The investment trust sector has a strong Scottish heritage dating back to the 19th century and 18% of the UK industry's assets are held in Scottish companies.
Winterflood analyst Innes Urquhart wrote in a note for clients: "Of course it is possible that an independent Scotland may prove a more welcoming regime for investment trusts, particularly in terms of tax treatment.
"However, while uncertainty exists, it is reasonable that boards and managers consider the potential downside as well."
Among the concerns highlighted by Mr Urquhart are the nature of financial regulation in Scotland, the impact of a different tax system, and uncertainties about how investment trust status would be formulated.
Investment trusts typically buy and sell shares in companies and their own shares are also listed on the stock market.
Under current rules, their capital gains are untaxed.
Some 40 investment trusts are incorporated in Scotland, according to Winterflood. Among them are some of the industry's biggest companies including the £3.1 billion Alliance Trust of Dundee and the £2.9bn Scottish Mortgage Trust run by Edinburgh's Baillie Gifford
Some of the most highly regarded investment trusts such as the £1.3bn Edinburgh Investment Trust and £556 million Personal Assets Trust are Scottish registered but run by managers based in England. Some 27 trusts are managed in Scotland.
One investment trust has calculated the cost of switching jurisdiction at hundreds of thousands of pounds, according to Winterflood.
Mr Urquhart said that it seems to switch residency a trust would have to be wound up with its shareholders subscribing for shares in a new company to be incorporated in England.
Ian Sayers, director general of trade body the Association of Investment Companies, said: "Scottish independence will be an important issue for a number of investment companies.
"We think it is still too early to identify all the steps independent boards will need to take to protect the interests of their shareholders."
Baillie Gifford has established a working group to monitor developments.
An Alliance Trust spokesman said: "We have a clear duty of care to ensure that our shareholders are not disadvantaged by a 'Yes' vote."
But he added: "The referendum should be seen as more akin to a starting gun than to a finishing post."