This paper frames a normative theory of stewardship engagement by large institutional investors and asset managers in terms of their theory of investment management – “Modern Portfolio Theory” -- which describes investors as attentive to both systematic risk as well as expected returns. Because investors want to maximize risk-adjusted returns, it will serve their interests for asset managers to support and sometimes advance shareholder initiatives that will reduce systematic risk. “Systematic Stewardship” provides an approach to “ESG” matters that serves both investor welfare and social welfare and fits the business model of large diversified funds, especially index funds. The analysis also shows why it is generally unwise for such funds to pursue stewardship that consists of firm-specific performance focused engagement: Gains (if any) will be substantially “idiosyncratic,” precisely the kind of risks that diversification minimizes. Instead asset managers should seek to mitigate systematic risk, which most notably would include climate change risk, financial stability risk, and social stability risk. This portfolio approach follows the already-established pattern of assets managers’ pursuit of corporate governance measures that may increase returns across the portfolio if even not maximizing for particular firms. Systematic Stewardship does not raise the concerns of the “common ownership” critique, because the channel by which systematic risk reduction improves risk-adjusted portfolio returns is to avoid harm across the entire economy that would damage the interests of employees and consumers as well as shareholders.