Other analysts, such as Goldman Sachs' Jim O'Neill, said they were optimistic about the prospects for stock markets as the world economy was on the mend due to good data on the U.S. economy.
"U.S. equities are around 50 percent overpriced but, absent unexpected shocks, are being kept up by corporate buying. This should continue until corporate cash flow falls, which is likely to coincide with a decline in the fiscal deficit," Smithers wrote in his research.
Smithers, whose book was published in 2000 when stock markets were peaking, uses the "q" ratio between the value of companies according to the stock market and their net worth measured at replacement cost to measure the value of the stock market. The "q" ratio was developed by Nobel Laureate James Tobin.
Replacement cost represents the amount it would cost to replace assets at current prices.
For his valuation of the market, Smithers also uses the cyclically-averaged price-earnings ratio (CAPE) and gets the data for both ratios from the "Flow of Funds Accounts of the United States Z1," a quarterly publication of the Federal Reserve.
Like Before Bear Markets
The Z1 data for the fourth quarter of 2011 was published on March 8 and on its basis and also on the basis of earnings-per-share data on the S&P 500, Smithers wrote that U.S. non-financials were overvalued by 36 percent at the end of the year. Adjusted for the subsequent rise in the stock market, they were overvalued by 52 percent on March 20, he added.
"Listed companies according to CAPE were 53 percent overvalued at the year end and 71 percent overvalued on 20th March," Smithers wrote.
He said the current degree of overvaluation was similar to the stock market peaks of 1906, 1937 and 1968, which "preceded long secular bear markets," although they are "well short of the extremes reached at the end of 1929 and 1999."
Smithers said that fiscal deficits must be exactly matched by cash surpluses in other sectors and that the business sector, which has habitually run a cash deficit that averaged 1 percent of gross domestic product between 1960 and 1990, is currently running a surplus of 3.1 percent of GDP.
As there has been a high negative correlation between fiscal balances and the cash flow of the business sector, "this supports the probability that a reduction of the deficit will be accompanied by a deterioration in business cash flow - and a large reduction in the deficit by a large deterioration in corporate cash flow," he wrote.
"We don’t know when, or even if, the fiscal deficit will start to be reined in, but it looks unlikely to be postponed beyond 2013. At any rate, the stock market has every reason to be nervous as the November election gets nearer," Smithers added.