The relevant features of a collateralized loan are the current value of its collateral and the remaining balance and thus the current exposure. The future value of the collateral is random and contingent on its prospective exposure. Risk intensifies when the market value of the collateral declines and the borrower defaults. As time progresses, the default risk is subject to two effects. First, uncertainty attached to the value of the collateral. This becomes acute the closer the term, thereby exacerbating default. Second, loan contracts, such as corporate loans or mortgages secured on the value of real estate property, involve cash flows that are paid over time. This reduces the remaining balances as the underlying loans amortize through time. As a result, the maximum exposure is unlikely to occur in the first year. The maximum exposure is also unlikely to be in the last years since most of the payments will already have been made by then. It is more likely that the maximum exposure will be in the middle of the tenure of the contract.
This proactively proposes a new method for tackling both risk shifting as well as underinvestment. This is conducted by quantifying and modifying the maximum exposure to default risk by looking forward into the payment schedule of a loan contract. We show that the probability of default can be minimized by making the initial loan-to-collateral value ratio small enough. Since the maximum exposure is in most cases located in the middle of the contract, a static model focusing on initial exposure or a specific default (terminal) date assumed ex-ante is inappropriate for the task. An optimal level of debt simultaneously addresses the underinvestment problem for the borrower. Thus, we need a forward-looking, stochastic and intertemporal model to solve this issue. Consequently, we choose a framework which is capable of incorporating the impact of: (a) the probability of default; (b) the present value of the maximum lifelong exposure, on the initial permissible loan to value ratio; while (c) endowing financial flexibility to the borrower to expand his venture.
Unlike prevailing practice, we go beyond the current exposure at origination approach. We also include the maximum life-long exposure into our analysis. Therefore, our new method also integrates the potential future loss that may occur over the lifetime of a contract due to a borrower defaulting on her/his loan. We are proactive and contribute above the standard approach which normally only considers the current value of the collateral and/or a specific default date. Our approach is inspired by the Credit Valuation Adjustment (CVA) concept which is now an integral part of the Basel III regulatory framework. CVA is the difference between the price of a default-free derivative and the price of a default-prone derivative, to account for the expected loss from counterparty default. Following the crisis of 2007, CVA adjustments are now required daily by Basel III for exposures to derivatives in the context of counterparty credit risk. What we essentially do is reverse the logic of CVA. In contrast, the CVA remains only a risk measuring too
Our enhanced framework can be applied to decrease (and, ideally, quasi-eliminate) the likelihood of default when approving the size of collateralized loans. We define ‘Loan Valuation Adjustment’ (LVA) as the difference between the value of a risk-free loan and the value of a risky loan, such that a default-prone loan has a lower value than a risk-free loan. This is because a borrower in a default-prone loan may renege on his/her obligations and the bank issuing such a facility will not receive the scheduled payments, i.e. the amortized fraction of principal plus interest on remaining balance. Our first contribution to the literature is to provide a method to minimize the LVA and thus to provide an answer to the problem of converting a risky loan into a quasi-risk-free loan. Unlike the CVA, which is exogenously driven by the state variables of the economy2 and thus cannot be changed, our LVA can be proactively implemented and modified. Our approach looks forward into future points in time for the lifetime of the loan. We obtain potential future exposures at each future time point. We then aggregate positions backwards, taking into account values of the collateral and remaining balances. We then derive implications on the maximum allowable quasi-risk-free loan which can be granted today, and thus maximize its value to the lending financial intermediary institution. Our second contribution is to offer a method which is capable of mitigating the twin issue of risk-shifting (illustrated in Figure 1) where the borrower defaults between periods t1 and t2 (when the equity is underwater) and underinvestment (illustrated in Figure 2) when the borrower’s cash-flows in period 2 are below its debt obligations. Tackling these twin issues is crucial, as they impact on economic fragility, dampen entrepreneurial activity and thus economic growth. Our approach is linked to the concept of margin loans where: (i) the underlying asset is over-collateralized (to offset risk-shifting); and (ii) an optimal tenure of facility is evaluated to allow the borrower to meet his/her debt obligations (to offset underinvestment).
Finally, our third contribution is to link our framework to the problem of pragmatically eliminating agency issues from debt, where the loan is collateralized with tangible (i.e., real) assets. Our proposal is consistent with Myers (2001), who infers the efficiency of default-free collateralized loan structure as mitigating agency cost. We: (i) illustrate that such a structure warrants a treatment different from that of information asymmetry; (ii) extend the scarce literature on pricing collateralized loans devoid of agency costs of debt; and (iii) introduce a novel margin approach to collateralized loan pricing, which provides a way to reduce the fragility of the financial system while endowing financial maneuverability to the borrower. Prudent underwriting warrants satisfaction of both (i) asset; and (ii) income constraints to thwart the risk-shifting and underinvestment issues, respectively. Our loan pricing mechanism is consistent with Baltensperger (1978) who advocates incorporation of not only the interest rate but also the loan-to-value ratio and the tenure of the facility. Archer and Smith (2013), and Foote, Gerardi, and Willen (2008) in their studies extend the parameters by including borrower income factors.3 This satisfies a higher order risk management approach in contrast to ad hoc credit rationing practices, and overall loan loss rehabilitation programs.
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