# A new pipeline paradigm.

This quantitative pipeline management approach is less dependent on
predicting customer behavior and helps manage risk through volatile
environments.

The structural changes in our industry since 1985 have forced mortgage bankers to re-evaluate their approach to pipeline management. The increased use of limited- and alternative-documentation programs has effectively reduced customers' cost of switching from one lender to another during the loan application process. The little-noted regulation appended to the 1991 tax act requiring a lender to provide the appraisal to the customer upon written request further exacerbates this problem. In a sense, the documentation necessary for a real estate credit decision has become fungible among lenders.

These structural changes are not limited to loan documentation. The emergence of mortgage brokers as intermediaries between borrowers and lenders has made customers more efficient in their choice of loan products and lenders. The maturity of adjustable-rate mortgages as a viable product line, increased competition from portfolio lenders and the emergence of national lenders with highly automated sourcing techniques have heightened consumers' awareness of the lending process. As a result, predicting a consumer's behavior with respect to the probability of closing the mortgage loan has become exceedingly difficult. In this article, we hope to demonstrate an alternative method or paradigm that may be used to manage the interest rate risk inherent in the mortgage origination process. The paradigm we will set forth is less dependent on predicting customer behavior, and hence, we believe it is more effective in managing pipeline risk through volatile environments.

The old-fashioned funding matrix

In those days of yore when obtaining mortgage credit was a cumbersome somewhat fearsome activity, borrowers were loathe to deal with more than one lender. We, as lenders, could reasonably ascertain the pain threshold a borrower would withstand prior to beginning the process anew with another lender. By using our insight and management judgment, we estimated the probability that a borrower would close the loan based on whether the all-in yield was above or below current prevailing yields and how far into the application process the borrower was. The result of this exercise is what many pipeline managers called a "funding matrix."

A sample of this funding matrix can be seen in Figure 1 and Figure 2. Changes in yield levels are depicted across the top of the matrix. Positive numbers indicate an increase in yield levels and negative numbers indicate a decrease in yield levels. The processing stages are depicted along the vertical axis. In this example, the pipeline manager assumes a new application with no change in yield levels, because the date of application indicates a 50 percent probability of funding. Loans that have been submitted to underwriting and have been approved with no changes in the prevailing market conditions have a 75 percent probability of funding. However, if the general level of interest rates has increased 50 basis points above the rate committed to the borrower, approved loans have a 95 percent probability of funding. Conversely, if rates decline by 50 basis points, approved loans have only a 35 percent probability of funding.

By stratifying the pipeline over a series of processing steps and comparing the yields committed to the borrower to current market conditions, the pipeline manager is estimating the amount of inventory he or she will have available for sale. This estimation is the basis for the quantification of the firms' net interest rate exposure associated with the origination of mortgage loans held for sale.

There are several fundamental problems with this type of analysis. Typically, the lender does not know when customer actually "fell out." Those of you who have originated loans know the customer does not tell you when he or she has opted for another lender. This unfortunate discovery is usually made when the loan officer informs the customer that the rate commitment is close to expiration. The customer then nonchalantly responds that the loan has been funded elsewhere. The pipeline manager does not know whether the borrower opted for another lender early in the process when the probability of the borrower closing the loan was 50 percent or much later when the probability of closing the loan might have been 95 percent.

Another fundamental problem with the "funding matrix" approach is the path-dependent nature of the borrower's decision. What drives the borrower to close or not to close a loan is not necessarily the level of interest rates at commitment expiration. Rather, where rates have been during the commitment period may be the operative factor. For example, a borrower may request a loan commitment from a lender when rates are 9 percent. Should rates drop by 50 basis points during the commitment period, the borrower might solicit another loan commitment at 8.5 percent from a new lender. As rates head back towards 9 percent, the original lender perceives the probability of loan closing would be associated with the "0 change" interest rate column in the funding matrix.

In reality, the probability of loan closing may be better aligned with the lowest interest rate point during the commitment period. In our example, the original lender may estimate there is a 75 percent probability of loan closing subsequent to loan approval. However, because rates have dropped by 50 basis points, providing an opportunity for a re-application with another lender, the actual probability of loan closing may be closer to 35 percent. A 40 percent variance in estimated closing ratio is not to be taken lightly.

The two-dimensional approach of predicting customer behavior based on exogenous interest rate levels and stages in the application process fails to consider other significant factors. These would include the relative competitive profile of the originating lender, a quantification of the "switching opportunities" associated with the lower-documentation and alternate-documentation programs and how the lender's own pricing strategy might impact the customer's behavior. The impact of a competing lender practicing a cannibalistic pricing strategy (lending at rates less than secondary market yield requirements) demonstrates several of the shortcomings associated with the funding matrix approach to pipeline management.

The fundamental flaw with the funding matrix approach to pipeline management is the manager's reliance on his or her ability to predict the correlation between the customer's fallout behavior and exogenous interest rate movements. At the end of the day, this correlation does not lie at the heart of the question. What is at issue is not determining the probability of a loan closing; it is calculating the probability of a loan closing with a market value less than book value. It is not a question of volume, it is a question of value.

The new pipeline paradigm: option-based evaluation

As most pipeline managers know, the extension of a loan commitment to a customer is tantamount to selling the customer a put option for the mortgage at a given yield level. That is, the borrower has the right, but not the obligation, to "put" the mortgage to the lender at a specified yield level during a specified period of time. This option has a tangible value that can be calculated in the marketplace. To perform this calculation, we need only know several easily identified data points. These include the yield level on the loan commitment, time to expiration, and the risk-free interest rate. The only necessary data point that is difficult to ascertain (or is subject to judgment) is the variance of mortgage yield levels in the marketplace. This variance is often referred to as a security price's "volatility." While historical volatility can be observed, it is the future volatility that will determine the success or failure of the option's hedging program. We believe estimating future volatility is significantly less difficult than estimating the correlation between a customer's "fall out" behavior with exogenous interest rate levels and the current stage of the borrower's application. In this fashion, we replace a matrix of uncertainty with a single data point of uncertainty.

As we noted above, the put option written to the borrower has a tangible value. Its value can be expressed in the following calculation: [Mathematical Expression Omitted]

Because this commitment to the borrower has no cash flow, the formula can be reduced to the following: [Mathematical Expression Omitted]

[d.sub.1] = [Mathematical Expression Omitted] [d.sub.2] = [Mathematical Expression Omitted]

This fearsome tangle of Greek letters may be daunting at first, but it is merely a quantification of what most pipeline managers know: how much they should be paid for taking this option risk. At the risk of being redundant, let us restate the fundamental question: What is the risk of loans closing with a market value less than book value? In a sense, our pipeline management position becomes one of assuming offsetting financial positions to hedge a change in the value of the option granted to the borrower. The relationship between the value of the option and the value of the underlying security on which the option is written is known as delta. Delta is defined as: [Mathematical Expression Omitted]

which can be reduced to: [Delta] = N([d.sub.1]) - 1

Put another way, delta represents the change in value of the option relative to the change in value of the underlying security. For example, a one point change in the value of the underlying security might produce a one quarter point change in the value of the put option. The delta in this relationship is .0025/.01 = .25. A delta neutral strategy calls for taking a delta equivalent position in the underlying security. A delta equivalent position is equal to the delta times the principal balance of the put option. In this example, one would sell $250,000 of Fannie Mae 8 percent securities for every $1,000,000 of commitments extended to borrowers to originate conforming conventional, fixed-rate loans at 8.5 percent. (Fannie Mae security rate of 8 percent plus service fee of .25 percent plus the required guarantee fee.)

As we mentioned, two of the fundamental components of an option's value and, consequently, its delta, are time to option expiration and the volatility of secondary market yield requirements. All other things being equal, the shorter the time to commitment expiration, the less valuable the option. Let us repeat that. The shorter the time to commitment expiration, the less valuable the option. This is exactly the opposite value direction our pipeline manager using the funding matrix approach estimated. Recall that with no change in interest rate levels, the pipeline manager estimated a new application (45 days to expiration) would have a 50 percent probability of closing. A loan whose documents had been drawn (for instance, 10 days to expiration) would have a 90 percent probability of closing. Given no change in interest rate levels, the pipeline manager following the funding matrix approach would have hedged more and more of the pipeline as it approached commitment expiration. The delta neutral manager, on the other hand, would have hedged slightly less of his pipeline as it approached commitment expiration.

As we can see from the figures, the delta neutral pipeline manager hedges more of the pipeline only as interests rates increase. As rates increase, the probability of closing loans with a market value lower than book value also increases. That is, the probability of closing loans in a loss position increases.

Alas, a delta neutral approach to pipeline management is not intuitive for most practitioners. The delta neutral approach is not as simple as it would seem. While it is true that, in a zero rate change environment, deltas reduce as we trend toward commitment expiration (See figure 3) the sensitivity of delta increases dramatically as we approach commitment expiration. With the passage of time, it takes a smaller and smaller move in the value of the underlying security to create a larger and larger change in the value of delta. Effectively, delta becomes highly leveraged in a zero rate change environment. The sensitivity of delta to changes in the underlying security is known as gamma. Gamma is expressed in the following equation: [Mathematical Expression Omitted]

In mathematical terms, gamma is known as the second derivative of the option value function. Gamma measures how quickly delta changes with changes in the value of the underlying security. Gamma is to delta as acceleration is to speed. Gamma is measured in increments of delta per one point change in the underlying security. For example, if a short put-options position has a gamma of .05, for each point decrease in the price of the underlying security, the put option will gain .05 in delta. If the original delta was .34, the delta calculated after a one point change in the underlying security would be .39.

The lower limit of delta is zero and the upper limit of delta is 1.00. Delta approaches 1.00 as options go deeply in the money. That is, an 8 percent commitment to a borrower has a delta approaching 1.00 when the prevailing mortgage rates are 10 percent. Conversely, delta approaches zero as the option position goes deeply out of the money. Using our example of the 8 percent commitment to the borrower in a 10 percent rate environment, would we expect delta of such a position to change significantly if market rates decline from 10 percent to 9.75 percent? Probably not. If the commitment to the borrower was 10 percent and market yields were 8 percent, would we expect the delta to increase meaningfully if market rates rose to 8.25 percent? Again, the answer is probably not. We see deltas associated with out-of-money options or in-the money-options are not particularly sensitive to minor changes in the value of the underlying security.

Now let us study the sensitivity of delta to underlying security prices for at-the-money options. (An option is called "at the money" when the security's current market price is close to, or "at", the security strike period of the option.) Suppose we made commitment to a borrower to close a loan at 8 percent. As the commitment approaches expiration, current market yields are 8 percent. Let us further assume our observed delta is .56. As yields increase from 8 percent to 8.15 percent, do we expect significantly change in the value of delta? Put another way, has the probability of the 8 percent rate commitment funding with a market value less than 100 increased? Clearly, the answer is yes.

Figure 4 depicts how gamma behaves for in-the-money, at-the-money and out-of-the-money commitments. As you can see, gamma, which measures the sensitivity of delta, increases dramatically as commitments approach expiration only for those commitments that are at the money. In essence, at-the-money loan commitments near expiration are highly leveraged. It is these very commitments that are most difficult for the pipeline manager to hedge. As the deltas of these commitments trend slightly lower, they become more and more leveraged.

Why do we still lose money when we do everything right?

By now you know how to modify your risk management systems to calculate the option value and its associated delta and gamma coefficients of each and every loan commitment extended to a borrower. Of course, you will perfectly hedge those option values without ever exposing your firm to any significant delta or gamma risk. Congratulations--you have just locked in a hedging loss exactly equal to the option value calculated. The only problem with the option value approach to pipeline risk management is that, in most parts of the United States, borrowers do not pay you for the option.

While the option-based approach to pipeline management currently quantifies risk exposure in an efficient market, we know borrowers' behavior is not always efficient. This axiom lies at the heart of the funding matrix approach. Perhaps we can borrow from the funding matrix approach to fine-tune our option-based pipeline management system.

The funding matrix approach assumes two things: mortgage loan borrowers will not behave efficiently; and pipeline managers can predict borrowers' inefficient behavior.

Clever pipeline managers create distinct funding matrices for each distribution channel. This is based on the premise that the indigenous characteristics of each channel affect the borrower's ability to behave efficiently. Typically, sourcing techniques, rate-lock policies, pricing policies and the target market will have an impact on the relative efficiency of the distribution channel. Imagine how complex the task becomes to correctly estimate the relative efficiency of the borrower's behavior at each stage of the lending process for multiple distribution channels. The funding matrix approach effectively creates a continuum of expected efficiency behavior, given certain interest rate environments.

The matrix displayed in Figure 1 requires the pipeline manager to forecast borrower behavior in 25 separate scenarios--and this is just for one distribution channel. If business is sourced through five different channels, the pipeline manager would have to estimate the borrowers behavior 125 times. At least the manager's downside is limited--he or she can only make 125 mistakes.

Clearly the objective of pipeline management is to hedge the firm's interest rate risk at a lower cost than the calculated premiums that should have been collected on the options that the firm extends to its borrowers. On the other hand, the risk associated with attempting to estimate borrower behavior in 25 scenarios per distribution channel is rather daunting. We propose a solution. For each distribution channel, ask yourself the following questions: * What percentages of the loans will

never fund? * What percentages of the loans will

always fund?

By answering these questions, you have estimated what subset of your pipeline behaves efficiently. In essence, you have replaced 25 separate behavioral forecasts with just two questions. The answers to these two questions should be different for each distribution channel. For example, a commercial bank sourcing mortgages through its depository branches might find that 20 percent of the mortgages originated always fund. They may also find that 15 percent of the mortgage originated are either rejected by their underwriters or cancelled for other reasons. We can expect 65 percent of the pipeline to behave relatively efficiently (See Figure 5). In a wholesale distribution channel, where the customer is a professional mortgage broker rather than a borrower, we might expect far more efficiency. Perhaps as few as 5 percent of mortgages would always fund, and 10 percent of mortgages would never fund. This leaves an efficient set of 85 percent associated with the wholesale distribution channel.

What loans will be efficient and what loans will not? We do not know. If you assume efficient behavior will be normally distributed over a pipeline, then in the case of the commercial bank distribution channel, we can assume that 15 percent of each loan will never close, 65 percent of each loan will behave efficiently and 20 percent of each loan will always close. The hedge ratio for a $100,000 commitment with a delta of .35 in such a distribution channel would be calculated as follows: Hedge Ratio = .35 X 100,000 X[1-.2-.15] + 100,000 X .15 = .3775

or generically,

Hedge Ratio = Delta X (1 - % never fund - % always fund] + % always fund

= Delta X [efficient set] + % always fund

In order to reduce our cost of hedging, we have attempted to quantify, through two simple questions, the relative inefficiency of the mortgage loan pipeline. In answering these questions, we assume very little correlation between the consumer's behavior and exogenous events. Rather, we look only to the internal characteristics of our distribution channel. Hopefully, we have some control over these distribution channel characteristics that we exercise through the clear articulation of our lending practices and policies. This estimate of a pipeline's relative inefficiency is a risk to be sure, but it is a limited risk taken in a highly controlled environment.

A real life example

Security Pacific Bank calculates pipeline risk exposure using both the funding matrix approach and the option-based paradigm. Figure 6 shows excerpts from Security Pacific's March 19, 1992 daily position reports comparing position exposure using the two different approaches. In the interest of propriety, we have modified the numbers but have left the relative values intact.

In this example, the option-adjusted approach results in a "longer" position than the funding matrix approach. The major exchange is in the app/docs out category; the pipeline component nearest to commitment expiration. You may recall from Figure 4, that the deltas of at-the-money options are most sensitive to market movement. On this particular day, there was an approximate 8bps adverse move in the market, not enough to influence behavior, as predicted by the funding matrix approach, but large enough to significantly change the option value of the pipeline. Note the loan inventory average coupon, when weighted by delta, was 4.26 basis points lower than the average coupon weighted by the expected funding ratio. This reflects higher delta values associated with lower coupon or in-the-money commitments.

Putting the mathematics to work

We have presented a pipeline management paradigm based upon an option-based theory that we believe correctly identifies the boundaries of interest rate risk exposure. These boundaries are predicted on the efficient behavior of the borrower. The structural changes in the industry, combined with the increased sophistication of borrowers, has caused consumers' behavior to become more and more efficient. The funding matrix approach to pipeline management fails to quantify this trend towards efficiency. By comparing the results of our option-based paradigm to that of the funding matrix, we can quantify the difference between expected behavior and efficient behavior on the part of the customer. Simply knowing this information will enhance your pipeline management skills.

Rather than making multiple guesses about multiple scenarios, the pipeline manager has only to answer three questions:

1. What will mortgage-backed securities' volatility be?

2. What percentage of loans will always fund?

3. What percentage of loans will never fund?

Mathematics will do the rest. Limiting the number of judgment calls a pipeline manager must make produces a higher degree of discipline in risk-management activities. And discipline will make you a better pipeline manager. Luke S. Hayden is senior vice president of consumer asset management at Security Pacific National Bank in Cypress, California. Dean M. Di Bias is vice president for mortgage sales and hedging at Security Pacific National Bank.

The structural changes in our industry since 1985 have forced mortgage bankers to re-evaluate their approach to pipeline management. The increased use of limited- and alternative-documentation programs has effectively reduced customers' cost of switching from one lender to another during the loan application process. The little-noted regulation appended to the 1991 tax act requiring a lender to provide the appraisal to the customer upon written request further exacerbates this problem. In a sense, the documentation necessary for a real estate credit decision has become fungible among lenders.

These structural changes are not limited to loan documentation. The emergence of mortgage brokers as intermediaries between borrowers and lenders has made customers more efficient in their choice of loan products and lenders. The maturity of adjustable-rate mortgages as a viable product line, increased competition from portfolio lenders and the emergence of national lenders with highly automated sourcing techniques have heightened consumers' awareness of the lending process. As a result, predicting a consumer's behavior with respect to the probability of closing the mortgage loan has become exceedingly difficult. In this article, we hope to demonstrate an alternative method or paradigm that may be used to manage the interest rate risk inherent in the mortgage origination process. The paradigm we will set forth is less dependent on predicting customer behavior, and hence, we believe it is more effective in managing pipeline risk through volatile environments.

The old-fashioned funding matrix

In those days of yore when obtaining mortgage credit was a cumbersome somewhat fearsome activity, borrowers were loathe to deal with more than one lender. We, as lenders, could reasonably ascertain the pain threshold a borrower would withstand prior to beginning the process anew with another lender. By using our insight and management judgment, we estimated the probability that a borrower would close the loan based on whether the all-in yield was above or below current prevailing yields and how far into the application process the borrower was. The result of this exercise is what many pipeline managers called a "funding matrix."

A sample of this funding matrix can be seen in Figure 1 and Figure 2. Changes in yield levels are depicted across the top of the matrix. Positive numbers indicate an increase in yield levels and negative numbers indicate a decrease in yield levels. The processing stages are depicted along the vertical axis. In this example, the pipeline manager assumes a new application with no change in yield levels, because the date of application indicates a 50 percent probability of funding. Loans that have been submitted to underwriting and have been approved with no changes in the prevailing market conditions have a 75 percent probability of funding. However, if the general level of interest rates has increased 50 basis points above the rate committed to the borrower, approved loans have a 95 percent probability of funding. Conversely, if rates decline by 50 basis points, approved loans have only a 35 percent probability of funding.

By stratifying the pipeline over a series of processing steps and comparing the yields committed to the borrower to current market conditions, the pipeline manager is estimating the amount of inventory he or she will have available for sale. This estimation is the basis for the quantification of the firms' net interest rate exposure associated with the origination of mortgage loans held for sale.

There are several fundamental problems with this type of analysis. Typically, the lender does not know when customer actually "fell out." Those of you who have originated loans know the customer does not tell you when he or she has opted for another lender. This unfortunate discovery is usually made when the loan officer informs the customer that the rate commitment is close to expiration. The customer then nonchalantly responds that the loan has been funded elsewhere. The pipeline manager does not know whether the borrower opted for another lender early in the process when the probability of the borrower closing the loan was 50 percent or much later when the probability of closing the loan might have been 95 percent.

Another fundamental problem with the "funding matrix" approach is the path-dependent nature of the borrower's decision. What drives the borrower to close or not to close a loan is not necessarily the level of interest rates at commitment expiration. Rather, where rates have been during the commitment period may be the operative factor. For example, a borrower may request a loan commitment from a lender when rates are 9 percent. Should rates drop by 50 basis points during the commitment period, the borrower might solicit another loan commitment at 8.5 percent from a new lender. As rates head back towards 9 percent, the original lender perceives the probability of loan closing would be associated with the "0 change" interest rate column in the funding matrix.

In reality, the probability of loan closing may be better aligned with the lowest interest rate point during the commitment period. In our example, the original lender may estimate there is a 75 percent probability of loan closing subsequent to loan approval. However, because rates have dropped by 50 basis points, providing an opportunity for a re-application with another lender, the actual probability of loan closing may be closer to 35 percent. A 40 percent variance in estimated closing ratio is not to be taken lightly.

The two-dimensional approach of predicting customer behavior based on exogenous interest rate levels and stages in the application process fails to consider other significant factors. These would include the relative competitive profile of the originating lender, a quantification of the "switching opportunities" associated with the lower-documentation and alternate-documentation programs and how the lender's own pricing strategy might impact the customer's behavior. The impact of a competing lender practicing a cannibalistic pricing strategy (lending at rates less than secondary market yield requirements) demonstrates several of the shortcomings associated with the funding matrix approach to pipeline management.

The fundamental flaw with the funding matrix approach to pipeline management is the manager's reliance on his or her ability to predict the correlation between the customer's fallout behavior and exogenous interest rate movements. At the end of the day, this correlation does not lie at the heart of the question. What is at issue is not determining the probability of a loan closing; it is calculating the probability of a loan closing with a market value less than book value. It is not a question of volume, it is a question of value.

The new pipeline paradigm: option-based evaluation

As most pipeline managers know, the extension of a loan commitment to a customer is tantamount to selling the customer a put option for the mortgage at a given yield level. That is, the borrower has the right, but not the obligation, to "put" the mortgage to the lender at a specified yield level during a specified period of time. This option has a tangible value that can be calculated in the marketplace. To perform this calculation, we need only know several easily identified data points. These include the yield level on the loan commitment, time to expiration, and the risk-free interest rate. The only necessary data point that is difficult to ascertain (or is subject to judgment) is the variance of mortgage yield levels in the marketplace. This variance is often referred to as a security price's "volatility." While historical volatility can be observed, it is the future volatility that will determine the success or failure of the option's hedging program. We believe estimating future volatility is significantly less difficult than estimating the correlation between a customer's "fall out" behavior with exogenous interest rate levels and the current stage of the borrower's application. In this fashion, we replace a matrix of uncertainty with a single data point of uncertainty.

As we noted above, the put option written to the borrower has a tangible value. Its value can be expressed in the following calculation: [Mathematical Expression Omitted]

Because this commitment to the borrower has no cash flow, the formula can be reduced to the following: [Mathematical Expression Omitted]

S = Security Price E = Exercise Price T = Time to Expiration r = Risk-Free Interest Rate [Delta] = Cash Flow from Security [Sigma] = Volatility N(.) = Cumulative Normal Distribution N/(x) = Normal density function = [Mathematical Expression Omitted]

[d.sub.1] = [Mathematical Expression Omitted] [d.sub.2] = [Mathematical Expression Omitted]

This fearsome tangle of Greek letters may be daunting at first, but it is merely a quantification of what most pipeline managers know: how much they should be paid for taking this option risk. At the risk of being redundant, let us restate the fundamental question: What is the risk of loans closing with a market value less than book value? In a sense, our pipeline management position becomes one of assuming offsetting financial positions to hedge a change in the value of the option granted to the borrower. The relationship between the value of the option and the value of the underlying security on which the option is written is known as delta. Delta is defined as: [Mathematical Expression Omitted]

which can be reduced to: [Delta] = N([d.sub.1]) - 1

Put another way, delta represents the change in value of the option relative to the change in value of the underlying security. For example, a one point change in the value of the underlying security might produce a one quarter point change in the value of the put option. The delta in this relationship is .0025/.01 = .25. A delta neutral strategy calls for taking a delta equivalent position in the underlying security. A delta equivalent position is equal to the delta times the principal balance of the put option. In this example, one would sell $250,000 of Fannie Mae 8 percent securities for every $1,000,000 of commitments extended to borrowers to originate conforming conventional, fixed-rate loans at 8.5 percent. (Fannie Mae security rate of 8 percent plus service fee of .25 percent plus the required guarantee fee.)

As we mentioned, two of the fundamental components of an option's value and, consequently, its delta, are time to option expiration and the volatility of secondary market yield requirements. All other things being equal, the shorter the time to commitment expiration, the less valuable the option. Let us repeat that. The shorter the time to commitment expiration, the less valuable the option. This is exactly the opposite value direction our pipeline manager using the funding matrix approach estimated. Recall that with no change in interest rate levels, the pipeline manager estimated a new application (45 days to expiration) would have a 50 percent probability of closing. A loan whose documents had been drawn (for instance, 10 days to expiration) would have a 90 percent probability of closing. Given no change in interest rate levels, the pipeline manager following the funding matrix approach would have hedged more and more of the pipeline as it approached commitment expiration. The delta neutral manager, on the other hand, would have hedged slightly less of his pipeline as it approached commitment expiration.

As we can see from the figures, the delta neutral pipeline manager hedges more of the pipeline only as interests rates increase. As rates increase, the probability of closing loans with a market value lower than book value also increases. That is, the probability of closing loans in a loss position increases.

Alas, a delta neutral approach to pipeline management is not intuitive for most practitioners. The delta neutral approach is not as simple as it would seem. While it is true that, in a zero rate change environment, deltas reduce as we trend toward commitment expiration (See figure 3) the sensitivity of delta increases dramatically as we approach commitment expiration. With the passage of time, it takes a smaller and smaller move in the value of the underlying security to create a larger and larger change in the value of delta. Effectively, delta becomes highly leveraged in a zero rate change environment. The sensitivity of delta to changes in the underlying security is known as gamma. Gamma is expressed in the following equation: [Mathematical Expression Omitted]

In mathematical terms, gamma is known as the second derivative of the option value function. Gamma measures how quickly delta changes with changes in the value of the underlying security. Gamma is to delta as acceleration is to speed. Gamma is measured in increments of delta per one point change in the underlying security. For example, if a short put-options position has a gamma of .05, for each point decrease in the price of the underlying security, the put option will gain .05 in delta. If the original delta was .34, the delta calculated after a one point change in the underlying security would be .39.

The lower limit of delta is zero and the upper limit of delta is 1.00. Delta approaches 1.00 as options go deeply in the money. That is, an 8 percent commitment to a borrower has a delta approaching 1.00 when the prevailing mortgage rates are 10 percent. Conversely, delta approaches zero as the option position goes deeply out of the money. Using our example of the 8 percent commitment to the borrower in a 10 percent rate environment, would we expect delta of such a position to change significantly if market rates decline from 10 percent to 9.75 percent? Probably not. If the commitment to the borrower was 10 percent and market yields were 8 percent, would we expect the delta to increase meaningfully if market rates rose to 8.25 percent? Again, the answer is probably not. We see deltas associated with out-of-money options or in-the money-options are not particularly sensitive to minor changes in the value of the underlying security.

Now let us study the sensitivity of delta to underlying security prices for at-the-money options. (An option is called "at the money" when the security's current market price is close to, or "at", the security strike period of the option.) Suppose we made commitment to a borrower to close a loan at 8 percent. As the commitment approaches expiration, current market yields are 8 percent. Let us further assume our observed delta is .56. As yields increase from 8 percent to 8.15 percent, do we expect significantly change in the value of delta? Put another way, has the probability of the 8 percent rate commitment funding with a market value less than 100 increased? Clearly, the answer is yes.

Figure 4 depicts how gamma behaves for in-the-money, at-the-money and out-of-the-money commitments. As you can see, gamma, which measures the sensitivity of delta, increases dramatically as commitments approach expiration only for those commitments that are at the money. In essence, at-the-money loan commitments near expiration are highly leveraged. It is these very commitments that are most difficult for the pipeline manager to hedge. As the deltas of these commitments trend slightly lower, they become more and more leveraged.

Why do we still lose money when we do everything right?

By now you know how to modify your risk management systems to calculate the option value and its associated delta and gamma coefficients of each and every loan commitment extended to a borrower. Of course, you will perfectly hedge those option values without ever exposing your firm to any significant delta or gamma risk. Congratulations--you have just locked in a hedging loss exactly equal to the option value calculated. The only problem with the option value approach to pipeline risk management is that, in most parts of the United States, borrowers do not pay you for the option.

While the option-based approach to pipeline management currently quantifies risk exposure in an efficient market, we know borrowers' behavior is not always efficient. This axiom lies at the heart of the funding matrix approach. Perhaps we can borrow from the funding matrix approach to fine-tune our option-based pipeline management system.

The funding matrix approach assumes two things: mortgage loan borrowers will not behave efficiently; and pipeline managers can predict borrowers' inefficient behavior.

Clever pipeline managers create distinct funding matrices for each distribution channel. This is based on the premise that the indigenous characteristics of each channel affect the borrower's ability to behave efficiently. Typically, sourcing techniques, rate-lock policies, pricing policies and the target market will have an impact on the relative efficiency of the distribution channel. Imagine how complex the task becomes to correctly estimate the relative efficiency of the borrower's behavior at each stage of the lending process for multiple distribution channels. The funding matrix approach effectively creates a continuum of expected efficiency behavior, given certain interest rate environments.

The matrix displayed in Figure 1 requires the pipeline manager to forecast borrower behavior in 25 separate scenarios--and this is just for one distribution channel. If business is sourced through five different channels, the pipeline manager would have to estimate the borrowers behavior 125 times. At least the manager's downside is limited--he or she can only make 125 mistakes.

FIGURE 1 Funding Matrix Changes In Market Conditions Process Stage 50 25 0 -25 -50 Funded 100 100 100 100 100 Docs Signed 99 99 95 90 70 Docs Drawn 99 95 90 80 60 Approved 95 85 75 65 35 Submitted 85 75 60 45 25 New App 75 60 50 40 20

Clearly the objective of pipeline management is to hedge the firm's interest rate risk at a lower cost than the calculated premiums that should have been collected on the options that the firm extends to its borrowers. On the other hand, the risk associated with attempting to estimate borrower behavior in 25 scenarios per distribution channel is rather daunting. We propose a solution. For each distribution channel, ask yourself the following questions: * What percentages of the loans will

never fund? * What percentages of the loans will

always fund?

By answering these questions, you have estimated what subset of your pipeline behaves efficiently. In essence, you have replaced 25 separate behavioral forecasts with just two questions. The answers to these two questions should be different for each distribution channel. For example, a commercial bank sourcing mortgages through its depository branches might find that 20 percent of the mortgages originated always fund. They may also find that 15 percent of the mortgage originated are either rejected by their underwriters or cancelled for other reasons. We can expect 65 percent of the pipeline to behave relatively efficiently (See Figure 5). In a wholesale distribution channel, where the customer is a professional mortgage broker rather than a borrower, we might expect far more efficiency. Perhaps as few as 5 percent of mortgages would always fund, and 10 percent of mortgages would never fund. This leaves an efficient set of 85 percent associated with the wholesale distribution channel.

What loans will be efficient and what loans will not? We do not know. If you assume efficient behavior will be normally distributed over a pipeline, then in the case of the commercial bank distribution channel, we can assume that 15 percent of each loan will never close, 65 percent of each loan will behave efficiently and 20 percent of each loan will always close. The hedge ratio for a $100,000 commitment with a delta of .35 in such a distribution channel would be calculated as follows: Hedge Ratio = .35 X 100,000 X[1-.2-.15] + 100,000 X .15 = .3775

or generically,

Hedge Ratio = Delta X (1 - % never fund - % always fund] + % always fund

= Delta X [efficient set] + % always fund

In order to reduce our cost of hedging, we have attempted to quantify, through two simple questions, the relative inefficiency of the mortgage loan pipeline. In answering these questions, we assume very little correlation between the consumer's behavior and exogenous events. Rather, we look only to the internal characteristics of our distribution channel. Hopefully, we have some control over these distribution channel characteristics that we exercise through the clear articulation of our lending practices and policies. This estimate of a pipeline's relative inefficiency is a risk to be sure, but it is a limited risk taken in a highly controlled environment.

A real life example

Security Pacific Bank calculates pipeline risk exposure using both the funding matrix approach and the option-based paradigm. Figure 6 shows excerpts from Security Pacific's March 19, 1992 daily position reports comparing position exposure using the two different approaches. In the interest of propriety, we have modified the numbers but have left the relative values intact.

In this example, the option-adjusted approach results in a "longer" position than the funding matrix approach. The major exchange is in the app/docs out category; the pipeline component nearest to commitment expiration. You may recall from Figure 4, that the deltas of at-the-money options are most sensitive to market movement. On this particular day, there was an approximate 8bps adverse move in the market, not enough to influence behavior, as predicted by the funding matrix approach, but large enough to significantly change the option value of the pipeline. Note the loan inventory average coupon, when weighted by delta, was 4.26 basis points lower than the average coupon weighted by the expected funding ratio. This reflects higher delta values associated with lower coupon or in-the-money commitments.

Putting the mathematics to work

We have presented a pipeline management paradigm based upon an option-based theory that we believe correctly identifies the boundaries of interest rate risk exposure. These boundaries are predicted on the efficient behavior of the borrower. The structural changes in the industry, combined with the increased sophistication of borrowers, has caused consumers' behavior to become more and more efficient. The funding matrix approach to pipeline management fails to quantify this trend towards efficiency. By comparing the results of our option-based paradigm to that of the funding matrix, we can quantify the difference between expected behavior and efficient behavior on the part of the customer. Simply knowing this information will enhance your pipeline management skills.

Rather than making multiple guesses about multiple scenarios, the pipeline manager has only to answer three questions:

1. What will mortgage-backed securities' volatility be?

2. What percentage of loans will always fund?

3. What percentage of loans will never fund?

Mathematics will do the rest. Limiting the number of judgment calls a pipeline manager must make produces a higher degree of discipline in risk-management activities. And discipline will make you a better pipeline manager. Luke S. Hayden is senior vice president of consumer asset management at Security Pacific National Bank in Cypress, California. Dean M. Di Bias is vice president for mortgage sales and hedging at Security Pacific National Bank.

Printer friendly Cite/link Email Feedback | |

Title Annotation: | Secondary Marketing; managing interest rate risk in the mortgage origination process |
---|---|

Author: | Hayden, Luke S.; Di Bias, Dean M. |

Publication: | Mortgage Banking |

Date: | May 1, 1992 |

Words: | 3775 |

Previous Article: | Lurking liability. |

Next Article: | Securitizing low-income multifamily mortgages. |

Topics: |