Bobbikins

Bobbikins is a 1959 British film directed by Robert Day and starring Shirley Jones and Max Bygraves. It was made in CinemaScope and released by 20th Century Fox.
Plot.
This adventure follows the story of a young navy man, his wife (Shirley Jones) and their baby son, Bobby aka "Bobbikins." To his surprise, Dad discovers his son talks, not baby-talk or gibberish but adult conversations with his father only. Bobbikins learns stock market tips and passes them to his Dad.
After making a killing on the stock market, problems really begin. The dad is presumed mad, the government is after him, and the break down of relations between the young couple ensues. But there is hope.