IMHO, it is possible to come up with a rough idea of fair value for a broad stock market.
Starting with the assumption that economy is going to survive and would continue to grow at more or less as in the 20th century, we can get a rough idea of the IV of the stock market. Earnings are cyclical, they go up and down quite a bit year to year but in the long term it tends to go up at roughly the nominal growth rate of the economy. In an open free market capitalist economy, various economic, social and political forces would ensure this. Total earnings of all the companies fluctuate within a narrow range as a percentage of the economy. Smoothing out the earnings, by whatever mechanism (Shiller 10 yr avg, etc), you can find the normal sustainable earnings power.
The way I define "fair value" for the stock market as a whole or a proxy like S&P 500 is the value at which the expected return over the very long term approximates the historial stock market real return of 6.5%. My calculated normal earnings power for S&P 500 is $65 in 2008. An earnings yield of 7% has historically delivered a return of 6.5% due to leakage - transaction costs, etc. This gives a fair value of somewhere in the 900-950 region for S&P 500. This tells nothing of what is going to happen in the near term but it gives a pretty good idea of your expected returns over the long term.
Vinod