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Yes, look at the ratio of a stock's price to it's current earnings to get a good prediction of how the company's earnings will change over the next decade.
I don't think I understand how that is consistent with EMH. You mean that P:E predicts high variance but the mean is still priced in correctly so one can't make a profit just by looking at P:E? A high P:E meaning something like the market saying 'this company's earnings will either go way up or way down but I don't know which'?