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A very different kind of mortgage product.

The Last Decade Brought With it a virtual explosion in new residential mortgage products, as well institutions buying, selling and brokering residential mortgages. Much of this growth has been due to the very active and liquid secondary mortgage market that has emerged, with players such as GNMA, Fannie Mae and Freddie Mac to name just a few.

Secondary mortgage market players pool residential mortgages together and then issue securities collateralized by these mortgages. These securities can take the form of mortgage-backed bonds, mortgage pass-through securities, mortgage pay-through bonds or collateralized mortgage obligation (CMOs). These securities are normally over-collateralized so that income from the mortgages is sufficient to ensure timely payment of interest and principal to the security holders.

CMOs first came on the scene in 1983 through Freddie Mac and were adopted later also by Fannie Mae. The CMO market has become huge - estimates appearing in Wall Street journal articles in October 1991 placed the total market of CMOs at $500 billion, with some single brokerage firms selling between $75 million and $100 million of CMOs each month to individual investors.

The greatest risk borne by investors in CMOs is "prepayment risk" (i.e., that a significant percentage of the mortgages backing the CMO will be prepaid early); this arises due to refinancings, sale of properties, borrower defaults and the like. As a result, CMO investors face substantial uncertainty with respect to the duration of their investment. For example, when interest rates are high, a mortgage-backed security might be offered with a very attractive coupon rate. The buyer might be led to believe that this coupon rate will be realized over a long period. However, if interest rates fall, a substantial number of the mortgages backing the CMO might be repaid early, potentially reducing both the yield and duration of the securities backed by the pool.

CMO's deal with this prepayment risk by separating cash flows from the pool into classes known as "tranches." Investors then have a choice of which tranche they wish to buy. Each tranche receives periodic coupon interest payments (or is credited with accrued interest), while principal repayments are first applied to tranche A, then B, then C and finally Z. If no mortgage in the CMO pool is prepaid, the Z tranche buyers might not see any principal payments for 10 or 15 years. However, as the rate of prepayment rises, the more accelerated becomes the repayment of principal to all tranches. And Z tranche investors might see their principal repaid in a very short time.

Because investors face this prepayment risk, especially when interest rates are high and expected to fall, prices of mortgage-backed securities are lower (yields are higher) than they would be if the prepayment risk were eliminated entirely. By contrast, because U.S. government bonds are not callable, they have no prepayment risk. To compensate investors for the prepayment risk, the mortgages backing the security itself will be priced lower as well. And because a large number of all new residential mortgages are immediately sold into the secondary mortgage market by primary mortgage lenders and brokers, interest rates to residential borrowers are also higher when the borrower can prepay any or all of the outstanding principal without penalty.

Getting primary mortgage

lenders involved

Because the secondary mortgage market is so pervasive and reducing the prepayment risk is so important in the pricing of mortgages, a logical question grows out of these circumstances. Can primary mortgage market lenders modify the mortgage products they offer to make them more attractive to the secondary market? One obvious way would be to include a prepayment penalty in the mortgage contract. However, the major secondary market players eliminated the prepayment penalty provision from their seller/servicer contracts, and many state laws have incorporated a ban on such provisions in home mortgages.

An alternative to explicit prepayment penalties is the creation of a mortgage that reduces prepayment risk. At one time, it was thought the adjustable-rate mortgage ARM) would serve this purpose because ARM borrowers benefit through a reduction in their monthly payments when interest rates fall. While ARM borrowers may be less likely to refinance when interest rates fall, there is still a tendency for ARM borrowers to refinance to a fixed-rate mortgage (FRM) when interest rates drop substantially, preferring to trade the potential lower rate offered by the option-laden ARM for the surety of fixed payments. But even if no ARM borrower were to ever refinance, prepayments would still exist due to property sales and borrower defaults.

The purpose of this article is to propose a new mortgage instrument that allows mortgage originators to mimic the behavior of the secondary mortgage market.

The zero-coupon, interest.

only, fixed-rate mortgage

While it may be impossible to create a mortgage instrument entirely protected from prepayment risk, there is a mortgage product that could be marketed by primary mortgage lenders that reduces prepayment risk using existing financial instruments. The mortgage product is the zero-coupon, interest-only, fixed-rate mortgage, or ZCIOFRM.

Here's how it works. Suppose a primary mortgage lender has qualified an applicant for a 30-year, self-amortizing FRM. Over the course of the next 30 years (or until the mortgage is prepaid), the borrower will make monthly payments of a fixed amount that includes both interest on the outstanding balance as well as a contribution to principal repayment.

As an alternative, suppose instead that the lender offers the borrower an interest-only mortgage for 30 years combined with the borrower purchasing a U.S. government zero-coupon bond that will mature in exactly 30 years with a terminal value equal to the face value of the interest-only mortgage. (A zero-coupon bond accrues interest over its life, but no cash is received until the bond is sold or matures.) The interest-only mortgage is collateralized by the borrower's home and by the zero-coupon bond.

If the borrower holds the ZCIOFRM the entire 30 years, at maturity the borrower delivers the zero-coupon bond to the lender in satisfaction of the entire outstanding principal balance. However, if the borrower chooses to prepay the zero mortgage at any point prior to 30 years, the zero-coupon bond only partially satisfies the outstanding principal balance (the remaining principal balance could come from the proceeds from the sale of the home, a new mortgage or other sources). But unlike a traditional fixed-rate mortgage where the entire remaining balance is prepaid, the prepaid ZCIOFRM still has a portion of its total value "alive" at prepayment, namely the zero-coupon bond. Thus the lender can retain this zero-coupon bond until it matures, or sell it, and has not suffered as great a degree of prepayment risk as with a traditional FRM.

The ZCIOFRM mortgage: an


Suppose a borrower seeks a mortgage for between $97,000 and $100,000 on a home with a market value of $125,000 (the loan-to-value ratio is then 80 percent or less). Alternative A is a standard FRM carrying an APR of 13 percent for 30 years. If the homebuyer borrows $97,218.33, the borrower will make monthly principal and interest payments of $1,075.43 for 360 months.

Alternative B is a ZCIOFRM. The homebuyer borrows $100,000 in an interest-only mortgage at 13 percent for 30 years. The monthly interest-only payment is $1,083.33. The borrower also buys a 30-year zero-coupon bond that will mature with a face value of $100,000 - the amount of the interest-only mortgage - and places this zero in trust in favor of the lender. Assuming a yield on the zero of 12 percent, this zero would cost the borrower $2,781.67.

Although interest accrues on the zero but is not paid until the zero is sold or matures, the borrower must pay taxes on the accrued increase in the value of the zero-coupon bond each year.

From the lender's perspective, the excess of collateral over market value is the same under each alternative - $27,781.67 ($125,000 - $97,218.33 for Alternative A; $125,000 + $2,781.67 - $100,000 for Alternative B).

Figures 1 and 2 illustrate the borrower's position under the FRM and ZCIOFRM, respectively, assuming the borrower pays taxes at the 28 percent marginal rate. Several key items are worth noting. First, column 6 of each table shows the borrower's net, after-tax, total mortgage payment each month. For the FRM, this is calculated by multiplying the monthly interest payment (column 3) by (1 - marginal tax bracket) and adding the monthly principal payment to this product.


For the ZCIOFRM, the after-tax total mortgage payment is calculated by first subtracting the accrued interest on the zero (column 2) from the interest paid on the interest-only mortgage (column 4) to determine the net taxable interest. This net interest (column 5) is then multiplied by the marginal tax rate. Finally, the interest outflow (column 4) is reduced by the interest tax saving to produce the after-tax payment.

The net, after-tax, monthly payment is roughly $8 per month greater for the ZCIOFRM than it is for the traditional FRM (due to the fact that the zero is accruing interest at 12 percent, while the FRM carries a 13 percent APR). In present value terms, the borrower repays about $900 more under the ZCIOFRM ($98,122.96 versus $97,218.33) if the mortgage is held for the entire 30 years.

Consider, however, what happens if either mortgage is prepaid after 5 years, or 60 months, because of a sale of the home. We'll also assume interest rates are the same as they were when the mortgages were originated. Under the FRM, the outstanding principal balance due is $95,353.35, or more than 98 percent of the original principal balance.

Under the ZCIOFRM, the borrower repays $94,946.55 in cash and then delivers the zero-coupon bond (now worth $5,053.45). Thus, under the ZCIOFRM, the cash repaid is less than 95 percent of the original mortgage amount. The results are similar for prepayments during other periods.

Now consider a prepayment that occurs due to a refinancing. Suppose after 60 months, or 5 years, 30-year mortgage rates have fallen to, say, 9 percent, and the interest rate on the zero-coupon bond has fallen to 8 percent. As illustrated in Figure 3, the original zero has increased in value dramatically to $13,623.65. If the ZCIOFRM provided for the borrower to deliver the zero-coupon bond upon refinancing based on a 12 percent yield, the lender enjoys a windfall, because the zero now has a market value of $13,623.35 (the value at an 8 percent yield) but the lender is only crediting the borrower for $5,053.45 (the value at a 12 percent yield). Thus the lender has received cash and securities with a total market value of $108,569.90 ($94,946.55 + $13,623.35).

Subsequent Market Value of
Zero-Coupon Bond

Beginning Principal $9,144.34
Interest Rate (% ARP) 8.000%
Term (Months) 360
Maturity Value $100,000.00

 1 2 3
 Beginning Interest Ending
Month Principal Received Principal

 1 $9,144.34 $60.96 $9,205.30
 12 9,837.73 65.58 9,903.31
 24 10,654.25 71.03 10,725.28
 36 11,538.55 76.92 11,615.48
 48 12,496.25 83.31 12,579.55
 60 13,533.43 90.22 13,623.65
 72 14,656.70 97.71 14,754.41
 84 15,873.20 105.82 15,979.02
 96 17,190.66 114.60 17,305.27
108 18,617.48 124.12 18,741.60
120 20,162.72 134.42 20,297.14
180 30,039.34 200.26 30,239.61
240 44,753.99 298.26 45,052.35
360 99,337.75 662.25 100,000.00

In fairness, suppose the lender agrees to split the windfall gain with the borrower. In this case, each receives half the difference between the zero's value at a 12 percent yield and its value at an 8 percent yield. This situation is illustrated in Figure 4. The lender credits the borrower with an additional $4,284.95 ($13,623.35 - $5,053.45 split equally). This leads to a win-win situation for borrower and lender. By choosing the ZCIOFRM, the borrower benefits in two significant ways from a drop in interest rates. Not only can the borrower refinance to a lower rate, but the borrower gains from the increased value of the zero as interest rates decline.

Compared with a traditional fixed-rate mortgage, the lender also wins. The total amount prepaid exceeds the original interest-only mortgage balance by the amount of the lender's share of the increased value of the zero. In this case, in lieu of an explicit prepayment penalty, the lender still receives an inflow almost 4.3 percent greater than the original mortgage amount.

In a declining interest-rate environment, the lender may extract a higher yield than a fixed-rate mortgage, while, simultaneously, the borrower enjoys a lower effective cost than under a standard FRM. This is best shown in Figure 5, which analyzes the borrower's effective cost (APR) under the ZCIOFRM for various prepayment months and various assumed market yields on the zero at prepayment. It is worth noting that a drop in zero-coupon bond yields of 2 percentage points or greater benefits the borrower for any refinancings occurring prior to 84 months after origination.

However, just as the borrower and lender may benefit from declining interest-rates, the borrower may suffer in a rising interest-rate environment when a "forced" prepayment occurs. In this situation, the zero may decline in market value to the point where the ZCIOFRM prepayment amount exceeds that of a fixed-rate mortgage.

Advantages to the lender

For the primary mortgage originator, there may be several advantages to offering a ZCIOFRM instead of a standard fixed-rate mortgage. Among these advantages are: * No reinvestment risk on the zero-coupon portion - because the principal amount of a ZCIOFRM is not paid off prior to maturity, the lender need not worry about reinvesting the principal proceeds prior to the maturity of the mortgage. The zero-coupon bond portion of the mortgage remains "alive" throughout. Because of this, the lender can resell each element of the ZCIOFRM separately (i.e., a zero-coupon "strip" as well as an interest-only "strip" just like secondary mortgage market buyers sell strips). In this respect, the primary lender conceivably could act just like a secondary market. Eliminating the "middle man" may improve the marketability of this type of mortgage, generating a more attractive price for the lender. * If interest rates drop, the lender may receive an implicit prepayment penalty - As suggested by the previous example, a borrower refinancing may create a win-win situation for both lender and borrower. If the increased value of the zero-coupon bond (due to a drop in interest rates) is split between borrower and lender, the lender implicitly exacts a "penalty" from the borrower for refinancing. The lender receives a larger cash inflow than would be received if either a fixed-rate mortgage or an ARM were refinanced. The borrower, however, also gains if interest rates drop, profiting from the marked-up value of the zero-coupon bond. * A potentially simpler conversion feature - if the borrower chooses to refinance a ZCIOFRM to a fixed-rate mortgage (due to a drop in interest rates), a lender may be able to finance this transaction in-house and eliminate many of the transaction costs associated with mortgage refinancing. * The zero-coupon bond represents riskless collateral - Mortgage defaults frequently occur when the collateral value of the house drops below the face value of the mortgage debt (the loan-to-value ratio exceeds 100 percent). Although the ZCIOFRM does not eliminate this risk, the fact that a portion of the collateral is in the form of a riskless bond may reduce default risk.

Advantages to the borrower

Within the previous section, the advantages to the lender were highlighted, but there are advantages to the borrower as well. The most distinct advantage to the borrower under a ZCIOFRM is the potential to share in the appreciation of the zero if interest rates drop. This is best illustrated by Figure 4. Here, it is assumed that it is now 60 months (5 years) after the origination of the mortgage and the market yield on the zero has declined from 12 percent to 8 percent. The zero is now worth more than $13,600 - more than $8,500 more than it would be worth if the market yield were still 12 percent. Even if the borrower splits this gain 50-50 with the lender, the borrower still enjoys a $4,300 gain - more than enough to pay the settlement costs on a mortgage refinancing. The borrower then gains in two ways - he can refinance to a lower interest-rate mortgage, saving finance charges; and, he can pay for the settlement costs on the refinancing through the increased market value of the zero.

Comparison of Fixed-Rate Mortgage and ZCIOFRM
Assuming Prepayment Prior to Maturity

Prepayment Month 60
Yield to Maturity on Zero at Prepayment 8.00% APR
Lender's Share of Surplus 50.00%
Lender's Share of Deficit 0.00%

 Market Price of Zerio at Prepayment $13,623.65
 Book Value of Zero at Prepayment $5,053.45

Surplus (Deficit) $8,570.20
 To Lender $4,285.10
 To Borrower $4,285.10

Lender's Yield on ZCIOFRM 13.60% APR
Lender's Yield on FRM 13.00% APR

 Yield Advantage to Lender of ZCIOFRM 0.60%

Borrower's Effective Cost on ZCIOFRM 12.49% APR
Borrower's Effective Cost on FRM 13.00% APR

 Cost Advantage to Borrower of ZCIOFRM 0.51%

Tax implications and pricing


So long as the ZCIOFRM is "alive," the zero portion is technically owned by the borrower, who is then responsible for paying taxes on the accrued interest. If the ZCIOFRM is liquidated by the borrower, however, the zero-coupon bond is delivered in satisfaction of a portion of the mortgage debt. At that point, the zero becomes the property of the lender (or secondary buyer), who assumes the tax liability for any subsequent accrued interest.

To price a ZCIOFRM, the lender (or buyer) must then estimate the likely duration of the mortgage and consider the tax implications of alternative duration scenarios. This issue will be the subject of subsequent research. The authors are currently working with a variety of private lenders and public sector housing finance officials to determine the feasibility of a pilot project that would use the ZCIOFRM as an alternative to other first-time homebuyer assistance programs. Under the proposal, a federal, state or local housing authority would assist first-time homebuyers by providing the zero-coupon bond portion of the ZCIOFRM. Five years after origination, assuming the borrower continues to make scheduled payments on the interest-only portion as required, the value of the zero would gradually be transferred to the borrower by the housing authority. Because issuing the zero-coupon bonds would require no cash outlay and because the housing authority would retain ownership of the zero for the first five years, issuing such bonds would not require any immediate tax revenues to fund them.


In summary, a new mortgage product, ZCIOFRM, is being proposed as an alternative to the standard fixed-rate mortgage as a method of housing finance. This new mortgage product offers several distinct advantages to the originator, namely the ability to mimic the behavior of the secondary mortgage market and the potential to extract an implicit prepayment penalty.

COPYRIGHT 1992 Mortgage Bankers Association of America
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1992 Gale, Cengage Learning. All rights reserved.

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Title Annotation:zero-coupon, interest-only, fixed-rate mortgage
Author:Thode, Stephen F.; Kish, Richard J.
Publication:Mortgage Banking
Date:Dec 1, 1992
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