Risk & volatility

Sharpe ratio

Sharpe ratio is a measure of historical excess return per unit of return volatility, calculated as average return minus the risk-free rate, divided by the standard deviation of returns.

What it means

The Sharpe ratio compares an investment’s average return above a risk-free rate with the variability of its returns. It is commonly used to describe historical risk-adjusted performance. A higher historical ratio means more excess return per unit of measured volatility over the period examined; it does not establish what will happen next.

Volatility counts returns above and below the average. The ratio therefore treats unusually strong gains as variability too. Results also depend on the observation period, how often returns are measured, and the risk-free rate selected. A ratio for a stock and one for a portfolio are not automatically comparable if those inputs differ.

How it is calculated

For returns measured at the same frequency, use Sharpe ratio = (average periodic return − periodic risk-free rate) / standard deviation of periodic returns.

  • Average periodic return: The arithmetic mean of the investment’s returns per day, month, or year, expressed as a percentage or decimal.
  • Periodic risk-free rate: A rate for the same period and in the same currency as the returns, expressed in the same units. If the risk-free rate changes, a calculation can instead use the average of each period’s return minus that period’s risk-free rate.
  • Standard deviation of periodic returns: The spread of observed returns around their mean, in the same percentage or decimal units. Historical calculations commonly use sample standard deviation; the chosen convention should be stated.

The ratio has no units: the return units cancel. A common annualized estimate from monthly data is annualized Sharpe ratio ≈ monthly Sharpe ratio × √12, assuming monthly excess returns are sufficiently independent and measured consistently. That shortcut can mislead when returns are serially correlated. Dividing annual average return by monthly volatility without first aligning their periods is incorrect.

Worked example

Consider a wholly hypothetical investment with four monthly returns: 1%, 3%, −1%, and 1%. Assume a monthly risk-free rate of 0.25% and use sample standard deviation.

  1. Average monthly return: (1% + 3% − 1% + 1%) / 4 = 1%.
  2. Average monthly excess return: 1% − 0.25% = 0.75%.
  3. Deviations from the 1% average are 0%, 2%, −2%, 0%. Their squared values sum to 8 in squared percentage-point units.
  4. Sample variance is 8 / (4 − 1) = 2.6667 squared percentage points. Sample standard deviation is √2.6667 ≈ 1.633% per month.
  5. Monthly Sharpe ratio: 0.75% / 1.633% ≈ 0.46. Under the annualization assumption above, the illustrative annualized estimate is 0.46 × √12 ≈ 1.59; using unrounded figures gives about 1.59.

Four observations are far too few for a dependable performance assessment. The numbers illustrate the arithmetic, not an expected return.

Why it matters before you trade

A historical Sharpe ratio can add context to a pre-trade review: it asks whether returns over a specified period were large relative to their observed variability. Compare calculations only when their return frequency, measurement window, risk-free rate, and treatment of costs are consistent.

It cannot show the likely cost of placing a particular order. Nor does it capture every risk: losses can be concentrated in rare events, and historical returns may not represent future conditions. Trading costs and portfolio concentration can matter even when a historical ratio looks favorable.

How PreTrAIde uses it

The product facts do not state that PreTrAIde calculates or uses a Sharpe ratio. Its pre-trade analysis instead assesses a proposed stock basket before an order is placed. The quantitative layer estimates daily volatility, a 1-day 95% value at risk, liquidity, spread and market impact, alongside portfolio breakdowns and concentration. Those measures address aspects of risk and execution that a historical Sharpe ratio does not directly measure.

PreTrAIde returns GO, NO-GO or MODIFY verdicts as decision support, not investment recommendations. Its success probability is a model estimate, not a forecast of returns.

Common mistakes

  • Mixing periods or currencies: Annual returns, monthly volatility and a risk-free rate in another currency do not form a consistent calculation.
  • Ignoring costs: Gross returns can produce a different ratio from returns after trading costs.
  • Equating volatility with all risk: Standard deviation does not separately describe tail losses, liquidity constraints or concentration.
  • Reading a high historical ratio as a promise: Short samples, unusual market conditions and overfitted strategies can make past results misleading.
  • Confusing the ratio with a trade verdict: It summarizes a return series; it does not determine whether an individual order will execute as intended.

Frequently asked questions

What is a good Sharpe ratio?

There is no universal cutoff. Interpretation depends on the measurement period, return frequency, risk-free rate, costs and the risks that volatility may miss.

Can the Sharpe ratio be negative?

Yes. A negative ratio generally means average return was below the risk-free rate over the measured period, provided return volatility is greater than zero.

What is the difference between the Sharpe ratio and the Sortino ratio?

The Sharpe ratio divides excess return by the standard deviation of all returns. The Sortino ratio uses downside deviation relative to a specified target, so it focuses on returns below that target.

Related terms

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. Standard deviation Standard deviation is a measure of how widely observations, such as daily stock returns, vary around their average, expressed in the same units as those observations. Annualized volatility Annualized volatility is the standard deviation of returns expressed on a one-year scale, commonly calculated by multiplying daily return volatility by the square root of 252 trading days. Value at risk (VaR) Value at risk (VaR) is an estimate of the loss threshold that a position or portfolio is expected to exceed with a specified probability over a specified time horizon. Transaction costs Transaction costs are the explicit fees and implicit trading costs incurred when executing a trade, including commissions, the bid-ask spread and market impact. Pre-trade analysis Pre-trade analysis is the assessment of a proposed stock order or basket before placement, estimating execution costs, liquidity and risk to inform the investor’s decision and execution approach.

Risk & volatility

Volatility Historical volatility Implied volatility Daily volatility Parkinson volatility estimator Yang-Zhang volatility estimator GARCH model Expected shortfall (CVaR) All glossary terms →

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Educational content, not investment advice. PreTrAIde is analysis software, not a broker: it never executes orders, and its verdicts are decision support, not recommendations to buy or sell.