Quantitative Trading Math: Calculating Sharpe, Sortino, Expectancy & Maximum Drawdown Like a Hedge Fund

A rigorous mathematical breakdown of modern quantitative portfolio metrics. Discover why Sortino outperforms Sharpe for asymmetric return profiles and how to calculate your true statistical edge.

In this guide

1. 1. Sharpe Ratio vs Sortino Ratio: Downside Volatility
2. 2. The Mathematical Formula for Trade Expectancy (E)
3. 3. Maximum Drawdown & Asymmetric Recovery Loss
4. 4. Risk of Ruin Matrix (Kelly Criterion & Fixed Fractional)
5. 5. Quant Math FAQs

FAQ

What is considered a good Sharpe ratio for intraday trading?

For retail and prop day trading, an annualized Sharpe ratio between 1.5 and 2.0 is considered strong. Over 2.5 is exceptional. Below 1.0 indicates that returns do not justify the volatility taken.

Why does Sortino matter more than Sharpe for options and trend following?

Because options buying and trend-following strategies exhibit positive skewness with occasional massive winning trades. Sharpe penalizes those huge wins as volatility, whereas Sortino ignores upside volatility and only penalizes downside losses.

How does LumenOS calculate the trader's Lumen Score?

LumenOS evaluates a multi-factor quantitative composite: Trade Expectancy, Sortino ratio, max drawdown control, adherence to stop losses, and consistency of position sizing.