Track 4 of 25

Probability, tails and simulation

Distributions, fat tails, drawdown, Monte Carlo and path dependency. Why the order of returns is irrelevant without leverage and decisive with it.

20 lessons

Mark a lesson complete and it is remembered here.

What a probability distribution isA distribution is a complete list of what could happen and how much of the total likelihood each outcome gets.6 min
The normal distribution, and why finance uses itThe bell curve is convenient, mathematically tractable, and the default for reasons that are mostly not about accuracy.6 min
Why returns are not actually normalReal markets produce far more extreme days than a bell curve allows, and the excess is not small.7 min
Fat tails, with a concrete exampleThe excess is not in the middle of the distribution; it is concentrated exactly where it hurts.6 min
Standard deviation as a unit of surpriseStandard deviation converts a move in dollars into a statement about how unusual it is.6 min
What a two-sigma or three-sigma move means in practiceSigma counts translate into frequencies only under an assumption, and the translation gets worse as the count rises.6 min
Volatility is not riskVolatility measures movement; risk is the chance of an outcome you cannot absorb. They are different questions.6 min
Drawdown versus volatilityDrawdown measures the worst peak-to-trough fall, which is what thresholds actually respond to.6 min
Why the average is a bad summary of a leveraged outcomeAverages add, but wealth multiplies, and leverage widens the gap between the two.7 min
What a Monte Carlo simulation actually does, step by stepIt generates thousands of possible paths from stated assumptions and counts what happened in them.7 min
How to read a fan chartA fan chart shows percentile bands over time, and the bands are not paths.6 min
Ten thousand runs is not a predictionA simulation reports the consequences of its assumptions with great precision and no additional knowledge.6 min
Path dependency: why the order of returns mattersThe same set of returns in a different order produces the same result without leverage and a different one with it.8 min
Sequence risk, through a leveraged exampleSequence risk is path dependency plus a schedule, and interest accrual supplies the schedule.7 min
Correlation, and why diversification fails when you need itCorrelations measured in calm markets are not the correlations you get in stressed ones.7 min
Stress testing versus forecastingA forecast asks what will probably happen; a stress test asks what happens if something specific does.6 min
Historical scenario replay, and its limitsReplaying real crises is a good discipline, and the sample is far too small to be a distribution.6 min
What a confidence interval does and does not promiseA 95% interval is a statement about a procedure under assumptions, not a guarantee about your outcome.6 min
Base rates, and why they get ignoredThe general frequency of an outcome usually predicts better than the specific story about your case.6 min
The difference between a model and the worldA model is a set of assumptions with the arithmetic done; the world is under no obligation to match it.7 min

Educational only. Nothing in this track is investment, legal or tax advice, or a recommendation to enter into any transaction. Completion is stored in this browser and nowhere else.