Dumas argues that including the Great Depression, two world wars and the Cold War into the long-run average makes it an "unduly poor comparator". Instead, if you disregard this period, the CAPE is only 7 percent above the post-Cold War average, according to Dumas.
"From such a level, the growth of U.S. profits and the inflow of funds to U.S. markets from much of the rest of the world hold out the promise of (a) significant further stock market advance," he said in a research note on Thursday. Dumas also suggests that another metric, also documented by Shiller, the S&P real value index is showing signs of significant potential upside for the bourse and is close to its long-run trend.
"What do we expect? For the next 12-18 months, barring major war(s), a significant rise in the index," he added.
Read More'Everything is pricey': Robert Shiller
On August 19, Shiller told CNBC that his CAPE ratio stood at 25, a level that has been surpassed only three times since 1881 – the years surrounding 1929, 1999 and 2008. The ratio averaged 15.21 in the 20th century and stood at 23 last year. He warned on the valuation of U.S. stocks, bonds and housing and sent ripples through global markets.
Dumas' analysis adds to criticism by Jack Boroudjian, the chief investment officer at Index Financial Partners, who told CNBC that Shiller's warning was unwarranted and believed that he uses a "strange equation". He predicted that stocks had much further to run.