Risk Management

Risk-to-Reward & Expected Value (EV) Calculator

Determine Trade Profitability, R:R Ratio, and Mathematical Expectancy

Formula & Mathematical Definition

\text{Expected Value (EV)} = (P_{win} \times \text{Reward}) - (P_{loss} \times \text{Risk})

Expected return per dollar risked based on win probability and reward-to-risk ratio.

Step-by-Step Calculation Guide

1Calculate Risk Amount

Subtract stop-loss price from entry price.

Risk = Entry - StopLoss
2Calculate Reward Amount

Subtract entry price from take-profit price.

Reward = TakeProfit - Entry
3Calculate R:R Ratio

Divide Reward by Risk.

RR_Ratio = Reward / Risk
4Calculate Expected Value (EV)

Compute probability-weighted payoff.

EV = (WinRate * Reward) - ((1 - WinRate) * Risk)

Frequently Asked Questions

What is a positive Expected Value (EV)?

A positive EV indicates that over a large sample of executions, the strategy generates net profit. Even a setup with a 35% win rate has high positive EV if the reward-to-risk ratio is 3:1 or higher.

What is considered a good Risk-to-Reward (R:R) ratio?

A minimum R:R ratio of 1:2 or 1:3 is standard in quantitative swing trading. Higher R:R setups allow traders to remain consistently profitable even with win rates below 40%.

How does win rate interact with the Risk-to-Reward ratio?

The required win rate to break even is calculated as 1 / (1 + RR). For an R:R of 1:2, the breakeven win rate is 33.3%. For an R:R of 1:3, the breakeven win rate is only 25%.

Why do many high-win-rate strategies fail in live trading?

High win rate strategies (e.g. 85%) often suffer from negative asymmetrical R:R (e.g. risking $500 to make $50). A single outlier loss can wipe out dozens of previous gains.

How do algorithmic execution bots optimize Risk-to-Reward in real time?

Trading algorithms dynamically adjust limit order take-profit levels based on opposing order book liquidity pools and historical ATR targets to ensure minimum positive EV thresholds.