- Also known as:
- heavy tails, tail risk, non-normal returns
“Fat tails” means extreme moves happen more often than a normal distribution would predict.
If you assume returns are normal, you’ll dramatically underestimate how often “impossible” days show up. This matters for investors because a lot of standard tooling (risk models, Sharpe ratios, even portfolio optimization) is quietly built on “volatility is enough to describe risk.”
Markets don’t cooperate. Real returns have jumps, regime shifts, and volatility clustering — all of which create fat tails.
How we look for fat tails at Gale Finance
We don’t rely on just one statistic. We use a few complementary lenses:
Excess kurtosis. High excess kurtosis is a quick “tails are heavy” signal.
Skew (direction). Skew tells you whether extreme moves lean more up or more down.
VaR vs Expected Shortfall gap. If Expected Shortfall is much worse than VaR, the tail isn’t just “a bit worse than normal” — it’s meaningfully heavy.
“How many 2σ days?” sanity check. In our tail-risk section we z‑score daily log returns and count how many days exceed a threshold like 2 standard deviations. Under a normal distribution, you’d expect a predictable number of such days; when the observed count is much higher, that’s fat tails showing up in the simplest possible way.
Why this changes how you should read risk metrics
Fat tails don’t make volatility “wrong,” but they make it incomplete.
- In a fat‑tailed asset, Sharpe can look fine until one or two outlier days dominate the realized outcome.
- Risk is often regime‑based (quiet → chaos), so a single-year volatility estimate can be misleading.
- Diversification can break in stress: correlations often rise exactly when you need them not to.
If you’re evaluating an asset class where fat tails are common (crypto is a prime example), you want tail-aware metrics on the page: VaR, Expected Shortfall, skew, kurtosis, and “tail day” counts — not just annualized volatility.