An eight-week-old baby had a 24in (60cm) machete held against him when three masked men raided a home.
The burglars, also armed with crowbars, forced their way into a property in Bedford Road, Sherington, near Milton Keynes.
They took two Rolex watches worth £46,750, keys to a Rolls Royce, a Louis Vuitton handbag and a camera.
They also threatened a 59-year-old man, a 31-year-old woman and a 13-year-old girl.
One of the victims, who does not wish to be identified but is a prominent businessman, has offered a £20,000 reward for information leading to the arrest and conviction of the thieves.
In a statement, he said: “Any person that holds a 24in machete to the throat of an eight-week-old deserves to feel the full weight of the law.
“These criminals not only attacked me for my watch, wallet and phone, but they then left one of their team standing over me with a raised crowbar while the other two went upstairs to our bedroom and held my partner and our baby with two-foot machetes to her throat and to our new baby’s throat.”
Thames Valley Police called the raid, which took place at about 22:45 GMT on 27 October, “horrible and frightening”.
The force said two of the burglars were white and one was Asian. All were wearing black face coverings, black clothing, black shoes and gloves.
Officers are calling for anyone with information to contact them, particularly if they have recently been offered or bought an 18 carat gold Rolex Daytona, valued at £26,750, or a Rolex Oyster with a black face and diamonds, valued at £20,000.