PROBLEMS WITH PROBABILITY

VALUE AT RISK (VAR)

“Quants” assigned a dollar figure representing how much the firm could lose each day with 99% probability

TOTAL PORTFOLIO RISK

VERY PRECISE

FALSE PRECISION

PROBABILITIES BASED ON PREVIOUS PERFORMANCE

IGNORED THE 1% RISK

There is no known probability distribution of a systemic crisis or wide-spread emergency. Almost by definition, these things are too rare.

THE QUANTS’ ERRORS

• Precision is not accuracy
• Estimates of underlying probabilities were wrong
• Neglected “tail risk”

Remember the metaphor of statistics as a gun? Can be incredibly useful in the right hands, but very dangerous in the wrong ones.

THE MOST COMMON PROB PROBS

ASSUMING EVENTS ARE INDEPENDENT

SIDS OR “COT DEATH” IN UK, 1990S

NOT UNDERSTANDING

GAMBLER’S FALLACY

HOT HAND

CLUSTERS HAPPEN

PROSECUTOR’S FALLACY

REVERSION TO THE MEAN

THE SPORTS ILLUSTRATED JINX

This does not contradict the gambler’s fallacy.

BUSINESSWEEK’S “BEST MANAGERS”

STATISTICAL DISCRIMINATION

EUROPEAN COMMISSION POLICY: GENDER

PREDICTIVE ANALYTICS = PROFILING

“STATISTICAL DISCRIMINATION”

How we use statistics have social implications. What we can and should do with this information is an ethical and legal question. We aren’t always ready for that.

JUST BECAUSE YOUR CALCULATION IS RIGHT,