as much as the risk measure. For a crypto trader, the fair comparison is holding Bitcoin.
- Averaging daily percentages flatters volatile records. Measures built on compounded returns do not.
Same return, different trader
Say two traders each start a quarter with $10,000 and finish it with $13,000. The first rose fairly steadily and was never more than 8% below their best point. The second was down to $6,000 by the middle of the quarter, 40% below where they started, and then needed a gain of 117% from the bottom to finish at $13,000.
Both made 30%. The second took far more risk to do it, and a slightly different run of days would have left them well short of where they started. Any measure that ranks the two equally is ignoring the most important thing about the second record.
The common measures
Table 1. Risk-adjusted measures and what each one counts as risk.
| Measure | Return measured | Divided by | What it asks |
|---|---|---|---|
| Sharpe ratio | average return above cash | the standard deviation of returns | how much return for each unit of swing |
| Sortino ratio | average return above a target | the deviation of returns below the target | how much return for each unit of bad swing |
| Calmar ratio | annual return | the largest drawdown | how much return for the worst fall |
| Information ratio | average return above a benchmark | the standard deviation of that difference | how steadily the benchmark was beaten |
The Sharpe ratio (Sharpe, 1966) treats every swing as risk, up or down. The Sortino ratio (Sortino and Price, 1994) counts only the swings below a target, on the view that nobody minds a large winning day. The Calmar ratio (Young, 1991) uses the maximum drawdown, the largest fall from a peak to a later low, which is the risk a trader actually feels. The information ratio (Goodwin, 1998) measures return against a benchmark instead of cash, and divides by how much the gap between the two swings, so that it rewards beating the benchmark steadily rather than by a lot once.
None of them is the right one in every case, and each answers a slightly different question. What they share is that a record which made its money by swinging hard scores lower than one that made the same money calmly.
Why averages flatter volatile records
The simplest way to average daily returns is to add up the daily percentages and divide. That average runs ahead of what the money actually did, and the gap grows with how much the record swings. A day of −50% followed by a day of +100% leaves an account exactly where it started, but the average of the two days reads +25%.
The fix is to measure in log returns, which add up to the compounded result. In logs the two days average to zero, which is what happened. A measure built on simple averages can score a record as skilled when its swings cost it money, and the more volatile the trading, the bigger the error.
The benchmark
Every one of these measures compares a return with something. The Sharpe and Sortino ratios compare it with cash or a fixed target. For a crypto trader, that comparison is generous: in a rising market almost anyone holding crypto shows a positive return, and the trading itself never enters the question. The alternative to trading crypto is holding crypto, and Bitcoin is the natural benchmark.
That is why Sharpe ranks traders with an information ratio against Bitcoin, measured day by day in log returns. The ratio is then discounted by half its own uncertainty, so that a short or lucky record counts for less, and placed on a ladder as Edge. The methodology gives the equations. Paste any Solana or Ethereum wallet into Sharpe to see how a record measures.