A recent study of Milton Sousa shows that modesty plays an important role for powerful leaders. It shows that the more powerful a leader is, the more relevant it is for him or her to be modest. Successful and humble leaders benefit from a more open culture. On your way to the top, you do have to be aware though that modesty could not be the best approach.
Another link to a related article:
rotterdam.watertalent.nl/nl/nieuws/11885/bescheiden_leiders_zijn_ook_in_zakenwereld_effectief.html