Beyond Diversification: What Every Investor Needs to Know About Asset Allocation

11

Fat Tails and Something About the Number of Particles in the Universe

We must accept that the normal distribution is just an approximation of the true distribution.

–JPP

EARLIER I STATED THAT HIGHER MOMENTS MATTER, BUT they are more difficult to predict than volatility. This issue merits further discussion. If returns are normally distributed (or Gaussian, i.e., part of a family of bell-shaped probability distributions), we can approximate exposure to loss based on volatility. If not, we’re likely to underestimate risk. By how much is the key question.

In our study, we estimated the persistence in risk measures, but we didn’t estimate the size of measurement errors. Volatility is too crude a risk measure. Most investors and academics agree ...