The connection between four cardinal virtues and Hellenistic kingship was a new idea to me. (I feel a little ashamed to admit this!)
I’ve been re-reading Katherine Steel’s Cicero, Rhetoric and Empire (p. 133) and this passage struck me:
How does this connect with the shield of virtues presented to Augustus by the Senate? Surely someone must have written something on this. I’m going to resist exploring at this moment and just leave this note for myself that I wish to revisit the topic, at least before the next time I teach the clipeus virtutis!!
Liv Mariah Yarrow 
As you suspect, someone has indeed written on this. When you come back to the topic, the article you need is Andrew Wallace-Hadrill 1981, ‘The emperor and his virtues’ in Historia 30: 298–323.