Murray International delivered less than a quarter of the returns of the wider market in the 12 months to December 31, in its first annual underperformance in the past 11 years.
Mr Stout said: "It was the same running money in 1998, 1999 when we were behind both years. Then it was the tech boom driving the US market.
"The prices people were paying for stock and the justifications they were dreaming up were not really in the realms of reality."
Today, he said a range of stocks have gone through a "massive re-rating".
Mr Stout argued that with company earnings barely rising, share price rises are being fuelled by loose monetary policies on both sides of the Atlantic and the unappealing nature of other asset classes such as bonds.
"The danger is these multiples can deflate quicker than they inflate as sentiment changes," he said.
Mr Stout, who joined Aberdeen in 1987 via the acquisition of Murray Johnstone, signalled there would be no change in strategy.
"We have to be disciplined at times like these," he said
He added: "We have never seen equity markets as highly valued."
Murray International mustered a total return of 4.6% in net asset value over the year against 21.2% for its benchmark 40% FTSE World UK Index and 60% FTSE World ex-UK Index.
This prompted the trust to claw back £5.3m of performance fees from past years.
Trust chairman Kevin Carter said: "At the beginning of 2013 conservative expectations would have been satisfied by a prospective increase of 4.6% in net asset value total return plus a 6.2% increase in a fully covered dividend.
"In the event this was achieved. Unfortunately, however, this represented the trust's largest annual relative underperformance against its benchmark for a very long time."
The trust will pay a final dividend of 14.5p on May 16.
Long a favourite with private investors, the premium of Murray International's share price over net asset value has slipped from 10% to 4.5%.
Analysts at Numis said: "We believe the best time to buy a manager with a strong long-term track record is often after a period of underperformance.
"In the near term, however, there remains a danger that the premium rating could slip further."