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Tail risk and black swans

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

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