Mike Turner, head of global strategy at the Scottish investment house, said: "Will markets beat this year's returns? My suspicion is it is going to be very hard to do so."
He warned that the US consumer, who accounts for 16% of the world economy, remained highly indebted.
The outcome of negotiations in the US to avoid the fiscal cliff, a series of automatic tax hikes and spending cuts that kick in if legislators are unable to reach a debt reduction deal, could further weigh on growth.
"A sub-par global growth outcome still seems most likely in 2013," Mr Turner said.
Many other fund managers remain cautious.
Katherine Garrett-Cox, chief executive of Dundee-based Alliance Trust, said: "The same old issues prevail, whether it is the ongoing eurozone crisis, the austerity plans for the UK, the looming fiscal cliff in the US or the potential of lower GDP [gross domestic product] growth in China."
However, she added that some companies were undervalued, giving investors opportunities.
Nick Train, whose Finsbury Growth and Income Trust holds shares in Irn-Bru maker AG Barr and Celtic Football Club, is more positive.
He said: "We know that a lot of investors – both private individuals and the big institutions – are disenchanted with equities. We see them throwing in the towel and embracing bonds or 'alternatives'."
Mr Turner said he expected emerging markets to do well after several years of relative under -performance.
Jeremy Tigue, fund manager at London and Edinburgh-based F&C Asset Management, which oversees the £2.4 billion Foreign & Colonial Trust, added: "The main hope for market and economic growth next year continues to be emerging markets."