Optimal Leverage of Commercial Real Estate Investments: A Trade Off Option Theoretic Approach

The determination of an optimal level of financial leverage for commercial real estate investment transactions is a central concern both for investors and financial institutions. Investors seek the maximization of the economic value of the investment firm while financial institutions need to adequately price the overall risk in accordance with the available regulatory capital budget. Excess leverage and large and/or unexpected shifts in the default risk of commercial real estate portfolios are a relevant potential threat to both objectives and need to be addressed from the perspective of macro prudential guidance. Traditional modelling of (commercial real estate) asset values as geometric Brownian motions may not be sufficient to capture tail events and risks relevant to investors and financial institutions for pricing and risk assessment purposes, since the distribution of returns of such properties does not seem to be normal. We examine the default, prepayment risk and optimal unitranche leverage level of single-borrower non- recourse mortgage loans, based on a trade-off option theoretic structural approach that captures asymmetry and kurtosis of asset values¡¯ returns distributions through the shifted lognormal distribution as in De Luna et al (2025). Our framework includes distress costs expanding the firm value paradigm of Modigliani and Miller (1958, 1963) to model interior optimal leverage solutions. We conduct several numerical experiments to examine how the different parameters of the model but also the returns distribution and load of distress costs affect the pricing of the CRE mortgage loan and the level of optimal and prudent leverage.