While there may be no tangible reason for this, full moons are associated with depressed mood (hence the word 'lunacy' derived from Luna, the goddess of the moon). The suggestion is that investors' moods could be lowered to the point that their behaviour is affected: they will tend to put lower values on shares during these periods and thus returns are lower. That half of all people are said to believe that mood is affected by the lunar cycle may also make this effect self-fulfilling. This linkage is also supported by the finding that the difference in returns is more pronounced among shares that are more widely held by private individuals - small caps, for example.
Source: Are investors moonstruck: lunar phases and stock returns
Kathy Yuan, Lu Zheng and Qiaoqiao Zhu
Journal of Empirical Finance, Vol 13 Issue 1, January 2006
Review by Steve Lodge