Demand Shocks and the Market for Income Producing Real Estate

Transcription

1 Demand Shocks and the Market for Income Producing Real Estate April 2002 Stephen Day Cauley The Richard S. Ziman Center for Real Estate The Anderson School at UCLA 110 Westwood Plaza, Los Angeles, CA Tel: (310) and Andrey D. Pavlov Simon Fraser University 8888 University Dr. Burnaby, BC V5A 1S6, Canada Tel: JEL Classification: G13 Special thanks to George Gallagher at CoStar COMPS for providing the data used for this research. The comments and suggestions of Avi Bick, Wayne Archer, and the participants at the Cambridge-Maastrich Symposium 2001, the University of California, Berkeley and DePaul University are greatly appreciated. Financial support from the Social Science Research Council of Canada is gratefully acknowledged.

2 Demand Shocks and the Market for Income Producing Real Estate Markets for income producing real estate frequently respond to negative demand shocks with long periods during which asset liquidity decreases but transaction prices change relatively little. This paper provides an explanation for this phenomenon that is consistent with individual rationality, results in an asymmetric response to positive and negative demand shocks and can generate long periods during which asset liquidity declines. Our explanation is based on the rational response of sellers and potential buyers to a widely used financing arrangement, the non-recourse mortgage loan. First, we undertake a theoretical investigation of the effect of non-recourse financing on a liquidity-motivated seller s reservation price and the conditions under which a mutually agreeable transaction will take place. We then use data for a specific real estate market, the Los Angeles County apartment building market, to estimate the empirical relevance of our model. Our estimates imply that for liquidity motivated sellers and buyers, with identical expectations about the price formation process, a negative demand shock can result in the seller s asking price for an apartment building exceeding the potential buyer s bid price. Finally, we estimate, as a function of the seller s Loan-to-Value ratio, the sum of the liquidity costs (motivation) to the current owner and the potential buyer that will induce a mutually agreeable transaction. JEL Classification: G13 2

3 I. Introduction In the short run the supply of income producing real estate is fixed and the market response to demand shocks should be symmetric: negative shocks resulting in price decreases and positive shocks resulting in price increases. However, the empirical evidence is frequently not consistent with this theory. Specifically, markets for income producing real estate typically respond to large negative demand shocks with long periods during which asset liquidity decreases but transaction prices change relatively little. In contrast, the same markets respond to positive shocks with increases in prices. Explanations for this phenomenon include market imperfections that result from high information cost and/or the combination of unrealistic (not rational ) expectation on the part of owners and the inability to sell real estate short. 1 While these are important characteristics of real estate markets, they provide a more convincing explanation of short-term market responses than they do of the long-term conditions that sometimes occur (e.g., Southern California between 1990 and 1996). This paper provides an alternative explanation for the phenomenon that is consistent with individual rationality, results in an asymmetric response to positive and negative demand shocks and can generate long periods during which asset liquidity declines. Our explanation is based upon the rational response of sellers and potential buyers to a widely used financing arrangement, the non-recourse mortgage loan. 2 1 Behavioral finance provides explanations for seemingly non-rational market behavior such as the asymmetric response to changes in market values. Hirshleifer (2001) provides an excellent description of this literature. An asymmetric response to demand shocks can be thought of as resulting from the disposition effect, (Shefrin and Statman,1985), that is the tendency to keep losers and sell winners. 2 A non-recourse loan precludes a deficiency judgment following loan default. Disregarding the cost of reduced credit availability, the most a property owner can lose, when a purchase is financed with a nonrecourse loan, is their equity investment. Cauley and Pavlov (2002) shown, by example, that for homeowners who have purchased a home with a non-recourse loan the optimal response to price 3

4 The purchase of income producing real estate is typically financed by the use of a non-recourse loan. When the ownership of real estate is financed in this way, the owner s interest in the property is equivalent to a portfolio comprised of the property, a mortgage loan, and a put option that gives the owner the right to sell the property to the mortgagee at a price equal to the loan balance (i.e., by defaulting on the loan). 3 For this reason, the value of a property, to the owner or potential purchaser, depends upon the exercise price of the put (i.e., the actual or potential mortgage loan balance). For organized financial markets, the characteristics of an option that is sold are the same as the characteristics of an option that is purchased. This need not be true for the sale of an owner s equity interest in income producing property. For example, following a large negative demand shock, a maximum loan to value requirement frequently results in the exercise price of the option that is being sold (i.e., the seller s mortgage loan balance) being greater than the exercise price of the option that would be bought (i.e., the maximum mortgage loan for a buyer). This paper develops a model of a market for income producing properties to investigate the effect of a non-recourse loan feature on a motivated seller s reservation price, and the conditions under which a mutually agreeable transaction will take place. We conclude that, at least theoretically, the non-recourse feature can generate the asymmetric responses to negative and positive demand shocks that are frequently observed. Specifically, we show that a negative demand shock can result in decreases in asset liquidity where as a positive demand shock can not. We then use data for a uncertainty may be to delay the sale of their home. They hypothesize that this can explain the response of home markets to negative demand shocks.. 3 A non-recourse loan precludes a deficiency judgment following loan default. Disregarding the cost of reduced credit availability, the most a property owner can lose, when a purchase is financed with a nonrecourse loan, is their equity investment. 4

5 specific real estate market, the Los Angeles County apartment building market, to estimate the empirical relevance of the effects that out model identifies. Our estimates imply that for motivated sellers and buyers, with identical expectations about the price formation process, a negative demand shock can result in the seller s asking price for an apartment exceeding potential buyer s bid price. Finally, we estimate the dollar value of the motivation to the current owner and the potential buyer that will induce a transaction. The remainder of this paper is divided into four sections that: (1) describe levered ownership of income producing real estate as a complex derivative security; (2) present our model of a real estate market; (3) describe how we estimate the value of this derivative; and (4) present our estimates for a typical Los Angeles County apartment buildings. II. Commercial Real Estate as an Option While a number of studies estimate the value of the put option contained in a mortgage contract based on the default history of loan pools (Deng, Quigley, and Van Order (1997), Kau and Kim (1994), Deng, Quigley, Van Order (1996), Shilton and Teall (1993)), the implications of non-recourse loans on markets for income producing real estate have not been widely studied. When income-producing property is bought with a non-recourse loan, the property owner (debtor) has the option of defaulting on the loan without recourse. As was noted above, this is equivalent to putting the property back to 5

6 the creditor at a price equal to the existing mortgage loan balance. 4 At each point in time (e.g., each month) the owner can take one of four mutually exclusive actions. He/she can: (1) make the mortgage loan payment; (2) refinance the property; (3) sell the property and pay off the mortgage loan; (4) default on the mortgage loan (i.e., the property is put to the creditor); or (5) renegotiate the loan (which is typically equivalent to one or a combination of the above alternatives). The valuation of an income producing property that ignores the implications of non-recourse loans is seriously flawed. When a property is purchased with a typical LTV ratio, the value of the put option is relatively small. 5 After a negative demand shock, when the actual LTV ratio frequently exceeds the initial LTV (e.g., when the owner has zero or negative equity), the value of the option may be relatively large. As we will see, consideration of the put option is essential to understanding the response of real estate markets to negative demand shocks. III. A Model of a Real Estate Market In this section we develop a model of a real estate market, designed to abstract from all other considerations to explore the impact of non-recourse loans on the response of real estate markets to demand shocks. The market is comprised of N identical, liquidity motivated sellers, who own identical income producing properties 4 There are costs in terms of reduced availability of credit associated with putting the property (i.e., defaulting on the loan) to the mortgagee 5 At the time of loan origination (ex-ante) the value (cost to lender) of the put inherent in the non-recourse loan will be reflected in the interest rate charged for the loan. Ex-post (e.g., for negative equity properties) the value of the put may exceed the risk premium incorporated in the interest rate. 6

7 (e.g., an apartment unit). 6 There are M (M=N) identical, liquidity motivated, potential buyers for the properties. There are no transactions costs, and information is symmetric and complete. Sellers or potential buyers receive no direct utility from ownership of a property and there is agreement as to the price formation and cash flow generation processes. The future is comprised of a countable infinity of periods. 7 At the beginning of a period, sellers and potential buyers are randomly allocated. They then negotiate over the sale of the property. After the negotiation is completed, the realizations of the asset price and cash flow stochastic processes for the period are observed. If the parties have not transacted during the first period, they are reallocated and negotiations start over. 8 In the remainder of this section we: (1) derive the effect of a non-recourse loan on a seller s reservation price; (2) determine the conditions under which a mutually advantageous transaction will take place; and (3) show that the combination of a nonrecourse loan and a negative demand shock will make a mutually agreeable transaction more difficult to achieve. At the beginning of a period, sellers and potential buyers agree that V is the investment value of the property (e.g., the present value of all future cash flows for a 100% equity investment). 9 As was previously mentioned, the parties are motivated to transact by liquidity considerations (i.e., the seller s (buyer s) portfolio contains more (less) real estate than is optimal). To represent (quantify) the owner s motivation to sell 6 Agents can be classified as information or liquidity motivated. Information motivated agents think they have an information advantage regarding a property s value, whereas, liquidity motivated agents do not. Their motivation is to change the composition of their portfolio because of factors such as tax considerations, change in risk tolerance and/or to the need to rebalance the owner s portfolio. 7 Implicitly continuous time, as reflected in the asset price and cash flow stochastic processes, is broken into a sequence of non-overlapping fixed length periods (e.g., month). 8 The assumption that M=N guarantees that if an owner does not sell his property during a period, he or she will be matched with a buyer during subsequent periods (similar results can be obtained if M>N). 7

8 we assume that if the property is not sold a non-negative per-period liquidity cost, 10 cs 0, is incurred. Analogously, by transacting, potential buyers do not have to incur per period liquidity costs c b 0. Analytically, the purpose of those private costs is to provide a motivation to transact other than differences in the perceived values of the property. In the absence of debt, the seller s reservation price, v S,, is the investment value of the property minus the liquidity costs that would be born if the property was not sold (i.e., V c s ). Without debt, the maximum price a potential buyer will pay, v b, equals the property s investment value plus the costs that are avoided if a property is owned (V + c b ). When the sum of the liquidity costs (motivations) of the seller and potential buyer are non-negative, a mutually agreeable transaction will always be possible. A transaction at any price between V c s and V + c b is Pareto optimal. An implication of this result is that in the absence of debt, a negative demand shock will never preclude a mutually agreeable transaction. A. Seller s Reservation Price With Debt We now introduce non-amortizing debt into our model. It should be noted that none of our conclusions would be changed qualitatively if debt were fully amortizing. At the start of the first period, the seller is assumed to have an existing, non-amortizing, non-recourse mortgage loan with an outstanding balance (face value) of F S and market value M S. The market and face value may differ because: (1) the contracted and market 9 In our model, a negative demand shock is a large decline in V that has occurred prior to the initial period. 10 These are the sum of the explicit and the dollar value of implicit costs of not transacting. 8

9 interest rates differ; and/or (2) because the value of the put option embedded in a nonrecourse loan has changed (e.g., because Vt V0 ). 11 The seller s surplus from a potential transaction equals the net value the seller would receive i.e., the sale price (S), net of the outstanding mortgage balance, minus the value of the portfolio representing the seller s interest in the property. For a transaction to be acceptable it must result in a non-negative surplus. That is, S F ( V M c ) 0 (1) S S S Consequently, the seller s reservation price, v S, equals: vs = V + FS MS c S (2) The above expression suggests that increases in mortgage interest rates can lockin a property owner with a fixed interest rate loan. Specifically, if M S < F S, the reservation price is increased and it may, in fact, exceed the property s investment value (i.e., (F S M S ) > c S ). Equation (2) also allows us to determine the effect of a non-recourse feature on the seller s reservation price. Let subscript n denote all variables related to a nonrecourse loan and subscript r denote the corresponding values for a full recourse loan. The difference of the reservation prices with a non-recourse and a full recourse loan is: 11 Note, the value of put incorporated in the value of the mortgage, M s, includes future period liquidity costs, c s, that would be incurred if the seller acted optimally with respect to the mortgage loan (e.g., 9

10 v v = ( V + F M c ) ( V + F M c ) n r n n S r r S (3) Assuming the outstanding balance is independent of loan type ( i.e., F n = F r ), equation (3) reduces to: v v = M M (4) n r r n That is, the effect of a non-recourse feature on the seller's reservation price is the difference between the market value of the mortgage with and without the non-recourse feature. This is the value of the put option incorporated in the non-recourse loan. 12 Note at origination, equilibrium mortgage interest rates should be set in such a way that the value of the non-recourse and full-recourse mortgages are equal to each other and to the face value of the mortgage (M r = M n = F n = F r ). Thus, at origination the seller s reservation price is the same with either mortgage or with no financing at all. 13 As property values change, the value of the non-recourse mortgage changes, while the value of the recourse mortgage doesn t. We discuss this asymmetry below. B. A Negative Demand Shock and a Seller s Reservation Price We now investigate the effect of a negative demand shock on a seller s reservation price. Specifically we show that such a shock results in a divergence defaulted or sold). 12 This may not be strictly true because the holding period may be a function of the mortgage type. 13 This argument assumes no information asymmetries between borrowers and lenders. 10

11 between the properties fundamental value V and the seller s reservation price and the larger the shock the greater the divergence. The seller s reservation prior to a negative demand shock, v p, equal: vp = Vp + F M p c S (5) and their reservation price after a negative demand shock, v a, is va = Va + F Ma c S. (6) Consequently, the change in reservation price because of the negative demand shock is: v = v v = ( V + F M c ) ( V + F M c ) S a p a a S p p S (7) Simplifying, we obtain: vs = ( V V ) + ( M M a p p a ) (8) The issue is, what declines more the reservation price or the investment value following a negative demand shock? By the definition of a negative demand shock ( Va Vp) < 0, consequently, the answer depends upon the relationship between Mp and M a. We know M that, > 0, V 2 M V < 0 2. Consequently, a negative demand shock results in M p > M a and we can conclude that the reservation price will decline less than the fair market value of the property. In addition, the fact that 2 M V < 0 2 results in the conclusion that the larger the negative demand shock, the greater in absolute value the difference between the reservation price and the fundamental value of the property. 11

12 C. Buyer s Maximum Bid Price If a transaction occurs, we assume the buyer will finance the purchase with a non-amortizing, non-recourse loan with face value F B and market value M B. 14 The buyer s surplus from a transaction is the value of the portfolio representing their interest in the property minus the price paid for the property. For a transaction to be agreeable from the perspective of a potential buyer it must result in a non-negative surplus. That is V M + c ( S F ) 0 (9) B B B This implies that the maximum price the potential purchaser will pay, v B, is : vb = V + FB M B + c B (10) We can now explore the effect of a negative demand shock on potential buyer s maximum bid price. Assuming the face and market value of loans used to purchase a property are equal, (F B =M B ). The maximum price a buyer will pay for a property becomes 15 : vb = V + c B (11) 14 As noted above, F will typically equal M at the time of purchase. Reasons why B B B B would include seller financing at a below market interest rate. 15 The buyer is paying the value of the option. F M 12

13 Equation (11) shows that a negative demand shock will lower, dollar for dollar, the maximum price a purchaser will pay for a property (i.e., D v = DV ). B D. Condition for a Transaction If a mutually agreeable transaction it to take place, the seller s reservation price must be less than or equal to the buyer s maximum bid price: V + FS MS cs V + FB MB + c B (12) Upon simplification, Equation (12) reduces to the following condition for transaction: c + c ( F M ) ( F M S B S S B B ) (13) That is, the sum of the liquidity costs that would be born if a transaction does not occur must be at least as large as the difference between the net values of the mortgage loans. If, as is to be expected, mortgage interest rates are set so that at origination the borrower pays for the put option inherent in a non-recourse loan, then at origination the face value will equal the market value of the loan i.e., FB = M. Then, for a mutually agreeable B transaction to take place, the sum of the liquidity costs have to exceed the difference between the face value (principal) and the market value of the seller s mortgage loan: cs + cb ( FS MS) = M S, (14) 13

14 where M S denotes the change in the value of the seller s mortgage from origination to date. Within our model, there are two reasons for the value of a non-amortizing mortgage to have changed from its origination: - Changes in property values (e.g., the put option contained in the mortgage becomes more valuable when property values decrease); and/or - Changes in interest rates (e.g., increases in mortgage interest rates that lockin a property owner with a fixed interest rate loan). Conceptually, we can decompose the market value of the mortgage, M S, into the present value of the mortgage loan payments (B) evaluated at a default-free (but not risk free) rate of interest and a put option, p. 16 If property values and interest rates are independent and we hold the loan balance constant, then declines in property values and increases in interest rates reduce the value of the mortgage, M. This, in turn, increases the liquidity costs needed to induce a mutually agreeable transaction. Changes in property values V are, however, negatively related to interest rate changes. If we view V as a function of r: dm ( V ( r), r) M V M = + dr V r r (15) M V M where > 0, < 0, and < 0. This implies that V r r dm ( V ( r), r) < 0. dr 16 The value of the mortgage is not strictly additive because exercising the put results in extinguishing the loan. 14

15 This relationship implies that negative demand shocks, either exogenously determined or resulting from a increase in interest rates, will make it more difficult to achieve a mutually agreeable transaction. Conversely, a positive demand shock will make it easier to achieve a transaction. Thus, at least theoretically, the value of the put option inherent in a non-recourse loan can result in the asymmetric response of real estate markets to demand shocks. Specifically, the put option can explain the decline in asset liquidity that is frequently observed following a negative demand shock. In the remainder of this paper we assess the empirical relevance of these results. E. Demand Shocks and Transaction Prices In the previous section we concluded that, at least theoretically, non-recourse financing can generate the declines in asset liquidity frequently observed after negative demand shocks. Now we investigate the implications of non-recourse financing on the price of the transactions that do take place. Specifically we show that our model implies the empirical observation that transaction prices fall relatively less than the properties investment value following a negative demand shock. We start by assuming that if a transaction is to take place (v B >v S ) the parties split the difference between the seller s reservation price and the potential buyer s maximum bid price according to a proportion a, 0<a<1. That is, the transaction price p equals: p = α( V + FS MS cs) + (1 α)( V + FB MB + c B ) (16) Simplifying we obtain: 15

16 p = V + (1 α) c + α( F M c ) (17) B S S S Taking the derivative of the transaction price with respect to the property s investment value, V, we obtain: dp dv dm dv S = 1 α (18) M Because S > 0 V and 0<a<1, when a transaction is still possible, the transaction price will fall less than the properties investment value. 17 Note, the above conclusion holds as long as the proportional split is independent of the change in V. IV. Evolution of the State Variables and Property Values In this section we describe the technique we use to estimate the value of an owner s interest in an income producing property (e.g., V F S M S ). The approach we use builds upon techniques developed by Cauley and Pavlov (2002). Specifically, we use the least-squares Monte-Carlo (LSMC) approach developed by Longstaff and Schwartz (2001) to value the portfolio of assets that is represented by an owner s interest in an apartment building financed by a non-recourse loan. The LSMC approach combines the principals of risk-neutral valuation with least-squares regression to estimate the value of complex American options. A. Joint Stochastic Processes 17 We will discuss the implications of this result for our empirical model later in this paper. 16

17 Without loss of generality, our analysis will be couched in terms of a single apartment unit. Underlying our implementation of the LSMC approach is the assumption that the per unit price of an apartment building, V, the per unit before tax cash flow yield, d, and the risk free rate of interest, r, are described by the following system of differential equations: 18 dv = µ vdt + σvdzv v dδ = µ dt+ σ dz (19) dr = µ dt + σ dz r δ r δ r d where the parameters m i, s i, ( i = v, d, r) are at most functions of the state variables v, d, and r and dz i are increments to Wiener processes. The correlation coefficients between the increments to the Wiener processes are denoted by r ij, ( i,j = v, d, r). In our model, as we describe below, the risk free rate of interest uniquely determines the equilibrium mortgage interest rate. In order to estimate the joint stochastic process (19) for the state variables we need to specify the functional form of the drift and diffusion coefficients. The basic assumption we make is that the expected rate of property appreciation, the drift of the cash flow yield, and the changes in the risk free interest rate are linear functions of the state variables. This specification implies that the joint stochastic process may be written as: 18 The risk free rate of interest is considered because of its relationship to the mortgage rate, and because it is used in risk neutral valuation. 17

18 dv = ( av 1+ av2δ + av3v + av4r) dt + σvdz v dδ = ( a + a δ + a r) dt + σ dz δ1 δ 2 δ3 δ dr = ( a + a δ + a r) dt + σ rdz r1 r2 r3 r r d v (20) where dz v, dz d and dz r are increments to standard Wiener processes with correlations r ij, ( i = v, d, r) and s v, s d and s r are the standard deviation of the respective time series. In this formulation, a negative demand shock is the occurrence of a z v that is negative and large in absolute value. This formulation excludes the possibility of negative property values and risk free rates of interest, but it does not exclude the possibility of negative cash flow yields. 19 Under the risk-neutral metric, the above model of property values is replaced by: dv = ( r δ) dt + σvdzv v dδ = ( a + a δ + a r) dt + σ dz δ1 δ 2 δ3 δ dr = ( a + a δ + a r) dt + σ rdz. r1 r2 r3 r d r (21) Notice that the process for d does not undergo a change under the risk-neutral metric because the cash flow yield (or dividend yield) is not an investment asset by itself and the risk-neutral preferences of the agents have no implication for its evolution over time. (Appendix A provides a formal rational for this conclusion). Going from a risky to a risk-neutral world will result in the correct value of a derivative based upon a traded 19 During the late 1980s many Los Angeles County properties had, as levered investments, negative cash flows. These may 18

19 asset because both the expected return and discount rate used to evaluate the cash flows are adjusted (Hull, 1997). The LSMC method starts by simulating price paths for the underlying asset (e.g., the value of an apartment unit), the cash flow yield and the risk free rate of interest. In our implementation of the LSMC we generate price paths for a typical apartment unit for 120 months into the future. 20 The simulated price paths are then used to estimate, by least squares, the pay-off for the portfolios conditional upon the state variables, v, d, and r at each point in time. The results of the regression are then used to estimates the expected value of continuation. The value of the portfolio is estimated by assuming that a risk-neutral seller or buyer acts optimally given the holding and liquidity costs. The value of the option that represents the owner s interest in the property then equals the expected present value (at the risk free rate) of the cash flows associated with optimal exercise of the option (i.e., sale of the property or default on the mortgage loan). The data needed to simulate the price paths are the risk free rate of interest, the variancecovariance matrix of the innovations of the processes given by (21), and the parameters a ij. (A detailed description of our implementation of the LSMC methodology is provided in Appendix B.) B. Empirical Estimates Given the above indices for real estate values and cash flow yields, we estimate, through the use of seemingly unrelated regression, the joint stochastic process (20). Appendix C provides the details of the data sources and the empirical estimation of the 20 We are assuming a 10- year, interest only balloon payment loan. Analysis of the optimal exercise of the option results in the conclusion that extending the life of the option, say to 30 years, has little effect on the estimates of value. 19

20 property value and cash flow yield series. The parameter estimates of process (20) are reported in Tables 6 and 7: Table 1: Joint Stochastic Process Driving the Property Markets dv/v 1.02 (5.95) dd.005 (2.64) dr (-2.48) d r V s (-5.84) (2.85) (-6.66) (-2.38) (-1.80) (3.62) (-1.25) Table 2: Correlation Matrix dv/v dd Dr dv/v 1 dd dr These results are statistically significant and consistent with our expectations. C. Bias-corrected Estimate of the Variance-Covariance Matrix The estimates of volatility of the price appreciation and cash flow yield reported in Table 1 contain an upward bias because the estimated rates of price appreciation and change in cash flow yield used to calculate them are subject to sampling error. Thus, even if the true appreciation rates and changes in the cash flow yield are perfectly explained by the model, the estimated volatility of the innovations will be positive simply due to the sampling error. Cauley and Pavlov (2002) derive a bias correction technique for similarly derived estimates of home price appreciation. This is the technique we used to derive our bias-corrected estimates of volatility. 20

21 Table 3 reports the bias-corrected estimate of volatility of the rate of price appreciation and change in cash flow yield. Note the risk free rate is not estimated. Consequently the estimated volatility does not have to be adjusted for bias. As we show in Appendix C, the covariance does not need to be adjusted. Table 3: Bias-corrected estimate of the volatility of the monthly appreciation rates and cash flow yield Naïve estimate of the volatility Bias-corrected estimate dv/v dd dr Our best estimate of the volatility of the monthly appreciation rates and cash flow volatility is the bias-corrected estimate of.0026 and.002 respectively (48 percent and 23 percent reductions in the estimated volatilities). Consequently, our estimates of the value of the portfolio of assets that correspond to the owner s interest in a property will be based upon these values. IV. A Non-Recourse Loan and a Seller s Reservation Price Above we showed that the effect of a non-recourse feature on the seller s reservation price is the difference between the market value of the seller s mortgages with and without a non-recourse feature. In the following example we illustrate the magnitude of this effect on a seller s reservation price. We assume: - The mortgage loan is non-amortizing 21 ; - Refinancing to obtain a lower interest rate is not possible, 21 Loan amortization increases carrying costs and reduces the exercise price of the option (i.e., loan balance) over time. The shorter the time to maturity the larger the fraction of the payment is to principal. As will be seen below, amortization has no qualitative effect on our conclusions. 21

22 - The loan is due (i.e., the option expires) in 10 years and the potential seller can exercise the option (default) at the end of each month (i.e., when the next payment is due); - There are no costs associated with mortgage loan default; 22 - The risk-free interest rate is 4%; - There are no transaction costs associated with the sale of the property. Throughout our analysis we derive the market mortgage interest rate from the risk free rate generated by equation (21). The key to computing the equilibrium fixed or adjustable-rate mortgage rate (the spreads over the risk free rate) is the assumption that at origination the value of the mortgage equals the outstanding loan balance. In other words, the mortgage interest rate, either variable or fixed, exactly compensates the lender for the put option imbedded in the loan and for the interest rate risk associated with a FRM. If the expected cost to the creditor of providing the non-recourse feature equals the expected benefits to the borrower, then, in a competitive lending industry, our estimates would be the equilibrium mortgage rate. Table 4 summarizes our estimates of mortgage rates and spreads when the maximum LTV is 80 percent, refinancing to obtain a lower interest rate is not possible, and there are no liquidity costs. Estimates are provided for both variable and fixed interest rate mortgage loans. We start with four risk-free rates. Then we use the LSMC approach (described in Appendix B) to find the mortgage rate that equates the mortgage value with the outstanding balance at origination. 22 Given the ownership entities used for commercial real estate default for a commercial mortgage is much less costly than it is for a residential loan. 22

23 Table 4: Equilibrium Interest Rates Equilibrium Interest Rates (Spread in parentheses) Risk-free rate 2% 3% 4% 5% Adjustable rate 10-year mortgage 4% (2%) 4.7% (1.7%) 5.5% (1.5%) 6.3% (1.3%) Fixed rate 10- year mortgage 5.7% (3.7%) 5.8% (2.8%) 6% (2%) 6.3% (1.3%) The assumption that all apartment purchases are financed with 80 percent LTV loans is a simplification from the rich mosaic of financing used in practice. Because buyers typically try to maximize leverage, relaxing this assumption would not qualitatively change our conclusions. A. Base Case The base case assumes that the owner incurs no liquidity costs if the property is not sold. Figure 1 depicts the relationship between the owner s equity, as represented by the LTV, and the effect of the non-recourse feature on a seller s reservation price. Our estimates are the difference, in terms of percent of the investment value, between the value of the portfolio with and without the non-recourse feature. In this analysis the investment value of the property, V 0, can be thought of as given. Variations in LTV are equivalent to variations in the exercise price of the put (i.e., loan balance) which, in turn, are associated with variations in the acquisition date of the property. 23 The volatility of property values is by far the most important determinant of the effect of the non-recourse feature on a seller s reservation price. Figure 1 depicts the effect of the non-recourse feature under two assumptions regarding this volatility. The 23 Implicitly we are assuming that all mortgage loans are made at a common initial LTV (e.g., 80%). 23

24 top line depicts the effect under monthly volatility of 2.6%, which is our best estimate, for Los Angeles County apartments, as reported in Table 3. As a form of sensitivity analysis we also report the estimated effect under assumption of volatility of ½ of our best estimate, i.e., 1.25%. Under our best estimate of volatility (2.6%), Figure 1 shows that if a person has zero equity (100% LTV), the effect of the non-recourse feature is the greatest and exceeds 7 percent of the properties investment value. For example, if the investment value of a complex was $50,000 per unit, and the owner loan balance was also $50,000 per unit, the seller s reservation price would be in excess of $53,500. The effect of the non-recourse on the reservation price falls until (by construction), at a LTV of 80 percent its value is zero. Percent Investment Value of Property Figure 1 Effect of Non-Recourse Feature on Seller's Reservation Price (assuming no liquidity costs) Volatility = 1.25% Volatility = 2.6% LTV Returning to Figure 1, we see the value of the option to put the property back to the creditor is substantial when the LTV exceeds 100 %. For example, with negative equity of 5 percent (a LTV of 115%), the seller s reservation price is approximately 4 percent greater than the properties investment value. This helps us understand why it 24

25 may be optimal to make loan payments on a property with negative equity. During the mid 1990s many Southern California properties were in this position. Even under the extremely conservative assumption of volatility being half of our best estimate, Figure 1 suggests that the effect exceeds 5% of property value at 100% LTV. Even if the Los Angeles County apartment market is much more volatile than typical real estate markets, the estimates reported in Figure 1 strongly suggest that our findings are applicable to other real estate markets even if they face a substantially lower volatility. 24 B. Liquidity Cost and the Reservation Price In the base case, the seller incurred no costs if they choose not to transact during the first period. Liquidity costs, motivation to transact, can be thought of as a per-period cost of maintaining the option to default. 25 Consequently, this cost would be expected to reduce the net value of the option, thereby reducing the impact of the non-recourse feature on the seller s reservation price. Figure 2 extends the analysis presented in Figure 1 to include liquidity cost. The monthly costs (in terms of percent of market price) that motivate the transaction are along one of the axes, the LTV ratio of the existing owner is along another axis, and the effect of the non-recourse provision on the reservation price of seller is along the vertical axis. Again, variations in LTV are equivalent to variations in the exercise price of the put option (loan balance) given the property s investment value V 0. This figure indicates that the value of the non-recourse 24 Clearly other parameters of the model have an effect on the estimate and it is conceivable that they may reduce the magnitude of the reported impact. However, given the robustness and economic significance of our findings, we find it unlikely that our results depend on the particular parameters. 25

26 feature decreases as the seller s LTV (F S /V 0 ) diverges from 100% and as the liquidity costs increase in absolute value. The range of liquidity costs where the non-recourse feature has an economically important effect on the seller s reservation price is quite large. Zero liquidity costs indicates that the owner is not motivated to sell and can wait indefinitely. Liquidity costs of ½ % of value per month are very high and represent an owner who is highly motivated to sell. Even this owner will reject an offer of V if their equity position is between approximately 4 and 4 percent. In these cases, the value of waiting exceeds the liquidity costs. The implication of demand shocks for reservation prices can be seen by considering a party who bought a property with 20 percent equity. At a LTV of 80 percent, the effect of the non-recourse feature on the seller s reservation price is, by construction, zero. If a positive demand shock occurs after the property is bought, thereby decreasing the LTV, the effect of the non-recourse feature will be still be zero. 26 Whereas, a negative demand shock will increase the LTV, which in turn will increase the value of the non-recourse feature of the loan and increase the difference between the seller s reservation price and the fair market value. 25 It should be remembered that liquidity costs are distinct from debt service. Within the simulation, the liquidity cost represents a percent of investment value V as an expense to each future node and affects the entire continuation value. 26 Owners of commercial real estate would be expect to borrow out so that the actual LTV would be close to the maximum LTV. 26

27 Figure 2: Effect of the Non-recourse feature on the Seller's Reservation Price Percent of value Low Liquidity Cost High Liquidity Cost LTV Ratio V. Liquidity Costs and a Mutually Agreeable Transaction We now return to our analysis of the relationship between non-recourse feature and a real estate market s response to demand shocks. In equation (14), we concluded that a mutually agreeable transaction will occur if, and only if, the sum of the liquidity costs (motivation) is greater than or equal to the difference between the principal (face value) and market value of the seller s mortgage, i.e., c + c ( F M ). In the S B S S remainder of this section, we use the Los Angeles County apartment data to examine the determinants of this decision for both fixed rate and variable rate mortgages. Figure 3 represents the result of an examination of the liquidity costs (for the buyer and/or the seller) that will induce a transaction when the seller has a 6 percent fixed interest rate mortgage (e.g., the loan was originated when the risk free rate was 4 percent). The figure depicts the sum of the liquidity costs, for the buyer and the seller, 27

28 necessary to induce a transaction as a function of the seller s LTV ratio and the current risk-free rate. 27 In this analysis, as was previously the case, the investment value of the property, V, is fixed, variations in LTV are the result of differences in the loan balance, F S, which induce variations in M s. Notice that the sum of the liquidity costs, not their distribution between the buyer and the seller, determines whether a mutually agreeable transaction is possible. Of course, the distribution between the buyer and the seller will have an impact on the transaction price. Furthermore, we take into account not just the current but expected future liquidity costs to both parties under the optimal exercise policy. Figure 3 shows that reductions in the market value of the mortgage, M, relative to the outstanding balance would require higher liquidity costs for the buyer and/or the seller to induce a transaction. In our model, there are two forces that reduce the market value of the mortgage: - Decreases in the investment value of property (pictured as increases in LTV) so that the owner has little or even negative equity, and - high current risk-free rate relative to the time of loan origination. 27 For simplicity of exposition, LTVs greater than 100 percent were not considered in this figure. Similar relationships would hold for initial mortgage loan rates greater or less than 6 percent. 28

29 Figure 3: Liquidity Costs Necessary to Induce a Transaction for a FRM Sum of the buyer s and the seller s liquidity costs as a percent of value per month Current risk-free rate LTV ratio Note: This figure takes into account not only the current period liquidity costs, but all expected future liquidity costs for both the buyer and the seller under the optimal exercise policy. Consistent with our expectation, as the LTV ratio approaches 100%, the probability of default (i.e., the value of the put) increases which in turn reduces the value (burden) of the mortgage for the seller. Consequently, combined costs of approximately 1% of value per month are needed to induce a transaction in this situation. High current interest rates have a similar, although much smaller, impact. 28 If the current owner has a FRM with a low interest rate relative to the current rates, then the market value of the mortgage is lower than the principal amount and substantial liquidity costs are necessary to induce a transaction (i.e., there is a mortgage loan lock- in). Notice, however, that for 80% LTV ratio, the combined liquidity costs necessary to induce a transaction at 6% 28 The effect of high current interest rates is partially mitigated because our estimates of the joint stochastic process (20) produced an increasing relationship between the level of r and dv/v. 29

30 risk-free rate are only.05% per month. In other words, we can expect to see only marginal declines in liquidity following an increase in interest rates. Our analysis of the fixed interest rate non-recourse mortgage example strongly suggests that a negative demand shock that results in LTV greater than the maximum LTV for a significant Figure 4: Liquidity Costs Necessary to Induce a Transaction for an ARM Sum of the buyer s and the seller s liquidity costs as a percent of value per month Current risk-free rate Current LTV ratio Note: This figure takes into account not only the current period liquidity costs, but all expected future liquidity costs for both the buyer and the seller under the optimal exercise policy. portion of the property owners will preclude many otherwise desirable transactions. Analogously to Figure 3, Figure 4 depicts the sum of the buyer s and the seller s liquidity costs necessary to induce a transaction, if the seller holds an adjustable rate mortgage (ARM). The implication of ARM financing is that changes in interest rates alone do not alter the value of the mortgage. While this is true for a default-free bond, 30

31 the market value of the mortgage still depends on interest rates because they affect the value of the imbedded put option. In general, increase in the risk-free interest rate decreases the value of a put option for two reasons: 1) the expected growth rate of the asset price increases, and 2) the present value of future cash flow received by the holder decreases. While both of these effects hold in our application, interest rates have one additional impact in the case of ARM: 3) the monthly carrying costs increase. Except for very high LTV ratios, the probability of delaying the sale over extended periods of time is low and the first two effects dominate. Figure 4 suggests that for LTV ratios below 98% an increase in interest rates reduces the value of the put option, which, in turn, reduces the liquidity costs necessary to induce a transaction. For very high LTV ratios, the probability of delaying the sale over extended time periods is high, and the increase in expected carrying costs is substantial enough to overcome the first two effects. Figure 4 suggests that for LTV ratios above 98%, an increase in interest rates increases the value of the imbedded put option, which, in turn, further increases the liquidity costs necessary to induce a transaction. Regardless of the type of mortgage and the fluctuation of the interest rates, Figures 3 and 4 suggest a clear conclusion: even small increases of the LTV ratio above 80%, (e.g., from a negative demand shock) require positive and increasing liquidity costs (motivation) for the buyer and/or the seller to induce a transaction. That is, a negative demand shock can result in a situation where no mutually agreeable transaction will occur for a portion of the potential sellers at the property's investment value. This can be interpreted as a decrease in asset liquidity. For LTV ratios close to 100%, the required liquidity costs for a transaction are substantial and approach 1% of the asset price per month. In contrast, a positive demand shock that decreases the seller's LTV 31

32 will facilitate transactions by reducing the cost needed to motivate the transaction. While our model has been for a specific type of property and a specific real estate market, we contend that it has identified an important general aspect of real estate markets where properties are purchased with non-recourse loans. VII. Conclusion Markets for income producing real estate frequently respond asymmetrically to large positive and negative demand shocks. This paper provides an explanation for this phenomenon that is consistent with individual rationality. Our explanation is based upon the rational response of sellers and potential buyers to a widely used financing arrangement, the non-recourse mortgage loan. The model of a market for income producing properties we develop allows us to explore the effect of the non-recourse feature on a liquidity motivated seller s reservation price and the conditions under which liquidity motivated sellers and buyers will transact. Using the model, we are able to show that a negative demand shock, in conjunction with non-recourse loans and maximum LTV, can result in a period during which no mutually agreeable transaction is possible between liquidity motivated sellers and buyers, with identical expectations about the price formation process. In contrast, we show that a positive demand shock will never result in a decline in asset liquidity. We then use data for a specific real estate market, the Los Angeles County apartment building market, to estimate the empirical relevance out model. We find that the non-recourse feature can have a substantial effect on the seller s reservation price. For example, when the option is at-the-money (i.e., the owner has zero equity), the nonrecourse feature can result in the seller s reservation price exceeding the investment 32

33 value of the property by up to seven percent. We also explore the effect of the nonrecourse feature on the sum of the seller s and potential buyer s liquidity costs necessary to motivate a mutually agreeable transaction. Based upon the Los Angeles County data, we conclude that the non-recourse loan feature can result in extended periods during which no mutually agreeable transaction is possible. While the traditional explanations, be they institutional or behavioral, of how real estate markets respond to demand shocks are likely to be important in the short run, our results strongly suggest that the prevalence of non-recourse loans is an important determinate of the markets long run response. 33