For those who like to trade stocks after hours, here is a quick empirical study that compares the return distributions between intraday trading and the after-hours trading for large cap US stocks (guest post).

The data sets cover 20 years of intraday and overnight returns for all the Dow Jones Index components (30 stocks). Distributions of z-scores rather than the actual returns are used because we are not measuring differences in means and standard deviations (comparisons of returns and volatility have been discussed elsewhere.) Instead this study is focused on the shapes of the distributions, i.e. higher moments.

As an example let's take IBM. Below is a chart comparing the shapes of the two distributions.

Here is a comparison of the **cumulative** distributions, where the difference in shape is clearly visible.

The overnight distribution is significantly more leptokurtic than the intraday distribution. The Kuiper statistic is used to see if null hypothesis can be ruled out (Kuiper is a form of Kolmogorovâ€“Smirnov test that is more sensitive to differences in the tails of a distribution.) The null hypothesis is in fact ruled out to better than 99.9%.

Here is the comparison of Skew and Excess Kurtosis for IBM shares:

Skew | Kurtosis | |

Intraday | 0.05 | 3.8 |

Overnight | -0.48 | 37.3 |

The Overnight Kurtosis minus the Intraday Kurtosis here is 33.5 when taking the full 20 years of data. That difference is only 8.6 for the last 5 years of the data. That may indicate that improved overnight liquidity in recent years **has diminished** the difference in Kurtosis.

Looking at all 30 stocks in the Dow Jones Index we can conclude the following:

1. The null hypothesis are ruled out to better than 99.9% confidence interval for all 30 stocks.

2. Kurtosis is higher for the overnight distribution vs. the intraday distribution for all 30 stocks.

3. Skew is lower (more negative) for the overnight distribution vs. the intraday distribution for 27 out of 30 stocks. An explanation for this has to do with negative earnings surprises in the after-hours markets (more studies on this subject could yield some interesting results).

4. The last five years shows a lower difference in Kurtosis than the full 20-year period for 24 out of 30 stocks.

Previous studies have shown that liquidity can cause certain differences in distribution shapes, so the result here should not be a surprise. Practically speaking, because of the extra costs associated with after-hours execution, portfolio managers will only trade if the price moves (or expected price moves) are significant. That behavior distorts the distribution, "superimposing" low volatility returns (nothing is happening) with high volatility returns (significant news/events.)

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.