I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean vs the variance:
I was rather surprised to see that there seems to be a negative correlation between return and variance. I was always in the belief that investments with higher risks should yield a higher expected return, otherwise no rational buyer would go with that option. I was wondering whether this could be correct at all and if so, what would be the explanation and why would anyone consider buying stocks from the lower right side of the plot.