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We set up a multiperiod, CAPM-type model with imperfect competition between investors in case of an additional price-insensitive market participant. The motivation for this additional actor comes from the ECB’s announcement to buy a substantial amount of securities “whatever it takes” which reflects the willingness to trade in a entirely price-inelastic way. Our model explains the effects on demand functions, equilibrium prices, portfolio holdings and investors’ expected utility. The interaction of price-inelastic additional demand by the ECB, on the one hand, and imperfect competition, on the other hand, causes differentiated results regarding timing strategies, development of prices over time, and utility implications.