Mathematics · core
Sharpe, Drawdown & Portfolio Risk
Sharpe, max drawdown, correlation matrices — risk-adjusted comparison.
Mental model
Sharpe = excess return per unit vol. Drawdown = peak-to-trough pain. Correlation matrix shows diversification.
How to study Sharpe, Drawdown & Portfolio Risk
Begin by restating the mental model in your own words, then connect it to a concrete system you have built or operated. Name the mechanism, the constraint it addresses, and the trade-off it introduces. Use Bailey & López de Prado — Deflated Sharpe to check details, but close the source before writing your explanation. Retrieval is the learning step; rereading is only preparation.
Next, compare Sharpe, Drawdown & Portfolio Risk with Momentum Backtest Discipline, A/B Testing for Engineers. Ask what changes in correctness, latency, resource use, operability, and failure recovery. Complete Sharpe ratio and max drawdown and preserve the command, input, output, and one failed attempt as evidence. Finish by explaining the idea without jargon to someone who has not studied the track.
Proof of understanding
- Explain the mechanism from first principles and identify the state it reads or changes.
- Give one situation where the concept is the right choice and one where it is not.
- Predict a realistic failure mode before running the drill, then compare the prediction with evidence.
- Connect the result to a roadmap or build artifact instead of treating the concept as isolated trivia.
Where it matters
Strategy gates, portfolio dashboards.
Common mistakes
- Sharpe on tiny samples
- Ignoring costs
- Different leverage comparisons
Learn from primary sources
Practice and explain it back
Sharpe ratio and max drawdown
Given 252 daily returns with mean 0.04%/day and σ=1%/day (rf=0), compute annualized Sharpe. Equity curve peaks at 1.20 then troughs at 0.95 — max drawdown?
Expected evidence: Sharpe ≈ (0.0004×252)/(0.01×√252) ≈ 0.63. Max DD = (0.95−1.20)/1.20 ≈ −20.8%.
Open the interactive drill →Review prompts
- What are limitations of the Sharpe ratio?
Build evidence
Volatility, Sharpe, drawdown, correlation matrix
On 2–5 tickers: annualized vol, Sharpe (assume rf=0 or document rate), max drawdown, pairwise correlation matrix.
- All metrics computed from returns you built (not pre-built risk APIs)
- Correlation matrix symmetric, diag = 1
- One paragraph interpreting whether diversification shows up
Simple momentum backtest vs SPY/QQQ
12-month momentum rule on 1–3 names; compare cumulative return to SPY or QQQ over the same window. State assumptions and survivorship bias.
- Rule written before seeing full-sample results (or use holdout half)
- Equity curve: strategy vs benchmark
- Honest limitations section (costs, slippage, overfitting)