Mr Fish said with the valuations are relatively high and the level of uncertainty in markets means any outcome from a 20 per cent gain to a 30 per cent loss would not be a surprise.
"The markets have gone up a lot, all markets. The difference with the US is that the share prices have deservedly gone up.
"But there is a lot of uncertainty out there and we are very late in the cycle, so while the market could go up 20 per cent, it wouldn't be a surprise if it went down 30 per cent either."
His relative caution on the outlook for the market is expressed by his having reduced the level of debt, which for investment trusts is known as gearing, he is using.
He said he is combating this by "investing in companies that can grow at a rate faster than GDP" and these include companies in the technology space such as Microsoft and Apple.
But Mr Fish is particularly wary of investing in the group of popular technology companies commonly called the FANGs - Facebook, Amazon, Google, and Netflix.
He said the stock market is moving from a phase where the shares of companies that are growing quickly, such as technology businesses, perform less well and companies such as banks do better.
This is because, when economic growth is sparse, the small number of businesses that are growing consistently, as technology companies have been, become very popular with investors.
But in a world where economic growth is more broad based, there are more companies growing and so investors spread their capital across more of them, leading to relative underperformance for the fastest growing companies.
Mr Fish has been investing in US banks, as he believes those are examples of companies that can benefit when interest rates rise.
Jacob De Tusch Lec, who runs the £4.8bn Artemis Global Income fund, said he expects growth in the US to “accelerate” this year, but to be slower in the rest of the world.
He also forecast weak growth in emerging markets as a result of the stronger dollar and implications of any trade war between the US and China.
Andrew Bell, chief executive of the £2.2bn Witan investment trust said a greater proportion of high growth stocks and tax cuts enacted at the end of 2017 have combined to give the US a particular advantage this year.
Jason Hollands, managing director for business development and communications at Tilney said ultra-low borrowing costs and decimated yields on savings have turbo-charged investment returns for several years, herding savers into riskier stock and bonds markets in search of elusive yields.
"They have also enabled companies to easily raise or refinance debt and often businesses - particularly in the US - have been able to use this financing to buy back their own shares.
"Companies buying their own shares has been a bigger factor driving the US market in recent years than purchases from mutual funds.
"It would therefore be churlish to assume that the withdrawal of stimulus measures that have boosted returns, is not without significant risk for investors who may have become complacent about risk."
David.Thorpe@ft.com
