The incident took place at a residential address in the Niddrie Mains Drive area shortly after 4am on Tuesday January 30.
An 80-year-old man awoke to find a man in his home, who demanded money from him before punching him twice in the face.
The victim was able to activate an alarm and the suspect made off.
He was treated by the Scottish Ambulance Service for minor facial injuries.
An item of jewellery was later discovered to be missing and enquiries continue to establish if anything else has been taken.
The suspect is described as white, in his early twenties, 6ft 1in tall, of slim build, with a local accent and clean shaven.
He was wearing grey jogging bottoms, and a matching top with either the hood up or a hat on, and gloves.
Detective Inspector Clark Martin of Gayfield CID said: “This was a despicable act and a traumatic experience for the victim, who was attacked within his own home.
“As part of our enquiries, we’re urging anyone in the local community who may have seen suspicious behaviour in the area, or who recognises the description of the suspect, to get in touch with us or Crimestoppers as soon as possible.
“There will be an increase in high visibility patrols in the Niddrie area over the coming nights and anyone with concerns or information is encouraged to speak to these officers.
“Please remain vigilant and ensure that doors and windows are kept secure at night, and report any suspicious behaviour to us through 101 - always dialling 999 if you see a crime in progress.”
Those with information can contact Gayfield CID via 101, quoting incident number 0368 of 30th January, or report this anonymously to the charity Crimestoppers on 0800 555 111.