Skew

Skew (skewness) describes whether a return distribution leans toward big upside moves or big downside moves.

• Negative skew means the left tail is heavier: think “calm most days, occasional trapdoor.”
• Positive skew means the right tail is heavier: lots of small-ish outcomes with a few big upside outliers.

In investing, negative skew is often what people really mean when they say “tail risk,” because ugly downside outliers hurt more than pleasant surprises help.

The definition

Skewness is the third standardized moment:

$$\text{Skew} = \frac{E[(r - \mu)^3]}{\sigma^3}$$

How we calculate skew at Gale Finance

1. Daily log returns. For tail-risk analysis, we compute skew on daily log returns:

$$r_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$

2. Sample moment estimate. Skew can be noisy in short windows because a handful of extreme days can dominate the third moment.

3. Native calendars per asset. We compute skew per asset on its own daily series (crypto includes weekends).

How to interpret skew (without overfitting it)

Skew is a directional hint, not a full risk summary. Two assets can both have negative skew, but one can have much fatter tails than the other (that’s kurtosis territory). And skew won’t tell you the actual size of the left tail the way VaR and Expected Shortfall do.