is the stock market over-valued?

In the long run, stock price should equal the expected discounted flow of future earnings.  However, it is difficult to measure these earnings.  Robert Shiller uses a ten year lag of inflation adjusted earnings to determine whether a stock's price is too high or low, called CAPE (wikipedia link).    According to this measure the stock market is still over valued relative to its earnings.

HOWEVER, there are other ways of measuring long term value.  The equity premia of stocks--the extra return you get for investing in stocks over bonds--is high right now (4-5%) which implies that the stock prices have to rise to bring it back to historical levels.  In other words, using the long run releationship between stocks and bonds, rather than stocks and earnings, says that stocks are under-valued.