She is the third generation to control the company and, like her family members, has maintained a low profile despite the reach of the firms mutual funds.
Bossen joined as director of ETF business development at the institutional intermediary division and will focus on the IndexIQ unit that MainStay acquired last year.
Baha helped Jeffrey Gundlach turn DoubleLine Capital into a $100 billion asset management firm.
The stock picker, known for beating the S&P 500 Index for 15 straight years when he ran the Legg Mason Value Trust, will buy Legg Mason's stake in LMM, an investment adviser that he and the company jointly own.
The legendary money manager is losing his No. 2, Kumar Palghat, who will become co-manager of a new Janus Short Duration Income ETF.