# Minimum track record length

How many monthly returns does a Sharpe ratio of 2 need before it beats a benchmark of 1?

With the paper's monthly inputs, skewness -0.72 and raw kurtosis 5.78, at 95 percent confidence the minimum track record length is 59.9 observations, so 60 complete months. Fatter tails or a lower Sharpe ratio raise that number.

Minimum track record length (MinTRL) estimates the observations needed for a Sharpe estimate to exceed a stated benchmark at a chosen confidence level.

## The confidence question

Bailey and López de Prado derive MinTRL by inverting the probabilistic Sharpe ratio (PSR). Specify the observed Sharpe, benchmark Sharpe, return skewness, raw kurtosis and confidence level at the same sampling frequency. The result is a length in observations; round up to the next completed observation in practice.

```
MinTRL = 1 + [1 - skew × SR + ((kurtosis - 1) / 4) × SR²] × [z(confidence) / (SR - SR*)]²
```

## Published monthly calculation

Use the paper's monthly inputs: annualized observed Sharpe 2, annualized benchmark 1, skewness -0.72, raw kurtosis 5.78 and confidence 0.95. Divide the two annualized Sharpe values by sqrt(12): SR = 0.577350 and SR* = 0.288675 per month. The variance factor is 1 - (-0.72 × 0.577350) + (5.78 - 1) × 0.577350² / 4 = 1.814026. With z(0.95) = 1.644854, MinTRL is 59.895 monthly observations, so 60 complete months are needed. The site's calculator uses the same per-period formula.

## Interpretation and limits

If the observed Sharpe does not exceed its benchmark, the formula has no finite qualifying length. A longer record under the same moments can raise PSR, but serially dependent returns and a Sharpe selected from many trials require separate treatment. MinTRL does not correct the selection process behind a reported strategy.

## Check the inputs

The browser calculator accepts per-period estimates and reports observations and years using the supplied observation frequency. It also shows how the required length changes with Sharpe and kurtosis. Calculation occurs in the visitor's browser.

## Frequently asked questions

### Is MinTRL the number of trades?

It counts observations at the frequency of the input returns. Monthly returns give a result in months, even if each month contains several trades.

### Why round 59.895 up?

The example uses completed monthly observations. The first integer count meeting that length is 60.

### Does MinTRL account for parameter search?

No. The displayed formula tests a stated Sharpe against a stated benchmark under its moment assumptions; selection across trials needs its own adjustment.

## Sources

Bailey and López de Prado (2012). [The Sharpe Ratio Efficient Frontier](https://doi.org/10.21314/JOR.2012.255). Journal of Risk 15(2).

Sharpe (1994). [The Sharpe Ratio](https://web.stanford.edu/~wfsharpe/art/sr/sr.htm). Journal of Portfolio Management 21(1), 49-58.

Bailey and López de Prado (2014). [The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality](https://doi.org/10.3905/jpm.2014.40.5.094). Journal of Portfolio Management 40(5), 94-107.

[Primary source for Minimum track record length](https://doi.org/10.21314/JOR.2012.255)

## In the library

[Minimum Backtest Length (MinBTL) & Minimum Track Record Length (MinTRL)](https://stochastly.com/library/backtest-overfitting/minimum-backtest-length-and-track-record)

## Related

[Minimum track record length calculator](https://stochastly.com/tools/minimum-track-record-length-calculator)

[Deflated Sharpe ratio](https://stochastly.com/learn/deflated-sharpe-ratio)

Probabilistic Sharpe ratio

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Source: https://stochastly.com/learn/minimum-track-record-length