Solving the Subprime Loan Problem
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Much has been written about the boom-bust real estate cycle. Of late, the boom has been called a bubble and the bust has been called a credit crisis. There are some general conclusions that can be reached by following this market movement. Since most states do not allow lenders to hold borrowers personally liable for debt incurred to buy a home (and federal bankruptcy law makes it a practical impossibility in the remaining states), the borrower has the option to stop making payments and give the property to the lender in satisfaction of the debt. We can think of the borrower's option to make this decision as a "put option". If the home appreciates, the borrower has an incentive to keep making payments and reap the benefits of home ownership. If the opposite happens, the borrower can abandon, thereby "putting" the property to the lender, at a put option price equal to the then-outstanding balance of the loan.[more]
A put option forces the writer of the put option to buy. When this situation happens en masse, lenders are swamped and cannot react to their new position as owners. In this situation, lenders are forced to (a) offer forbearance to the borrower in the form of a recast or other compromise; (b) delay exercising their foreclosure rights in the hope the market will recover and borrowers will resume making payments; or (c) sell their debt instrument at a discount. The latter course is usually done in bulk with a portfolio of, say, 2000 loans having a nominal value (aggregate outstanding balance) of $500 million being sold for perhaps $200 million to an investor who may then undertake alternatives (a) or (b) with individual borrowers.
Financial maneuvers aside, people need somewhere to live and homes are buildings that need to be occupied to remain in habitable condition. Ignoring the tax and community benefits of promoting home ownership during "normal" times, the primary reason that buying a home is more desirable than renting is the expectation of future growth in value that accrues to the homeowner. A renter does not receive this value. Hence, the "bust" part of the cycle suggests that market participants could benefit from the use of a "call" option in connection with a lease arrangement. As the transaction costs of foreclosure, eviction, relocation of the evicted former owner, rehabilitation of the building, re-marketing, and sale to a new buyer are very high, it behooves the parties to recast their failed loan-and-put-option relationship to a lease-and-call-option arrangement.
The Demonstration presumes fixed values for (i) the original debt ($240,000), (ii) the discount a realistic lender is prepared to make (55%), (iii) an operating expense ratio (37%), (iv) available monthly household budget ($1,500) for a combination of housing cost and a sinking fund payment at (v) a safe rate of interest (5%) to permit the borrower-turned-tenant to accumulate a down payment to be used when the option is exercised. It allows the user to adjust three critical decision variables: projected annual growth, the length of the lease (Term), and a sharing ratio (Share) that divides the parties' benefits equally or disproportionately. The output shows the range of option price and rent that produces a particular investor yield to the party who bought the discounted debt. Along the line in the plot any combination of rent and option price leaves the investor yield unchanged. In the default example (yield = 8.162%) it is evident that lower yields argue powerfully for the original lender to make this arrangement directly with the borrower rather than selling the debt to a third party at a discount.[less]
Contributed by: Roger J. Brown (March 2011)
Reproduced by permission of Academic Press from Private Real Estate Investment ©2005
Open content licensed under CC BY-NC-SA
Note that a paternalistic lender, wishing to avoid a repeat of the first failure in a different form, can require all of the household budget to be paid monthly. The lender can then accumulate the sinking fund payments for the eventual purchase of the home via the call option. This activity is common for paying property taxes and insurance through a lender-maintained impound account. Although home ownership is usually not a decision centered on risk, the plot shows how risk can be "tilted" toward one party. Longer terms and lower growth assumptions make the proposition safer for the occupant; the alternative makes it more risky for that party.
A further variation would convert the lease option to a loan when the down payment was sufficient to convince the lender that, at the new loan-to-value ratio, the loan was well-secured. Including the income tax ramifications (mortgage interest is deductible and lease payments are not) adds mind-numbing complexity. The occupant can gain a tax advantage at any time. But the point at which that tax advantage is economically justified is a difficult, separate calculation.
The goal of the maximization problem is to seek the optimal rent and call option value that maximizes the investor's net present value subject to the constraint that it is equal to the occupant's net present value multiplied by the sharing factor (initial value = 1, in which the investor and occupant share equally). The investor's yield is determined from these optima under the assumption that the call option will be exercised. As the sharing factor changes, the investor's yield will change, but the occupant's incentives (rent and call option price) also change in a way that makes exercise of the option more (sharing factor < 1) or less (sharing factor > 1) certain.
More information is available in Chapter Nine of Private Real Estate Investment and at mathestate.com.
R. J. Brown, Private Real Estate Investment: Data Analysis and Decision Making, Burlington, MA: Elsevier Academic Press, 2005.
"Solving the Subprime Loan Problem"
Wolfram Demonstrations Project
Published: March 7 2011