GEVORDERD · DERIVATEN & ALGO

Risk Models

VaR, Kelly criterion, correlation risk, and portfolio-level thinking.

VaR, correlatie, stresstesting en het Kelly Criterion voor gevorderden.

Beyond Per-Trade Risk

In the Beginner track, you learned to risk a fixed percentage per trade. That's necessary but not sufficient. As you manage multiple positions, correlations, and varying market conditions, you need portfolio-level risk models.

Portfolio risk is not simply the sum of individual position risks. Two positions that are correlated can create concentrated risk even if each one looks small individually.

Value at Risk (VaR)

VaR estimates the maximum loss your portfolio is likely to experience over a given time period at a given confidence level.

Example: "1-day 95% VaR = $5,000" Meaning: There is a 95% probability that your portfolio will not lose more than $5,000 in a single day.
  • VaR is useful for setting risk budgets and comparing risk across different portfolios.
  • VaR does NOT tell you what happens in the worst 5% of cases - that's where the real danger lies.
  • Conditional VaR (CVaR) or Expected Shortfall addresses this by estimating the average loss in the tail (the worst cases).
VaR limitation: VaR assumes normal market conditions. During crises, correlations spike, volatility explodes, and losses can far exceed VaR estimates. VaR is a useful tool but a dangerous one if you treat it as a guarantee.

The Kelly Criterion

The Kelly criterion calculates the optimal fraction of your capital to risk on a bet, given your edge and odds:

Kelly % = (Win Rate × Average Win - Loss Rate × Average Loss) / Average Win Simplified for equal wins/losses: Kelly % = (2 × Win Rate) - 1
  • Kelly maximizes long-term growth rate - but it also produces large drawdowns.
  • Most practitioners use fractional Kelly (e.g., half-Kelly or quarter-Kelly) to reduce volatility.
  • Kelly requires accurate estimates of win rate and payoff ratio. If your estimates are wrong, Kelly can be destructive.
Practical rule: If you don't have at least 100+ trades of data to estimate your edge, don't use full Kelly. Use a conservative fraction (25-50%) or stick with fixed percentage sizing.

Correlation Risk

Correlation measures how much two assets move together. Correlation of +1 means they move identically; -1 means they move opposite; 0 means no relationship.

  • If you're long BTC and long ETH, you're not diversified - they're highly correlated. A crypto crash hits both.
  • If you're long stocks and long bonds, you have some diversification - they're often negatively correlated (but not always).
  • Correlation is not constant. In crises, correlations tend to spike toward +1 ("everything sells off together"). This is exactly when you need diversification most, and exactly when it fails.
The correlation trap: Building a portfolio of 10 "different" crypto positions doesn't reduce risk if they're all 90%+ correlated. You effectively have one big position with 10 names.

Maximum Drawdown as a Constraint

Rather than optimizing for returns, many professional risk models optimize for returns subject to a maximum drawdown constraint:

  • "I want to maximize returns, but my maximum drawdown must not exceed 15%."
  • This forces you to size positions conservatively enough to survive bad periods.
  • The constraint is based on your psychological tolerance and financial situation - how much can you lose before you can't continue?

Stress Testing

Stress testing asks: "What happens to my portfolio in extreme scenarios?"

  • What if BTC drops 40% in a week?
  • What if correlations spike to 1.0 across all positions?
  • What if volatility triples overnight?
  • What if the exchange goes down for 24 hours and you can't exit?

If any of these scenarios would cause unacceptable losses, your risk is too high - regardless of what VaR or Kelly says.

Practice

Exercise 1

You have a strategy with 55% win rate and 2:1 reward-to-risk. Calculate the Kelly percentage. Then calculate half-Kelly. Which would you use and why?

Kelly = (0.55 × 2 - 0.45 × 1) / 2 = 0.325 = 32.5%. Half-Kelly = 16.25%.

Exercise 2

List 3 positions you might hold simultaneously. Estimate their correlations. Calculate your effective exposure - are you more concentrated than you think?

Key Takeaways

  • Portfolio risk ≠ sum of individual risks. Correlations matter.
  • VaR is useful but dangerous if treated as a guarantee - it ignores tail risk.
  • Kelly criterion maximizes growth but requires accurate edge estimates. Use fractional Kelly.
  • Correlations spike in crises - diversification fails when you need it most.
  • Stress test your portfolio against extreme scenarios, not just normal conditions.

Risicobeheer voor gevorderden

Gevorderd risicobeheer gaat verder dan stop-losses. Het omvat portfoliorisico, correlatie, scenario-analyse en stresstesting.

Geavanceerde concepten

  • Value at Risk (VaR): Het maximale verwachte verlies over een bepaalde periode met een bepaald betrouwbaarheidsniveau.
  • Correlatiematrix: Meet hoe je posities samen bewegen — hoge correlatie = minder diversificatie.
  • Stresstesting: Simuleer extreme scenario's (crash, liquiditeitscrisis) om te zien hoe je portfolio reageert.
  • Kelly Criterion: Een wiskundige formule voor optimale positiegrootte.

Belangrijkste punten

  • Risicobeheer is een continu proces, geen eenmalige instelling.
  • Diversificatie werkt alleen als correlaties laag zijn.
  • Stresstesting bereidt je voor op het onverwachte.
  • De beste traders zijn de beste risicomanagers.

Les afgerond

Je hebt afgerond: Risk Models.