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Distributions and tail risk

Black swan events explained

Extreme, unexpected market events and their impact on financial markets, risk and portfolios.

Play with it

Tail risk and black swans. Feel the math of a 50% loss, then stress a portfolio that looks safe until it doesn't.

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50%
7.0% a year
Loss-50%
Gain needed to break even+100%
Years to get back10.2at 7.0% a year

After a 50% loss you need a 100% gain just to get back to where you started. At 7.0% a year that takes about 10.2 years. Losses and gains aren't symmetric, which is why avoiding a loss you can't recover from matters more than any single good year.

Try this

  • Set the loss to 50%, like the episode. Is the gain needed 50% or 100%?
  • Compare a 20% loss with an 80% loss. The curve isn't a straight line. Where does it bend sharply upward?
  • Lower the growth rate and see how many years a deep loss can cost.

The math

gain needed=L1−L\text{gain needed} = \frac{L}{1 - L}
LL
the loss, as a fraction (0.5 for 50%)
1−L1 - L
what's left of each dollar

Quick check

Two questions to see if it clicked. Answers explain themselves.

Which is not one of the three features of a black swan?
Why are black swans dangerous for financial models?