According to the modern critics (Pollini 1987), the marble portrait would rather be identified as Gaius Caesar [20 BC AD 4], the oldest son of Agrippa and Julia, grandson and designated heir of Augustus, [Stemma Augusti 3.1]. He died prematurely in 4 AD, at 24 years old. In this case the model of the sculpture would be dated in the last years of the life of the young, between 1 and 3 AD.
The beard could recall the mourning for the death of his brother Lucio [17 BC AD 2] or assimilate the character of Mars, god of war (Pollini 1987).
Tacitus Annales [I, 3] about Gaius Caesar fate:
Each of his [Augustus] step-children, Tiberius Nero and Claudius Drusus, was given the title of Imperator, though his family proper was still intact: for he had admitted Agrippas children, Gaius and Lucius, to the Caesarian hearth, and even during their minority had shown, under a veil of reluctance, a consuming desire to see them consuls designate with the title Princes of the Youth. When Agrippa gave up the ghost, untimely fate, or the treachery of their stepmother Livia, cut off both Lucius and Caius Caesar, Lucius on his road to the Spanish armies, Caius wounded and sick on his return from Armenia.