The housing consumption capital asset pricing model with an antichresis rent market: Nonseparability and composition risk

We develop a housing consumption capital asset pricing model for economies with an antichresis rent market wherein property owners receive up-front lump-sum deposits from renters instead of monthly rents and use it as leverage to acquire housing assets for rent. We estimate the model using antichresis rent market and stock market data for Korea. We find that housing consumption and nonhousing consumption, which are complementary over the long term, have sufficient cross-sectional elasticity of substitution, leading to a meaningful composition risk premium. We find that the housing expenditure share is procyclical, while intratemporal elasticity of substitution between housing and nonhousing consumption is close to but larger than one and greater than intertemporal elasticity of substitution. As a result, the composition risk arising from the nonseparability of housing and nonhousing consumption induces a sizable positive risk premium. Finally, we examine the effect of interest rate risk by decomposing composition risk into interest rate risk and noninterest rate risk and find that interest rate risk is primarily responsible for the positive composition risk premium.