# Sortino ratio

Sortino ratio is a measure of return above a chosen target per unit of downside deviation, counting returns below the target rather than all fluctuations as risk.

## What it means

The Sortino ratio compares a portfolio’s average return with a chosen target while focusing on returns that fall short of that target. It is usually calculated from a history of periodic returns, such as monthly returns. A higher ratio means more return above the target relative to the downside deviation measured over that history; it does not establish what will happen next.

Unlike the Sharpe ratio, which uses the standard deviation of all returns, the Sortino ratio does not treat above-target returns as downside risk. That distinction can be useful when an investor cares more about falling short of a goal than about returns varying in either direction.

## How it is calculated

For equally spaced returns, one common version is:

`Sortino ratio = (mean(R) − T) / sqrt[sum(min(0, R_i − T)^2) / N]`

- `R_i` is the return in period `i`, expressed as a decimal; 2% is `0.02`.
- `mean(R)` is the arithmetic average of all the periodic returns, not just the below-target ones.
- `T` is the target return **per period**, in the same units as `R_i`. It might be zero or a periodic minimum acceptable return.
- `N` is the number of periods. The square-root expression is *downside deviation*: only shortfalls contribute to the squared sum, but the sum is divided by **all** `N` periods.

The numerator and denominator are both returns per period, so the ratio has no units. Other published conventions exist, including different denominators for downside deviation; ratios calculated under different conventions should not be compared without adjustment. If downside deviation is zero, the ratio is undefined, not a finite score.

## Worked example

Suppose a hypothetical portfolio has four monthly returns: `+4%`, `+2%`, `−2%` and `0%`. Set the monthly target at `0%`.

1. Average monthly return: `(4% + 2% − 2% + 0%) / 4 = 1%`.
2. Shortfalls below the target: only `−2%` contributes. The other three periods contribute zero.
3. Downside deviation: `sqrt[(0² + 0² + (−2%)² + 0²) / 4] = 1%` per month.
4. Sortino ratio: `(1% − 0%) / 1% = 1`.

This is a monthly ratio calculated from only four observations, not an annual ratio or a reliable estimate of future results. Using a different target would change both the numerator and the downside deviation.

## Why it matters before you trade

A historical Sortino ratio can help frame whether a portfolio’s recorded returns have compensated for falling below a specified target. Before comparing portfolios, check that they use the same return frequency, time span, target and calculation convention. Short histories can make the figure particularly sensitive to a single loss.

The ratio also leaves important questions unanswered: it does not show the size of a prospective order, whether the stock can be traded efficiently, or how a new position changes portfolio concentration. Trading costs can reduce realized returns, so a return series that omits them may overstate the return available after execution.

## How PreTrAIde uses it

The product facts do not say that PreTrAIde calculates or uses the Sortino ratio. Its pre-trade analysis instead evaluates a proposed stock basket before an order is placed, including estimated spread, market impact, daily volatility, 1-day 95% value at risk and portfolio breakdowns. It returns a GO, NO-GO or MODIFY verdict with supporting reasoning; those verdicts are decision support, not recommendations. These checks address aspects of a proposed trade that a historical Sortino ratio does not measure.

## Common mistakes

- **Counting only losing periods in the denominator:** In the formula above, divide the squared shortfalls by all periods, including periods at or above the target.
- **Mixing time units:** A monthly target belongs with monthly returns. Do not label a monthly ratio as annual without a stated conversion method and assumptions.
- **Comparing unlike targets:** A zero-target ratio and a ratio using a positive minimum acceptable return answer different questions.
- **Treating it as a complete risk measure:** Downside deviation summarizes historical shortfalls; it does not describe every tail event, maximum drawdown or execution cost.

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Source: https://pretraide.com/glossary/sortino-ratio