Loan-to-value and the price-rent ratio

The purpose of this paper is to highlight the relation between the loan-to-value (LTV) ratio and the price-rent (PR) ratio. The paper intends to relate the PR-ratio to housing return and the potential for a leverage gain in housing investments by considering the funding structure of housing investments.

Combining a PR-ratio approach with the housing return in the case of mortgage-financed housing, as presented by Borgersen and Greibrokk (2012), this paper relates LTV to the PR-ratio.

When formalising the relationship between leverage and housing return, as given by Muellbauer and Murphy (1997), the paper finds the effect of a higher LTV on the user cost of housing as the net effect of a higher borrowing cost and the associated leverage gain. The latter depends on the relationship between house price growth and the mortgage rate and, because the leverage gain has an ambiguous effect on the user cost of housing, the relation between the LTV-ratio and the PR-ratio is context-specific.

The paper aims to contribute to the literature on PR ratios in two ways. First, by explicitly including the LTV-ratio in the user cost of mortgage financed housing and, correspondingly, in the PR-ratio derived from the user cost. Second, by including the funding structure of housing investments the expression for the capital gain, which often is discussed in the PR-ratio literature, is related to the funding structure and includes both a price gain and a leverage gain.