The City usually ignores Costain because three shareholders hold 71% of its stock, namely Intria, which holds 37%, Kuwaiti company, Mohammed al-Kharafi, which owns 23% and Saudi Arabia's Raymond International, which owns 11%.
But the share price strengthened steadily from 11p to 15p earlier this week, with the City viewing the appointments as "solid".
Doughty admitted he was "mindful" of the group's low share price and the dominance of the shareholders.
He said: "I will have to handle the situation with care and attention. I need to get the latitude to operate how we need to but I have to be mindful of their concerns."
I will have to handle the situation with care. I need to get the latitude to operate how we need to
Stuart Doughty, Costain chief executive designate
Doughty said there was a gap in the market for a mid-sized contractor such as Costain, after many of its competitors had moved into facilities management and support services in the last few years.
He said: "I think Costain is well placed. I'm open- minded regarding what we will be doing. Maybe going for more secure contracts at slightly lower margins is an option."
Costain had said it was considering following Carillion and WS Atkins in appointing an industry outsider to the chief executive's role, but in the end chose a man with more than 35 years' experience in contracting.
This is Doughty's first posting as chief executive of an entire group. He was previously chairman of Kennedy Construction, a director of Hyder and chief executive of Hyder's engineering consultancy business and overseas interests. He has also headed the civil engineering divisions at Laing, Alfred McAlpine and Tarmac.