Villagers are baffled by his violent behaviour but it remains unclear why Mr Francis, a mergers and acquisitions specialist for London-based Keystone Law, or his wife have been targetted.
The couple's five-year-old golden retriever was shot dead with an airgun at 10.30pm on July 12 last year.
Speaking at the time, Mr Francis said: "The police conclusion is we may have been targeted.
"Somebody with a weapon which may or not be licensed has entered our grounds and shot our pet. We believe he was probably in the grounds. She was found within three to four yards of the kitchen door."
A few weeks after their dog was shot, Mrs Francis was assaulted as she was confronted by an "athletic" man brandishing a 14in light pine coloured cosh near her house.
A statement from Andover CID states: "The family have suffered harassment over a period of 14 months which includes a male pushing and assaulting Clare Francis, the shooting of their golden retriever dog and culminating in the assault of Graeme Francis on February 8 this year. All these incidents have occurred in the confines of the garden of their home.
"The suspect is a white male, perhaps Aryan, 30s, 6ft 2-3ins, of fit build, with fair/ blond hair neatly cut and swept back, piercing staring eyes, a narrow mean looking mouth, a round face with a light complexion and good clear skin.
"He was carrying a cosh which was light pine coloured, thinner at the holding end and about 14in long and 2in in diameter. On each occasion he was totally silent."
Police said on one occasion the suspect may have been wearing a balaclava and blue plastic gloves.
Detective Sergeant Russ Hodges said: "Since December 2010 these premises have been subject to a range of very concerning activity."