# Using private information: a pricing strategy.

Using Private Information A Pricing Strategy

How do prepayments enter into mortgage lenders' pricing procedures? Typically, the mortgage banker arrives at a price by factoring in all the anticipated sources of income and all the associated costs and working toward a pre-specified return on equity or net present-value target. Prepayment enters the loan pricing analysis through two major sources of income: loan sales and the value of servicing rights. Because both loans and servicing rights are traded in active secondary markets, participants on either side of the transaction have every incentive to obtain precise estimates of their values.

At a time when Wall Street is devoting considerable resources to the development of increasingly sophisticated valuation models, mortgage lenders should be aware of any comparative informational advantage that their role as originator may give them. Although some caveates will be discussed in terms of the amount of information to which the lender has access and the role of interest rate fluctuations, this article argues that well thought-out loan pricing can provide such an advantage when it comes to estimating prepayment speeds.

Prepayment and private information

Predicting the expected life of a loan or pool of loans remains one of the greater challenges for mortgage bankers today. The analysis of mortgage-backed securities (MBS), as well as the decision to retain or release servicing rights, would be fairly straight-forward in the absence of prepayments. The cash flow generated by a pass-through security, for example, would simply be the aggregate cash flow from all of the underlying mortgages less the servicing and guarantee fees kept by the originator and/or the issuer. Even though there might still be some uncertainty about the composition of the pool, the mix of interest rates and maturities would usually be known accurately enough to forecast pass-through payments with a high degree of precision.

When prepayments come into play, a security's yield is calculated from the cash flow pattern generated by an assumed distribution of prepayments over the life of the underlying pool (referred to as "cash flow yield"). Constant Prepayment Rate (CPR) and the PSA Standard Prepayment Model have been the most commonly used prepayment estimation methods for computing cash flow yields. When a pool is said to have a 10 percent CPR, for example, the assumption is that 10 percent of the outstanding mortgage balance is prepaid every year. CPR yields are frequently based on the actual prepayment activity in the pool (e.g., the average CPR of the most recent 12 months). The PSA model is essentially a very specific series of CPRs over the life of a mortgage pool. When a mortgage security's underlying pool prepays according to the PSA benchmark pattern, it is said to prepay at 100 percent PSA.

More recently, econometrically fitted models, which forecast prepayments with higher accuracy than the PSA benchmark, have gained wide acceptance. While these models are a considerable improvement over earlier assumptions, such as prepaid life and FHA experience, they are still not predictive in the true sense of the word. A truly predictive model should be based on a theory that incorporates the variables underlying the decision to prepay.

The motivation to prepay

It is well-known that the prepayment decision is influenced by factors such as interest rate variability, economic activity, seasonality, age and coupon rate of the mortgages, demographic and geographic effects and specifics (such as due-on-sale clauses). Of all these factors, the incentive to refinance prompted by the relationship between the current market rate and the contractual rate on the mortgage is usually considered to have the greatest predictive power. Prepayments of mortgages having a coupon rate higher than the prevailing market rate by a margin large enough to cover refinancing transaction costs are often referred to as "economic" prepayments. In this dichotomy, "uneconomic" prepayments, which are not necessarily irrational, refer to the prepayment of mortgages for reasons other than interest rate variability (e.g., divorce, death and so forth).

Within this class of so-called "uneconomic" motivations to prepay, we would like to focus on one particular source of information that seems to have been neglected by mortgage bankers: the borrowers' private reasons for prepaying their mortgages. This information is clearly of potential value in estimating prepayment speeds. In fact, personal circumstances about which a borrower is better informed than a lender may have as great an impact on prepayment as interest rate fluctuations.

For example, a young couple purchasing a single-bedroom condominium will most likely have a short prepayment horizon if they plan to have children, which will necessitate purchasing a larger space in the near-term. Professionals might have a fairly good idea of how their short-term income is likely to evolve and are, therefore, in a better position to assess how long it will take before they can afford to "trade up" their condominium. In addition, these professionals might have superior information about company relocation prospects. Conversely, couples with grown children, or whose career paths and incomes have stabilized, are more likely to have longer prepayment horizons.

In any event, if borrowers' private information could be accessed by the lender, it could be of considerable value for estimating prepayment speeds. Other authors have recognized the potential value of this information. For example, in her April 1989 article in Mortgage Banking, "Building Servicing Value Through Secondary Market Decisions," author Mary Bruce Batte points out that in order to maximize servicing value, it is necessary to develop "an average life grading system in the origination process where some idea of the homebuyer's plans and previous financing patterns can be ascertained."

In this article, we argue that it might be possible for lenders to elicit mortgage borrowers' private prepayment information via a careful design of their pricing schedules. Furthermore, we point out certain profit opportunities in the secondary markets.

Private information and

product choice

Questions of this kind have been the object of a substantial body of research in the field of information economics (see in particular the pioneering work of Michael Rothschild and Joseph Stiglitz, The Quarterly Journal of Economics [1976]).

To illustrate the mechanics of these so-called situations of asymmetric information, consider the auto insurance industry. Typically, the insured is better informed about his or her driving style - and hence accident-proneness - than the insurer. When given a choice between a number of different deductible/premium combinations, a rational individual who knows himself to be highly accident-prone will opt for a low deductible. An individual with a safe driving style will not mind a higher deductible if it lowers the premium, as he or she does not expect to be involved in an accident very often anyway. The key element is that a rational insurer will anticipate this "self-selecting" behavior and structure the "menu" of deductible/premium combinations accordingly. In particular, the insurer will structure the menu so that it is optimal for a rational individual of a certain risk-type to select one specific "entree" (deductible/premium combination) in the menu. In choosing an entree, the insured effectively reveals his or her private information or risk type, allowing the insurer to adjust the combination so that it is, on average, profitable when chosen by that specific insurance customer.

A similar argument can be made with respect to the asymmetric information situation of the borrower and the lender. Mortgage lenders commonly use discount points in combination with the coupon rate in order to achieve a specific effective interest rate. As it turns out, the practice can be used to structure a menu of discount points/interest rate combinations through which the borrower's private information can be elicited. Specifically, as we illustrate below, such a menu will result in borrowers with short-time horizons choosing products involving low points, while those with long-time horizons will choose high-points products.

Although current pricing schemes for mortgage products do not, to the best of our knowledge, incorporate private prepayment information, the importance of this information to the borrower's decision process seems to be widely recognized.

In a recent article in Money magazine ("When to Refinance Your Home" by John Sims, December 1991) mortgage holders were given advice on refinancing. The borrower's expected prepayment horizon was explicitly mentioned as an essential element in the calculation: "[F]or each loan you are considering, figure out how long you would have to stay in your house before the total of your monthly savings would offset the closing costs... If you don't think you'll be in your house long enough to reach the break-even point, forget the whole deal.... But if you plan to be in the house for, say, three to five years past break-even, choose the loan with the lowest monthly payment - even if you have to pay a few extra points or higher closing costs to get it." The fact that borrowers are advised to base their refinancing decision on an assessment of their expected prepayment horizon provides anecdotal evidence to the potential importance of this source of information for estimating prepayment speeds.

At this point, the reader might argue that the question as to how prepayments affect pricing is not really an issue. After all, it is well recognized that the market incorporates its estimate of prepayments, based on the coupon rate (specifically, the pool's weighted average coupon [WAC] and the coupon rate spread), into the prices of MBS and, therefore, into the prices of mortgage pools.

We stress, however, that the two factors - prepayment due to interest rate movements (about which the borrower is not likely to have superior information) and prepayment due to personal reasons (about which the borrower has private information) - are fundamentally distinct. (The question of how these two factors interact is one of the subjects of a current research project, extending the scope of this article, with Darrell Duffie, associate professor of finance, Stanford University). To simplify our analysis as well as to highlight the significance of the private information aspect, we focus on a scenario in which players expect interest rates to go up. This extreme assumption makes prepayment due to private considerations the dominant concern.

An illustration

To illustrate these ideas, we consider a highly simplified setting in which a mortgage banker originates 30-year fixed-rate mortgages (FRMs), immediately sells the loans in the secondary market (for instance, Fannie Mae's cash window) and retains the servicing rights. Our example is constructed in a way to effectively preclude prepayment due to interest rate fluctuations by assuming that all parties expect interest rates to move up in the foreseeable future. We assume that the market requires a yield of 8.5 percent on such loans. Following industry practice, we further assume that the lender requires a target net present value of 50 basis points on each loan. (The appropriateness of such a criterion is an interesting question in its own right, but beyond the scope of this paper.)

The pool of loan applicants is assumed to consist of four equally weighted classes, each applicant in a certain class having a specific prepayment horizon for personal reasons, unknown to the lender (5, 10, 20 and 30 years). This defines an empirical distribution of prepayments in the spirit of the FHA experience schedule or the PSA benchmark, except that here prepayments are not caused by interest rate movements. This distribution is assumed to be common knowledge to the lender and the market. In order to avoid the issue of choosing among alternative mortgage instruments, we focus on a set of borrowers who have already chosen 30-year FRMs over other mortgage products (e.g., ARMs, GPMs). Table 1 provides a summary of the assumptions. While the situation can be made as complex as necessary to reflect the full reality of the pricing process, such additional complexity would obscure the main point of this article. The simple setting considered here still reflects the fundamental mechanics of mortgage loan pricing.

Table : Table 1: Assumptions of the Illustration

Initially, the only information used by the lender is the empirical distribution of prepayment horizons. Based on this distribution, all five of the points/rate combinations shown in Table 2, yield, on average, 50 basis points in present value. Note that the numbers are somewhat unrealistic; in practice, a 1/8th change in coupon rate does not trigger such a large change in discount points. Recall, however, that we assumed away refinancing due to interest rate fluctuations. Had this factor been taken into account, the points increments would have been more realistic.

Table : Table 2: Borrowers' Choices and APRs under the Original Menu

(*) The highlighted APRs indicate self-selection.

When we calculate for each type of borrower the annual percentage rates (APRs) corresponding to these combinations, the self-selection phenomenon becomes apparent: both the 5-year and the 10-year borrower have the lowest annual percentage cost under the first alternative, which features the combination of the highest coupon rate and the lowest discount points. Whereas the 20-year and the 30-year borrower find cost to be lowest under the fifth alternative, which has the lowest coupon rate and the highest discount points.

Intuitively, shorter-horizon borrowers (the 5- or 10-year borrower) benefit from low points and a higher rate, while the converse is true for longer-horizon borrowers. For the parameters of our simple setting, the three middle combinations are not chosen by any of the borrowers. This will not always be the case: for a large number of borrower types (in terms of prepayment horizon) and for carefully chosen points/rate combinations, the separation of types can be cut much finer.

The key point is that a lender who knows the range of possible prepayment horizons, without necessarily knowing the actual horizon for each borrower, can replicate the calculation of the cost-minimizing borrower, thereby determining which types have chosen which combinations. To be specific, in our case, the lender should infer that rational 5-year and 10-year borrowers will choose the first alternative, while rational 20-year and 30-year borrowers will choose the last. Realizing this, the lender could restructure the menu to take advantage of the fact that, through their choices, two borrower subgroups can be identified from the initial group. Whereas the initial group had an average prepayment horizon of 16.25 years and large variance around that average, the subgroups have averages of 7.5 and 25 years respectively, and smaller variances around those averages.

There are two key considerations in restructuring the menu of points/rate combinations. First, the combination that will be chosen by a specific subgroup of borrowers must be calculated in anticipation of the servicing value of a loan made to that subgroup (because we assume that the secondary mortgage market still uses the original prepayment assumption, only the expected servicing value is affected). For example, a combination designed to be chosen by the subgroup of 20-year and 30-year borrowers must reflect the anticipated 25-year average servicing life of loans made to this group. Such a combination will have a lower rate and/or points than the corresponding combination in the original menu. The converse will be true for the short-horizon subgroup.

Second, and this is crucial, the self-selection pattern of behavior must not be destroyed by introducing these new combinations. In other words, it must remain optimal for the shorter-horizon borrowers to choose the (new) low points/high rate combination, and not the (new) high points/low rate combination designed for the longer-horizon borrowers.

Table 3 shows the new points/rate combinations offered by the lender, and the corresponding APRs for the different types of borrowers. Clearly, self-selection would be preserved by the new menu. The five points in the second combination may seem unrealistically high. Again, this is due to the simplifying assumptions we adopted in order to demonstrate the basic point more clearly. In Table 4 we compare the present value to the lender for each class of borrowers and for both menus of loan pricing. Note how the present values are more closely centered around 50 basis points in the second menu. This occurs because self-selection enables the lender to separately target two subgroups that have a lower prepayment horizon variance than the larger, less homogenous group. Also note that although the lender receives less from the 20- and 30-year borrowers under the new menu, the break that these borrowers get on the APR will undoubtedly boost sales volume. At the same time, previously unprofitable loans will be lost to competitors who still apply the "average pricing" of the old menu. This, in turn, will free up the necessary funds to make the more-profitable (long-term) loans.

Table : Table 3: Borrowers' Choices and APRs under the New Menu

Table : Table 4: Net Present Value to the Lender under Both Menus

(basis points)

The next step would be to refine the menu in order to separate the 5-year from the 10-year borrowers and the 20-year from the 30-year borrowers. Again, the points/rate combinations must be designed so that the lender earns 50 basis points on each subclass and it is optimal for borrowers to choose exactly the combination targeted at their own private prepayment horizon. As presented in this example, the process is a sequence of moves in which the lender designs the initial menu, observes the reactions (choices) of the borrowers, then redesigns the menu, again observes the borrowers' reactions, and so on, until the sequence converges to perfect separation.

Caveats

At this point we should discuss caveats to this situation, as they are obviously tied to implementation problems. One caveat lies in the assumption that the lender has full knowledge of the distribution of private prepayment horizons (this means both the range of horizons and the proportional representation of the different borrower types in the population). This distribution could be estimated empirically from lenders' historical data. The key complication lies in disentangling prepayments due to private personal reasons from those due to interest rate fluctuations. For example, when a mortgage is prepaid while the market rate is above the coupon rate (adjusting for transaction costs), the period from origination to prepayment is a reasonable proxy for the private prepayment horizon of the borrower in question. On the other hand, if the prepayment is a refinancing, we lose that proxy (e.g., the borrower was planning to relocate or trade up after about 10 years, but interest rates dropped below his refinancing threshold after, say, 6 years). However, because of the random nature of interest rates, these refinancings should average out in large samples (under certain technical conditions), leaving us with a reasonable empirical distribution of private prepayment horizons. Apart from these considerations, further research should determine to what extent the separation of borrower types will stand to uncertainty about the distribution of private prepayment horizons on the part of the lender.

A second caveat is in order concerning our assumption that the borrower would have perfect knowledge of his or her own prepayment horizon. In reality, borrowers are obviously uncertain about their horizons. However, as long as their private information is sufficiently more precise than that of the lender, then that information would be helpful in trying to construct a better loan pricing menu. In designing the menu, the lender now must take into account the fact that borrowers no longer evaluate points/rate combinations with a single-point estimate of their prepayment horizon, but rather with a probability distribution. Borrowers make their choices taking into account a number of alternative scenarios, and thus have a range of prepayment horizons.

The third caveat arises from the fact that, in order to focus on prepayment due to private reasons, we have built a hypothetical example that attempts to render moot the influence of interest rate fluctuations. The interaction between the personal factor and the interest rate factor is a critical ingredient of a realistic model. As was mentioned, this question is the object of ongoing research. We will only point out the main, additional complication that the borrower's private information affects his decision whether to refinance when market rates drop, given that transaction costs are non-negligible. For example, when rates drop, transaction costs (fees and points) may be such that a borrower who is planning to prepay in 5 years would be better off holding on to the old mortgage, while a borrower with a horizon of 10 years would refinance.

As a last caveat, it might be argued that borrowers are often in no position to calmly and rationally choose from among a menu of points/rate combinations. Cash-pressed purchasers (first-time borrowers) might forego an otherwise optimal combination because the points are too high relative to their liquidity position. Two remarks are in order here. First, borrowers with liquidity problems are often given the option to borrow the points necessary to obtain the lower rate (this is effectively increasing the loan amount and is, of course, subject to qualification requirements). Second, even if the ability or disposition of purchasers to optimize their product choice seems tenuous, the private information argument still holds true for those who refinance, who are typically in a much better position to make a careful choice of a points/rate combination.

Extending our simple model to take into account these complications and other institutional features of the pricing procedure is a challenging task. Notwithstanding the complexity, however, the main point is clear: the industry practice of using discount points in conjunction with coupon rates can be instrumental in eliciting borrowers' private information about their expected prepayment horizons.

Advantages

The potential value of a pricing schedule that effectively elicits borrowers' expected prepayment horizons seems clear. This information might enable us to obtain a significant refinement of prepayment speed estimates. We note that this refinement is different from conventional refinements in that the informational advantage lies entirely with the lender/originator, who can observe and record the points/rate combinations chosen by particular borrowers.

The advantage of this refinement is twofold. First, recognizing that borrowers self-select into points/rate combinations puts the mortgage banker in a better position to decide which servicing rights to sell and which ones to retain. Also, if this new prepayment information can be credibly conveyed to investors, loan sales in the secondary market could command a premium for the reduced variance in expected prepayment horizons.

Another important advantage mentioned in this example, is that the new (repriced) menu could conceivably increase production of the profitable, longer-term loans and decrease production of the less profitable, shorter-term loans. Furthermore, the loans attracted by the new menu should command a premium from investors because they have a longer average life on top of the reduced variance.

Nahum D. Melumad is an associate professor of accounting and Guy Weyns is a doctoral candidate in accounting at Stanford University's Graduate School of Business in Stanford, California. This article is based on a speech delivered to the Presidents Conference of the Mortgage Bankers Association of America, June 1991.

How do prepayments enter into mortgage lenders' pricing procedures? Typically, the mortgage banker arrives at a price by factoring in all the anticipated sources of income and all the associated costs and working toward a pre-specified return on equity or net present-value target. Prepayment enters the loan pricing analysis through two major sources of income: loan sales and the value of servicing rights. Because both loans and servicing rights are traded in active secondary markets, participants on either side of the transaction have every incentive to obtain precise estimates of their values.

At a time when Wall Street is devoting considerable resources to the development of increasingly sophisticated valuation models, mortgage lenders should be aware of any comparative informational advantage that their role as originator may give them. Although some caveates will be discussed in terms of the amount of information to which the lender has access and the role of interest rate fluctuations, this article argues that well thought-out loan pricing can provide such an advantage when it comes to estimating prepayment speeds.

Prepayment and private information

Predicting the expected life of a loan or pool of loans remains one of the greater challenges for mortgage bankers today. The analysis of mortgage-backed securities (MBS), as well as the decision to retain or release servicing rights, would be fairly straight-forward in the absence of prepayments. The cash flow generated by a pass-through security, for example, would simply be the aggregate cash flow from all of the underlying mortgages less the servicing and guarantee fees kept by the originator and/or the issuer. Even though there might still be some uncertainty about the composition of the pool, the mix of interest rates and maturities would usually be known accurately enough to forecast pass-through payments with a high degree of precision.

When prepayments come into play, a security's yield is calculated from the cash flow pattern generated by an assumed distribution of prepayments over the life of the underlying pool (referred to as "cash flow yield"). Constant Prepayment Rate (CPR) and the PSA Standard Prepayment Model have been the most commonly used prepayment estimation methods for computing cash flow yields. When a pool is said to have a 10 percent CPR, for example, the assumption is that 10 percent of the outstanding mortgage balance is prepaid every year. CPR yields are frequently based on the actual prepayment activity in the pool (e.g., the average CPR of the most recent 12 months). The PSA model is essentially a very specific series of CPRs over the life of a mortgage pool. When a mortgage security's underlying pool prepays according to the PSA benchmark pattern, it is said to prepay at 100 percent PSA.

More recently, econometrically fitted models, which forecast prepayments with higher accuracy than the PSA benchmark, have gained wide acceptance. While these models are a considerable improvement over earlier assumptions, such as prepaid life and FHA experience, they are still not predictive in the true sense of the word. A truly predictive model should be based on a theory that incorporates the variables underlying the decision to prepay.

The motivation to prepay

It is well-known that the prepayment decision is influenced by factors such as interest rate variability, economic activity, seasonality, age and coupon rate of the mortgages, demographic and geographic effects and specifics (such as due-on-sale clauses). Of all these factors, the incentive to refinance prompted by the relationship between the current market rate and the contractual rate on the mortgage is usually considered to have the greatest predictive power. Prepayments of mortgages having a coupon rate higher than the prevailing market rate by a margin large enough to cover refinancing transaction costs are often referred to as "economic" prepayments. In this dichotomy, "uneconomic" prepayments, which are not necessarily irrational, refer to the prepayment of mortgages for reasons other than interest rate variability (e.g., divorce, death and so forth).

Within this class of so-called "uneconomic" motivations to prepay, we would like to focus on one particular source of information that seems to have been neglected by mortgage bankers: the borrowers' private reasons for prepaying their mortgages. This information is clearly of potential value in estimating prepayment speeds. In fact, personal circumstances about which a borrower is better informed than a lender may have as great an impact on prepayment as interest rate fluctuations.

For example, a young couple purchasing a single-bedroom condominium will most likely have a short prepayment horizon if they plan to have children, which will necessitate purchasing a larger space in the near-term. Professionals might have a fairly good idea of how their short-term income is likely to evolve and are, therefore, in a better position to assess how long it will take before they can afford to "trade up" their condominium. In addition, these professionals might have superior information about company relocation prospects. Conversely, couples with grown children, or whose career paths and incomes have stabilized, are more likely to have longer prepayment horizons.

In any event, if borrowers' private information could be accessed by the lender, it could be of considerable value for estimating prepayment speeds. Other authors have recognized the potential value of this information. For example, in her April 1989 article in Mortgage Banking, "Building Servicing Value Through Secondary Market Decisions," author Mary Bruce Batte points out that in order to maximize servicing value, it is necessary to develop "an average life grading system in the origination process where some idea of the homebuyer's plans and previous financing patterns can be ascertained."

In this article, we argue that it might be possible for lenders to elicit mortgage borrowers' private prepayment information via a careful design of their pricing schedules. Furthermore, we point out certain profit opportunities in the secondary markets.

Private information and

product choice

Questions of this kind have been the object of a substantial body of research in the field of information economics (see in particular the pioneering work of Michael Rothschild and Joseph Stiglitz, The Quarterly Journal of Economics [1976]).

To illustrate the mechanics of these so-called situations of asymmetric information, consider the auto insurance industry. Typically, the insured is better informed about his or her driving style - and hence accident-proneness - than the insurer. When given a choice between a number of different deductible/premium combinations, a rational individual who knows himself to be highly accident-prone will opt for a low deductible. An individual with a safe driving style will not mind a higher deductible if it lowers the premium, as he or she does not expect to be involved in an accident very often anyway. The key element is that a rational insurer will anticipate this "self-selecting" behavior and structure the "menu" of deductible/premium combinations accordingly. In particular, the insurer will structure the menu so that it is optimal for a rational individual of a certain risk-type to select one specific "entree" (deductible/premium combination) in the menu. In choosing an entree, the insured effectively reveals his or her private information or risk type, allowing the insurer to adjust the combination so that it is, on average, profitable when chosen by that specific insurance customer.

A similar argument can be made with respect to the asymmetric information situation of the borrower and the lender. Mortgage lenders commonly use discount points in combination with the coupon rate in order to achieve a specific effective interest rate. As it turns out, the practice can be used to structure a menu of discount points/interest rate combinations through which the borrower's private information can be elicited. Specifically, as we illustrate below, such a menu will result in borrowers with short-time horizons choosing products involving low points, while those with long-time horizons will choose high-points products.

Although current pricing schemes for mortgage products do not, to the best of our knowledge, incorporate private prepayment information, the importance of this information to the borrower's decision process seems to be widely recognized.

In a recent article in Money magazine ("When to Refinance Your Home" by John Sims, December 1991) mortgage holders were given advice on refinancing. The borrower's expected prepayment horizon was explicitly mentioned as an essential element in the calculation: "[F]or each loan you are considering, figure out how long you would have to stay in your house before the total of your monthly savings would offset the closing costs... If you don't think you'll be in your house long enough to reach the break-even point, forget the whole deal.... But if you plan to be in the house for, say, three to five years past break-even, choose the loan with the lowest monthly payment - even if you have to pay a few extra points or higher closing costs to get it." The fact that borrowers are advised to base their refinancing decision on an assessment of their expected prepayment horizon provides anecdotal evidence to the potential importance of this source of information for estimating prepayment speeds.

At this point, the reader might argue that the question as to how prepayments affect pricing is not really an issue. After all, it is well recognized that the market incorporates its estimate of prepayments, based on the coupon rate (specifically, the pool's weighted average coupon [WAC] and the coupon rate spread), into the prices of MBS and, therefore, into the prices of mortgage pools.

We stress, however, that the two factors - prepayment due to interest rate movements (about which the borrower is not likely to have superior information) and prepayment due to personal reasons (about which the borrower has private information) - are fundamentally distinct. (The question of how these two factors interact is one of the subjects of a current research project, extending the scope of this article, with Darrell Duffie, associate professor of finance, Stanford University). To simplify our analysis as well as to highlight the significance of the private information aspect, we focus on a scenario in which players expect interest rates to go up. This extreme assumption makes prepayment due to private considerations the dominant concern.

An illustration

To illustrate these ideas, we consider a highly simplified setting in which a mortgage banker originates 30-year fixed-rate mortgages (FRMs), immediately sells the loans in the secondary market (for instance, Fannie Mae's cash window) and retains the servicing rights. Our example is constructed in a way to effectively preclude prepayment due to interest rate fluctuations by assuming that all parties expect interest rates to move up in the foreseeable future. We assume that the market requires a yield of 8.5 percent on such loans. Following industry practice, we further assume that the lender requires a target net present value of 50 basis points on each loan. (The appropriateness of such a criterion is an interesting question in its own right, but beyond the scope of this paper.)

The pool of loan applicants is assumed to consist of four equally weighted classes, each applicant in a certain class having a specific prepayment horizon for personal reasons, unknown to the lender (5, 10, 20 and 30 years). This defines an empirical distribution of prepayments in the spirit of the FHA experience schedule or the PSA benchmark, except that here prepayments are not caused by interest rate movements. This distribution is assumed to be common knowledge to the lender and the market. In order to avoid the issue of choosing among alternative mortgage instruments, we focus on a set of borrowers who have already chosen 30-year FRMs over other mortgage products (e.g., ARMs, GPMs). Table 1 provides a summary of the assumptions. While the situation can be made as complex as necessary to reflect the full reality of the pricing process, such additional complexity would obscure the main point of this article. The simple setting considered here still reflects the fundamental mechanics of mortgage loan pricing.

Table : Table 1: Assumptions of the Illustration

Mortgage instrument 30-year FRM Lender's net present value target 50 basis points Lender's discount rate (%) 10 Market rate (%) 8.5 Servicing fee, net of cost 10 basis points Prepayment distribution: Group 1 (25%): 5 years Group 2 (25%): 10 years Group 3 (25%): 20 years Group 4 (25%): 30 years

Initially, the only information used by the lender is the empirical distribution of prepayment horizons. Based on this distribution, all five of the points/rate combinations shown in Table 2, yield, on average, 50 basis points in present value. Note that the numbers are somewhat unrealistic; in practice, a 1/8th change in coupon rate does not trigger such a large change in discount points. Recall, however, that we assumed away refinancing due to interest rate fluctuations. Had this factor been taken into account, the points increments would have been more realistic.

Table : Table 2: Borrowers' Choices and APRs under the Original Menu

Combination 1 2 3 4 5 Coupon Rate (%) 8.375 8.25 8.125 8 7.875 Discount Points 0.7 1.6 2.4 3.3 4.2 APR (%): Group 1 8.89(*) 8.99 9.1 9.21 9.32 Group 2 8.82(*) 8.83 8.84 8.86 8.87 Group 3 8.79 8.76 8.74 8.71 8.68(*) Group 4 8.78 8.75 8.72 8.69 8.65(*)

(*) The highlighted APRs indicate self-selection.

When we calculate for each type of borrower the annual percentage rates (APRs) corresponding to these combinations, the self-selection phenomenon becomes apparent: both the 5-year and the 10-year borrower have the lowest annual percentage cost under the first alternative, which features the combination of the highest coupon rate and the lowest discount points. Whereas the 20-year and the 30-year borrower find cost to be lowest under the fifth alternative, which has the lowest coupon rate and the highest discount points.

Intuitively, shorter-horizon borrowers (the 5- or 10-year borrower) benefit from low points and a higher rate, while the converse is true for longer-horizon borrowers. For the parameters of our simple setting, the three middle combinations are not chosen by any of the borrowers. This will not always be the case: for a large number of borrower types (in terms of prepayment horizon) and for carefully chosen points/rate combinations, the separation of types can be cut much finer.

The key point is that a lender who knows the range of possible prepayment horizons, without necessarily knowing the actual horizon for each borrower, can replicate the calculation of the cost-minimizing borrower, thereby determining which types have chosen which combinations. To be specific, in our case, the lender should infer that rational 5-year and 10-year borrowers will choose the first alternative, while rational 20-year and 30-year borrowers will choose the last. Realizing this, the lender could restructure the menu to take advantage of the fact that, through their choices, two borrower subgroups can be identified from the initial group. Whereas the initial group had an average prepayment horizon of 16.25 years and large variance around that average, the subgroups have averages of 7.5 and 25 years respectively, and smaller variances around those averages.

There are two key considerations in restructuring the menu of points/rate combinations. First, the combination that will be chosen by a specific subgroup of borrowers must be calculated in anticipation of the servicing value of a loan made to that subgroup (because we assume that the secondary mortgage market still uses the original prepayment assumption, only the expected servicing value is affected). For example, a combination designed to be chosen by the subgroup of 20-year and 30-year borrowers must reflect the anticipated 25-year average servicing life of loans made to this group. Such a combination will have a lower rate and/or points than the corresponding combination in the original menu. The converse will be true for the short-horizon subgroup.

Second, and this is crucial, the self-selection pattern of behavior must not be destroyed by introducing these new combinations. In other words, it must remain optimal for the shorter-horizon borrowers to choose the (new) low points/high rate combination, and not the (new) high points/low rate combination designed for the longer-horizon borrowers.

Table 3 shows the new points/rate combinations offered by the lender, and the corresponding APRs for the different types of borrowers. Clearly, self-selection would be preserved by the new menu. The five points in the second combination may seem unrealistically high. Again, this is due to the simplifying assumptions we adopted in order to demonstrate the basic point more clearly. In Table 4 we compare the present value to the lender for each class of borrowers and for both menus of loan pricing. Note how the present values are more closely centered around 50 basis points in the second menu. This occurs because self-selection enables the lender to separately target two subgroups that have a lower prepayment horizon variance than the larger, less homogenous group. Also note that although the lender receives less from the 20- and 30-year borrowers under the new menu, the break that these borrowers get on the APR will undoubtedly boost sales volume. At the same time, previously unprofitable loans will be lost to competitors who still apply the "average pricing" of the old menu. This, in turn, will free up the necessary funds to make the more-profitable (long-term) loans.

Table : Table 3: Borrowers' Choices and APRs under the New Menu

Combination 1 2 Coupon Rate (%) 8.375 7.75 Discount Points 0.9 5 APR (%): Group 1 8.94 9.41 Group 2 8.85 8.87 Group 3 8.81 8.65 Group 4 8.81 8.61

Table : Table 4: Net Present Value to the Lender under Both Menus

Original Menu New Menu Present value to lender: Group 1 18 38

(basis points)

Group 2 42 62 Group 3 65 59 Group 4 74 68

The next step would be to refine the menu in order to separate the 5-year from the 10-year borrowers and the 20-year from the 30-year borrowers. Again, the points/rate combinations must be designed so that the lender earns 50 basis points on each subclass and it is optimal for borrowers to choose exactly the combination targeted at their own private prepayment horizon. As presented in this example, the process is a sequence of moves in which the lender designs the initial menu, observes the reactions (choices) of the borrowers, then redesigns the menu, again observes the borrowers' reactions, and so on, until the sequence converges to perfect separation.

Caveats

At this point we should discuss caveats to this situation, as they are obviously tied to implementation problems. One caveat lies in the assumption that the lender has full knowledge of the distribution of private prepayment horizons (this means both the range of horizons and the proportional representation of the different borrower types in the population). This distribution could be estimated empirically from lenders' historical data. The key complication lies in disentangling prepayments due to private personal reasons from those due to interest rate fluctuations. For example, when a mortgage is prepaid while the market rate is above the coupon rate (adjusting for transaction costs), the period from origination to prepayment is a reasonable proxy for the private prepayment horizon of the borrower in question. On the other hand, if the prepayment is a refinancing, we lose that proxy (e.g., the borrower was planning to relocate or trade up after about 10 years, but interest rates dropped below his refinancing threshold after, say, 6 years). However, because of the random nature of interest rates, these refinancings should average out in large samples (under certain technical conditions), leaving us with a reasonable empirical distribution of private prepayment horizons. Apart from these considerations, further research should determine to what extent the separation of borrower types will stand to uncertainty about the distribution of private prepayment horizons on the part of the lender.

A second caveat is in order concerning our assumption that the borrower would have perfect knowledge of his or her own prepayment horizon. In reality, borrowers are obviously uncertain about their horizons. However, as long as their private information is sufficiently more precise than that of the lender, then that information would be helpful in trying to construct a better loan pricing menu. In designing the menu, the lender now must take into account the fact that borrowers no longer evaluate points/rate combinations with a single-point estimate of their prepayment horizon, but rather with a probability distribution. Borrowers make their choices taking into account a number of alternative scenarios, and thus have a range of prepayment horizons.

The third caveat arises from the fact that, in order to focus on prepayment due to private reasons, we have built a hypothetical example that attempts to render moot the influence of interest rate fluctuations. The interaction between the personal factor and the interest rate factor is a critical ingredient of a realistic model. As was mentioned, this question is the object of ongoing research. We will only point out the main, additional complication that the borrower's private information affects his decision whether to refinance when market rates drop, given that transaction costs are non-negligible. For example, when rates drop, transaction costs (fees and points) may be such that a borrower who is planning to prepay in 5 years would be better off holding on to the old mortgage, while a borrower with a horizon of 10 years would refinance.

As a last caveat, it might be argued that borrowers are often in no position to calmly and rationally choose from among a menu of points/rate combinations. Cash-pressed purchasers (first-time borrowers) might forego an otherwise optimal combination because the points are too high relative to their liquidity position. Two remarks are in order here. First, borrowers with liquidity problems are often given the option to borrow the points necessary to obtain the lower rate (this is effectively increasing the loan amount and is, of course, subject to qualification requirements). Second, even if the ability or disposition of purchasers to optimize their product choice seems tenuous, the private information argument still holds true for those who refinance, who are typically in a much better position to make a careful choice of a points/rate combination.

Extending our simple model to take into account these complications and other institutional features of the pricing procedure is a challenging task. Notwithstanding the complexity, however, the main point is clear: the industry practice of using discount points in conjunction with coupon rates can be instrumental in eliciting borrowers' private information about their expected prepayment horizons.

Advantages

The potential value of a pricing schedule that effectively elicits borrowers' expected prepayment horizons seems clear. This information might enable us to obtain a significant refinement of prepayment speed estimates. We note that this refinement is different from conventional refinements in that the informational advantage lies entirely with the lender/originator, who can observe and record the points/rate combinations chosen by particular borrowers.

The advantage of this refinement is twofold. First, recognizing that borrowers self-select into points/rate combinations puts the mortgage banker in a better position to decide which servicing rights to sell and which ones to retain. Also, if this new prepayment information can be credibly conveyed to investors, loan sales in the secondary market could command a premium for the reduced variance in expected prepayment horizons.

Another important advantage mentioned in this example, is that the new (repriced) menu could conceivably increase production of the profitable, longer-term loans and decrease production of the less profitable, shorter-term loans. Furthermore, the loans attracted by the new menu should command a premium from investors because they have a longer average life on top of the reduced variance.

Nahum D. Melumad is an associate professor of accounting and Guy Weyns is a doctoral candidate in accounting at Stanford University's Graduate School of Business in Stanford, California. This article is based on a speech delivered to the Presidents Conference of the Mortgage Bankers Association of America, June 1991.

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Author: | Melumad, Nahum; Weyns, Guy |
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Publication: | Mortgage Banking |

Date: | Jan 1, 1992 |

Words: | 3990 |

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