These studies about rapid stock price rises are nonsense. Stocks are in a bubble if (and only if) they are very expensive in relation to probable future earnings. Period. And whether or not they are judged to be very expensive depends very much on the return available on bonds. If interest rates are to stay historically low then stock P/E ratios are quite logical at high levels. Past movements of stock prices are completely irrelevant in this assessment. Warren Buffett just pointed out that the U.S. ten year bond has a P/E of 40 and with zero chance the E or interest paid on that bond will increase. (Interest on new bonds may rise but interest on a bond you biuy today is fixed for its life). Stocks at a P/E of 25 and where the E may rise can be considered attractive on that basis. There is no bubble on that basis. Which is not to say that stocks may not crash tomorrow. They may indeed.