There is some truth in this theory. Since 1986 gilt returns have been below average in February, March and April whilst equities have done well then. This is consistent with the lighter nights increasing investors' appetite for risk and so causing a shift from bonds to equities.
However, the differences in gilts' monthly average returns are not significant in the classical statistical sense. This could be because gilts are less sensitive than shares to changes in risk appetite, simply because their future cashflows are known for sure which means the market is less likely to over-react to good or bad news.
What's more, there are exceptions to the negative correlation between returns. In June, both gilts and equities do badly, and in December both do well.
This reminds us that changes in risk appetite aren't the only influences upon gilts and equities. In fact, since 1986 the correlation between monthly returns on the two assets has been positive (0.15) which tells us that some things cause the two to move in the same direction.
One of these things is simply liquidity: if we have more cash - or if we simply want to hold less of it - we'll buy more of both assets. Cynics might think that equities and gilts both do well in December because fund managers want to appear to be more fully invested before they issue year-end reports.
Another factor causing co-movement in the two is appetite for duration; if we want assets that offer cashflows in the more distant future we'll dump cash in favour of gilts and shares. This appetite for duration seems to increase at the end of the year; both gilts and equities do well in October, November and December.
And herein lies a curious thing. The autumn was traditionally a time when our ancestors also prepared for the future by slaughtering animals for meat over the winter and storing crops they had harvested. In this sense, the winter has seen a desire for longer duration assets, and preparation for the future, for thousands of years. Maybe, therefore, our investment decisions today are more driven by atavistic urges than our rationalist selves would like to admit.
