# Using boxplots of previous day’s percentage change in S&P index to predict today's return based on yesterday's movement

In the book "An Introduction to Statistical Learning with Applications in Python, Trevor Hastie et al., Springer", there's the following paragraph:

The left-hand panel of Figure 1.2 displays two boxplots of the previous day’s percentage changes in the stock index: one for the 648 days for which the market increased on the subsequent day, and one for the 602 days for which the market decreased.

Figure 1.2 (the left-hand panel)

It's not obvious to me why then the authors concluded:

The two plots look almost identical, suggesting that there is no simple strategy for using yesterday’s movement in the S&P to predict today’s returns.

Suppose in the boxplot for the "Up" bucket on the right, the median drops to $$-4$$ for example, then my understand is that in this case there's some strategy to predict today's return based on yesterday's movement. If so then what is that and why it's not applicable for the case in the image?

If the “up” plot were shifted downward to have the median around $$-4$$ while the “down” plot remained the same, that would not be the case. The distributions would be dramatically different. In that case, the values you would expect to see after a “down” day might be like $$1, -1.4, 0.7, 0.8, -0.2$$, while the values you would expect to see after an up day would be like $$-3, -6, -3.5, -4.5$$. Instead of a mix of increases and decreases of comparable magnitude after a “down” day, and “up” day would strongly suggest a forthcoming “down” day.