The Lab

Where the idea comes from

• The ratio comes from William Sharpe (1966), who called it the "reward-to-variability" ratio. The name "Sharpe ratio" came later.
• How sure a measured Sharpe is, and how much of the best of many tries is luck, were worked out by Andrew Lo (2002) and by David Bailey and Marcos López de Prado (2012, 2014). This page applies their formulas to our own results.
• Why every test needs a random twin, and how luck grows with the number of tries, is on our theory page "Hard-to-beat markets, and why every test needs a random twin".

The Sharpe ratio, introduced by William Sharpe in 1966, is the number most often used to say a strategy is good. It compares the average return with how much the returns swing. We asked three things:

1. How long does a strategy have to run before its Sharpe means anything?
2. When you pick the best of many settings, how much of its Sharpe is luck?
3. Does the Sharpe flatter bots like ours, which earn small and often, then sometimes lose big?

The maths, step by step

1. The Sharpe ratio. Take a run's daily returns. Divide their average by their spread (the standard deviation, called σ, sigma), then multiply by √365 to make it yearly.

• Example: a yearly Sharpe of 1.7 is 1.7 ÷ √365 = 0.089 a day.
• In plain words: on an average day the run makes about a tenth of its typical daily swing.

2. How sure can we be? The probabilistic Sharpe ratio (PSR), from Bailey and López de Prado (2012), is the chance the true Sharpe is above zero, given how many days we have seen.

• It grows with the number of days. With a daily Sharpe of 0.089 and ordinary bell-curve returns:

• It also counts the shape of the returns:
  • skew below 0 means rare big losses;
  • kurtosis above 3 means fat tails, more extreme days than a bell curve.
  • Both make a Sharpe less sure.

3. The minimum track record (from the same 2012 paper): the days needed for that chance to reach 95%. It is

1 + (1 − skew × SR + (kurtosis − 1) ÷ 4 × SR²) × (1.645 ÷ SR)²,

with SR the daily Sharpe, and 1.645 the bell curve's 95% point.

• With bell-curve returns (skew 0, kurtosis 3) and SR = 0.089:
  • the bracket is 1 + 0.5 × 0.0079 = 1.004;
  • (1.645 ÷ 0.089)² = 342;
  • so it takes 344 days.
• With skew −1 and kurtosis 10, more like a bot's returns, it takes 379 days.

4. The luck of many tries. Test many settings that have no skill at all, and the best one still comes out with a good Sharpe by chance. If the settings' Sharpes spread by 1:

• the best of 10 is about 1.57;
• the best of 112 is about 2.57.

The deflated Sharpe ratio (Bailey and López de Prado, 2014) asks whether the winner beat that lucky best, not just zero.

5. Settings that are alike are not separate tries. If the settings' returns move together with an average correlation r, then N settings count as about r + (1 − r) × N. 112 settings at r = 0.51 count as about 56.

What we found

1. A Sharpe needs most of a year. At a yearly Sharpe of 1.7, telling it apart from zero at 95% takes about 344 days of daily results. With a bot's shape of returns (rare big losses) it takes longer. A few weeks prove nothing.

2. The best of many settings shrinks. Our grid study tried 112 settings (14 coins, 4 ranges, with and without a stop), each over 15 months, then 15 more.

• The best in the first half had a yearly Sharpe of +3.15, a 97% chance of being above zero on its own.
• But the best of 112 tries with no skill would show about +2.98 by luck, or +2.69 counting the 56 effective tries. Against that, the chance it was real was only 54–61%.
• In the second half the same setting made −1.05, 90th of 112.

In our leveraged DCA study:

• Up years: the best settings passed the luck test easily, and kept about a third of their Sharpe in the second half.
• Falling market: the best settings at 2–10x also passed the luck test, yet went negative in the second half.

The luck test guards against picking by chance. It doesn't guard against a market that changes.

3. The Sharpe and the ruin it can't see. In the leveraged DCA study (240 settings in each market, 2–10x on perpetuals and on margin, two windows, each split in halves):

• Inside the period it measures, a lost account wrecks the Sharpe. The −100% day dominates. Settings with a higher Sharpe were ruined less in the same half, in 17 of 18 markets.
• The danger is a loss after the period measured. Of the runs that lost the account in the second half, many had looked good in the first. At 2x on perpetuals in the falling market, 23% had a first-half Sharpe over 1.
• Choosing on the first half, then judging the second half's ruin (the falling market, 2–10x):

• Choosing by Sharpe was better than choosing by profit, and far better than at random.
• Choosing the smallest drop was safer still, but those settings earned almost nothing, about +1% a half.
• The Sortino ratio (Sortino and van der Meer, 1991), a Sharpe that counts only the losing days, was no steadier.
• The more leverage, the more lopsided the returns. The share of runs with rare big losses (negative skew) rose from 11% on spot to 86% at 10x on perpetuals, and 97% at 10x on margin, in the falling market. That shape looks good on a Sharpe right up until the big loss.

On our paper accounts

Our own paper bots, on exchange demo and testnet accounts, with no real money. Ratios only.

Each account's daily closes, from 4 August 2026 (or its first day) to 14 October 2026:

• Worked, for the main demo:
  • daily Sharpe 0.0875, skew 0.55, kurtosis 11.3;
  • the bracket is 1 − 0.048 + 0.020 = 0.972;
  • (1.645 ÷ 0.0875)² = 353.4;
  • so it needs 344 days in all, about 280 more.
• No paper account's Sharpe can yet be told from luck.
• The record has a gap of about 6.5 days from 25 September. One daily return spans it.
• The main demo had 21 sudden swings of over 5% within minutes, mostly on 8 October and early on 13 October. They swing both ways and match the bots trading through fast moves at high leverage on purpose, as a stress test. They are not deposits.
• Leaving those days out raises the Sharpe, but shows the rare-big-loss shape (skew −2.35).
• The panel now shows, beside each Sharpe, the chance it is above zero and the days still needed.

Update, 21 October 2026: the monthly re-read

Added after this page was published. The text above is left as it was.

The same readings on the paper accounts, on daily closes to 21 October 2026:

• Still no paper account's Sharpe can be told from luck. The main demo is closest, at 83%.
• The main demo's sudden swings now number 37, on six days. The new ones came on 15 October (20 of them) and 16 October, again both ways, from the high-leverage stress test. Leaving those days out shows the rare-big-loss shape again (skew −1.1).
• The testnet's Sharpe rose from −1.84 to +0.24 with a better week. Its returns are very lopsided (skew −2.9, kurtosis 22). At that Sharpe it would need decades: in effect, never.
• The carry account's record includes a deliberate stress test on 16 October. For about two and a half hours its hedges were mostly missing (our page "The same long, held two ways" has the soak's score).
• A new record starts. At 06:26 UTC on 21 October the main demo, testnet and slow accounts restarted on wider grids and buy-the-dip bots, built to last longer. That is a new strategy:
  • the figures above close their old record, as it was;
  • their Sharpe from the restart on is read as a new record, from zero days, and never blended with the old.
  • The carry and tilt accounts restarted on unchanged terms, so they keep one record.

Credits

• William F. Sharpe, "Mutual Fund Performance", Journal of Business, 1966: the Sharpe ratio.
• David H. Bailey and Marcos López de Prado, "The Sharpe Ratio Efficient Frontier", Journal of Risk, 2012: the probabilistic Sharpe ratio and the minimum track record.
• David H. Bailey and Marcos López de Prado, "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality", Journal of Portfolio Management, 2014: the deflated Sharpe ratio and the expected best of many tries.
  • Overfitting is tuning a rule until it fits the past's noise rather than a real pattern, so it fails on new prices. For example, of 100 settings with no skill, the best on last year's prices will usually look good by luck, and do no better than the rest the year after.
• Andrew W. Lo, "The Statistics of Sharpe Ratios", Financial Analysts Journal, 2002: why a Sharpe measured over a short run is so uncertain.
• Frank A. Sortino and Robert van der Meer, "Downside Risk", Journal of Portfolio Management, 1991: the Sortino ratio.
• The formulas are theirs; we applied them to our own studies and paper accounts. The count of effective tries is a rough rule of our own.
• Data: our studies' results and our paper accounts on exchange demo accounts.
• PerpGremlin and Claude, How far to trust a Sharpe ratio, TerminalGremlin, 2026: the tests, the code and the words.