This paper demonstrates that, in the context of U.S. housing data, rents and ex ante user costs diverge markedly—in both growth rates and levels—for extended periods of time, a seeming failure of arbitrage and a puzzle from the perspective of standard capital theory. The tremendous volatility of even appropriately-smoothed ex ante annual user cost measures implies that such measures are unsuitable for inclusion in official price statistics. The divergence holds not only at the aggregate level, but at the metropolitan-market level as well, and is robust across different house price and rent measures. But transactions costs matter: the large persistent divergences did not imply the presence of unexploited profit opportunities. In particular, even though detached housing is readily moved between owner and renter markets, and the detached-unit rental market is surprisingly thick, transactions costs would have prevented risk-neutral investors from earning expected profits by buying a property to rent out for a year, and would have prevented risk-neutral homeowners from earning expected profits by selling their homes and becoming renters for a year. Finally, computing implied appreciation as a residual yields a house price forecast with huge errors; but either longer-horizon or no-real-capital-gains forecasts—which turn out to have similar forecast errors—imply a far less divergent user cost measure which might ultimately be useful for official price statistics. Some conjectures are offered.