Consider a one-period economy where the assets are correctly priced by a state-price deflator M. A nutty professor believes that the assets are priced according to a model in which Y is a state-price deflator, where Y is a random variable with E[Y] = E[M].
Refer to this model as the Y-model.

(a) Show that the Y-model prices a risk-free asset correctly.

(b) Argue that the expected return on an arbitrary asset i according to the Y-model is given by EY [Ri] ≡ 1 E[M]
− 1 E[M]
Cov[Y, Ri].

(c) Show that | E [Ri] − EY [Ri]|
σ[Ri] ≤ σ[Y − M]
E[M]
so that the mispricing of the Y-model (in terms of expected returns) is limited.

(d) What can you say about the returns for which the left-hand side in the above inequality will be largest?

(e) Under which condition on Y will the Y-model price all assets correctly?