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## Saturday, February 8, 2014

### Fwd: negative skew intuitively (mean < median

Update: now I know the lognormal squashed bell curve has Positive
skew. This post is about Neg skew. Better remember a clear picture of
the Neg skew distribution.

Neg skew is commonly observed on daily returns -- lots of large neg
returns than large positive returns. Level return or log return
doesn't matter.

---
I knew the definition of median and the interpretation of the median on the
histogram/pdf curve. But The mean is harder to visualize. The way I
see it, the x-axis is a flat plank. The histogram depicts chunks of
"probability mass" to be balanced on the plank. The exact pivot point
(on the x-axis) to balance the plank is the mean value.

In our case of negative skew, the prob mass left to the mean value
(pivot point) is... say 40.6%. This small mass could hold the other
59.4% prob mass in balance. Why? Because part of the 40.6% prob mass
is far out to the left.

Therefore, as we both mentioned earlier, the neg skew seems to reflect
(or relate to) the occurrence of large negative returns.

---- Mark earlier wrote --
Negative skewness means that the mean is to the left of the median.
(Recall that the median is the point at which half the mass is to the
left and half is to the right.) Thus, negative skewness implies a bit
of the probability mass hangs out to the left. In finance, this means
that there are more "very large" negative returns than "very large"
positive returns.