Security baskets and index-linked securities whose values are aggregates of the cash flows or values of other assets. Creation of these "composite" securities improves the welfare of uninformed investors by reducing their trading losses. The introduction of composite securities can also affect real investment decisions. When investors are exposed to nontradeable, heterogeneous risks, different trading equilibria are possible. Markets for multiple composite securities may exist or, when the degree of heterogeneity is high, markets for a single composite security and its component securities may coexist. No results depend on the existence of exogenous "noise" traders.