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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?
It depends what kind of people inhabit your world (or your model).
If people are risk neutral, then indeed they will look only at expected return. They will rush into stocks and raise their price until the return is equal to the risk free rate. The risk premium on stocks will drop to zero.
But there is a lot of evidence that this is not how real human beings behave. They really are risk averse and they will not all decide to buy stocks. Historically the risk premium on stocks does not seem to be dropping to zero but remains positive. And in my experience those who are initially enthusiastic about being in stocks moderate their opinion considerably when the first recession hits and they personally experience just how unpleasant it is to lose money. (In fact some give up on stocks altogether).
Yes, the existence of non-zero market price of risk implies the existence of strategies with a positive expected return. The expected return is the compensation demanded for bearing market risk.
The demand for positive expected return strategies doesn't decrease the market price of risk to zero (equivalently, it doesn't decrease the expected return of risky strategies to zero). Why would it? Why would you buy stocks if the expected return was the same as holding cash?
