# Does MPR imply strategies with positive average return?

Doesn't the existence of Market Price of Risk make investment strategies relying on the average outcome of a risky investment attractive as compared to the expected value of it (computed under the risk free measure)?

I understand there is some heterogeneity going on but, wouldn't the demand for such a strategy anyway decrease the MPR until making it zero, so that the average payoff of the security matches the risk-free computed value?