This paper offers a "simple" model of housing markets with interdependent values. Here, we introduce private information on the quality of a house, which is known only to the initial owner. An ex-post preference of an agent is assumed to depend on such information. We prove that ex-post incentive compatibility together with another axiom leads to an impossibility: (i) a rule satisfies ex-post individual rationality and ex-post incentive compatibility if and only if it is the no-trade rule; (ii) there exists no rule that satisfies ex-post efficiency and ex-post incentive compatibility; and (iii) a rule satisfies non-bossiness and ex-post incentive compatibility if and only if it is agent-wise constant. Our results differ significantly from those of the private values model in which there exist non-trivial strategy-proof rules that satisfy desirable axioms.