Analysts have questioned Cox's potential earnings growth and recommended shareholders to sell.
Investment house Numis issued a broker's note last week critical of the personal lines insurer's performance and dropped its target price from 90p to only 53p, with a recommendation moving from buy to sell.
Numis said: "We believe the outlook for the group's broking and insurance services have become more challenging. We now question whether Cox can deliver earnings growth in this area.
"It is clear that the group's underwriting earnings are peaking with the cyclical downturn in margins beginning to bite."
The broker also highlighted what it termed 'balance sheet strains' in particular Cox's underwriting business being financed by "usually low levels of regulatory capital".
It said: "For 2004 the group's own account underwriting capacity of £252m is supported by a capital commitment of £55m in the form of funds at Lloyd's. This equates to a solvency ratio of 22% as compared to the standard Lloyd's minimum for motor syndicates of 35%."
Numis said that with the FSA capital requirements about to override Lloyd's own rules, "it is likely
Cox's regulatory capital requirement is set to change".
As such Cox would have to increase regulatory capital levels in order to meet the new FSA standards, according to the broker.
But Cox's new chief executive Andrew Fisher is described as someone who "appears to be addressing Cox's challenges by embarking on a growth strategy. In our view this could involve non-core business disposals" such as Can Do, Cox's premium finance arm.
Fisher hit back at the report: "We have no reason to believe that our earnings should change over the coming year. There is some softening in certain sectors, but our combined ratio is very good and we clearly have the underwriting and distribution capabilities."
On whether he would be interested in selling Can Do he said: "I am looking at centralising parts of the business but also asking the question, is it more efficient to have this in-house, or should we outsource it? I'm still asking those questions.
"As to whether we need to raise our capital requirements for the FSA, absolutely not. The FSA and Lloyd's are perfectly happy and know it is not necessary. There seems to be some naivety in this assumption."