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

External question — Data Science Stack Exchange Author: Tran Khanh Original post: https://datascience.stackexchange.com/questions/128293 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. 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?

External answer — Data Science Stack Exchange Author: Oxbowerce Original post: https://datascience.stackexchange.com/a/128299 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. If the median for the 'up' bucket is much lower than for the 'down' bucket, this means that days that have a negative market return are more likely to be followed by a day with a positive return. This information can be used to predict the market (and possibly make a profit), i.e. buy/go long for the next day if the current day's return is negative and sell/go short for the next day if the current day's return is positive. Since in this image the distributions for the return on the previous day looks roughly the same it contains no information on what you can expect the market to do the day after.