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                         NBER WORKING PAPER SERIES




                        INTEREST-ONLY/PRINCIPAL-ONLY
                          MORTGAGE-BACKED STRIPS:
                       A VALUATION AND RISK ANALYSIS




                               Alan J. Marcus

                                Arnold Kling




                           Working Paper No. 2340




                    NATIONAL BUREAU OF ECONOMIC RESEARCH
                          1050 Massachusetts Avenue
                            Cambridge, MA 02138
                                 August 1987




We thank Bob Taggart for helpful comments. The views expressed in this
paper are not necessarily those of the Federal Home Loan Mortgage Corporation
of the Federal Home Loan Bank Board. The research reported here is part
of the NBER's research program in Financial Markets and Monetary Economics.
Any opinions expressed are those of the authors and not those of the National
Bureau of Economic Research.
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                                                  NBER Working Paper #2340
                                                  August 1987


            Interest-Only/Principal-Only Mortgage-Backed Strips:

                        A Valuation and Risk Analysis



                                  ABSTRACT



    We examine the risk characteristics of each portion of 10/PO mortgage

strips, present results of a valuation model of these securities, and examine

market prices of both the interest—only and principal—only portions of

mortgage pools. We show that 10/PC securities are highly sensitive to the

prepayment behavior of the underlying mortgage pool. Because that behavior

varies systematically with the interest rate, and because prepayments affect

the values of 10 and P0 components in opposite ways, the interest—rate risk of

strip securities can differ substantially from that of the underlying mortgage

pool. The P0 component has much longer duration than the underlying mortgage

pool. In contrast, the 10 component typically will have a negative duration,

at least In ranges for which interest—rate movements induce meaningful changes

in mortgage prepayment behavior. We also show how market prices of

partially—stripped MBSs that are actively traded on secondary markets can be

used to infer market values of pure 10/PC strips. Recent market data is fully

consistent with the theoretical insights offered by our valuation model. When

interest rates spiked last April, P0 values fell far more dramatically than

those of the underlying mortgage pooi while 10 values actually rose.




Arnold Kling                                     Alan J. Marcus
Federal Home Loan Bank Board                     School of Management
1776 G Street, NW                                Boston University
Washington, DC 20013                             704 Commonwealth Avenue
                                                 Boston, MA 02215
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    The huge trading losses of Merrill Lynch and other investment bankers

recently focused considerable attention on interest—only/principal—only

(lO/PO) mortgage—backed securities. These securities are formed by separating

interest payments on mortgage pools from principal repayments and selling

claims to each income stream separately. The 10 security receives all the

interest payments made on the mortgages in the pool. These payments cease

when mortgages are prepaid. PC securityholders, in contrast, benefit from

early payment of principal. Neither the risk characteristics nor the

appropriate pricing of these new securities are yet well understood. Equally

important, it is not widely recognized that in some cases market data is

available that can be used by issuers to price these securities precisely. In

this paper, we examine the risk characteristics of each portion of lO/PO

strips, present results of a valuation model of these securities, and show how

market prices of traded securities can be used to infer the values of both the

interest—only and principal—only portions of mortgage poois.



1. Interest—Rate Risk in lO/PO Securities



    The major difficulty in analyzing all mortgage—backed securities lies in

the analysis of prepayments. A 30—year 10% conventional mortgage selling at

par would have a duration of about 8.4 years if prepayments were

disallowed.1 In practice, of course, prepayments shorten durations of

mortgage pools considerably. For example, a prepayment rate of 5 percent of

outstanding mortgages per year would reduce duration to 6.2 years. The

peculiarity of IC/PC securities is that the risk of interest—rate increases is

borne overwhelmingly by the owner of the principal—only security. The
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 duration of the P0 portion greatly exceeds that of the underlying mortgage

 pool, while the duration of the 10 portion is correspondingly smaller. In

 fact the IC portion is likely to have negative duration, and thus potentially

may   serve   as a hedging asset for fixed—income portfolios.

      This disparity in interest—rate exposure derives primarily from the

interaction of prepayment behavior with interest—rate movements. When

interest     rates increase, the value of the P0 security falls for two reasons.

First, future repayments of principal are worth less as the discount factor

for the time value of money increases. Second, mortgage prepayment rates fall

when interest rates rise, thereby increasing the average time until repayment

of principal. The increase in the time until receipt of principal payments in

conjunction with the increase in the discount rate results in a substantial

decrease in the present value of those payments. These factors lend the P0

security a duration substantially longer than that of the underlying pool of

mortgages.        -




      In   contrast, the 10 portion of the mortgage is affected in offsetting ways

by interest rate movements. A decline in interest rates increases the present

value of scheduled interest payments, but simultaneously increases the

incidence of prepayments of principal. Since these prepayments terminate the

stream of interest payments made on the mortgage pooi, they lower the value of

the 10 security. The net effect on the value of the 10 security may be either

positive or negative. However, for interest rates near the coupon rate of the

mortgage pool, prepayments tend to increase enough in response to a fall in

the interest rate that the 10 security loses value. In this empirically

relevant region, the termination of interest payments dominates the effect of

lower discount rates, resulting in a negative duration for the IC security.




                                        —2—
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    To illustrate these points, consider a 30—year l00,0O0 mortgage with a

10% coupon rate. If prepayments were disallowed, then 84.2% of the present

value of the total cash flows on the loan would derive from the interest

component of payments while only 15.8% would derive from principal

repayments. At the other extreme, if the mortgage were prepaid immediately,

an Interest—only claim would become worthless while the value of the principal

claim would jump from 15,80O to the principal balance of l00,00O.

    The effect of prepayment behavior is examined in Table 1 where prepayment

per year is assumed to be a constant fraction of outstanding mortgages. The

effect of prepayment experience is evident. An unanticipated increase in the

prepayment rate from 5% to 7.5% would, even without coincident interest—rate

movements, reduce the value of interest payments from 6l to 53.2 per 100

principal balance, inducing a capital loss to an 10 security holder of 12.8%.

The corresponding gain on the P0 security would be from 39 to 46.8, for a

capital gain of 20%. These calculations are incomplete, of course, because

they ignore the interaction between prepayment behavior and changes in

interest rates, but they do illustrate the wide swings in the relative shares

of the mortgage value that accrue to interest versus principal claimants when

prepayment rates change. Market values in practice should be even more

volatile than suggested by Table 1 since prepayment rates in fact vary in

response to interest—rate swings.

    The weighted average of the durations of the 10 and P0 securities must

equal the duration of the underlying pooi of mortgages. Thus, the great

disparity in durations of the component securities are necessary

counterparts: the short or negative duration of the 10 security must be

matched by correspondingly long durations of the P0 security.




                                     —3—
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                  Table 1: Components of Mortgage Values



Prepayment Rate            Percent of Value Due      Percent of Value Due
(per year)                 to Interest Payments      to Principal Repayments


     0.0%                         84.2%                     15.8%

     2.5                           71.0                     29.0

     5.0                          61.0                      39.0

      75                          532                       46.8

    10.0                          47.1                       52.9

    15.0                          38.1                       61.9

     20.0                         31.9                      68.1

     25.0                         27.4                      72.6




                                   —4—
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2.   Contingent—Claims Analysis

     The right to prepay a mortgage is in essence a call option that gives the

homeowner the right to call back the loan from the lender at a price equal to

the scheduled balance remaining on the loan. Thus, mortgage—backed securities

may be valued using the same techniques that have been developed for other

option—valuation problems. In fact, option—pricing techniques have been

applied to GNMA mortgage—backed security valuation by Dunn and McConnell

(1981a, 198lb), Brennan and Schwartz (1985), and others. Here, we apply

similar techniques to the valuation of the IC and P0 components of a

mortgage—backed pool. Following their lead, we assume that there are two

types of mortgage prepayments: economically—motivated prepayments (and

refinancings) that exploit interest rate declines, and "autonomous"

prepayments that arise when homeowners change their residences. We will

assume that 5% of all outstanding mortgages prepay for autonomous reasons in

each year. Such a simplistic specification is arbitrary, but does little harm

to the analysis of the interest—rate dependence of these securities, which
                                                       2
depends primarily on economically—motivated prepayment.

     Economically—motivated prepayment will occur when the interest rate

reaches a critical point at which refinancing is optimal for the homeowner.

This critical point will be determined by the process under which interest

rates evolve over time. We will assume that the interest rate is expected

to increase when it is below 10% and to fall when above 10%. Hence, 10% is

the natural or long—run equilibrium value of the interest rate. The épeed

with which rates are impelled toward that long—run value is assumed to be

proportional to the difference between the interest rate and its long run
                     3
equilibrium value.




                                     —5—
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     In addition to the expected drift in the interest rate, there are

continuous shocks to rates due to unanticipated economic events. We model

interest rate uncertainty as increasing with the level of rates, specifically

that the variance of the interest rate is proportional to the level of the

rate.4 In our numerical simulations, we set the proportionality constant

equal to .25. At a 10 percent interest rate, this results in a standard

deviation of the interest rate of 1.6 percent annually.

     Using this particular set of assumptions, we can use a valuation model to

examine the response of 10, P0, and mortgage—pool values to interest rate

changes. Our mathematical approach is modelled after Brennan and Schwartz

(1977), which provides a full discussion of the techniques used to value

interest—rate—dependent option—like securities.

     In brief, the valuation methodology uses the dynamics for interest rate

movements given in footnotes 2 and 3 to derive the corresponding dynamics for

the value-of interest—rate dependent securities. These, together with

'boundary conditions" for the values of the security at extreme values of the

interest rate orat optimal prepayment dates, uniquely determine both the

value of the security at all points and the optimal prepayment schedule. In

our model, we employ a version of the liquidity preference theory, and assume

that the expected risk premium earned by each security is proportional to the

instantaneous standard deviation of that security's rate of return, with a

proportionality constant of 0.1.   Such a specification generates a liquidity

premium of about 1.5% for an 8—year duration asset.

    Figure 1 is a graph of the value of the 3 securities (10, P0, and the

mortgage pool itself) backed by a mortgage pool with a coupon rate equal to

the long—run equilibrium interest rate, 10%, as a function of the current




                                     —6—
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market interest rate. The mortgage pool is assumed to have been issued 10

years ago with an original life of 30 years. The current principal value is

90.78 per l00 original principal. Notice that, as anticipated, the value of

the PC security falls most dramatically with interest rate increases,

especially at interest rates near the optimal prepayment point of about 8

percent. As economically—motivated prepayment becomes more likely at lower

interest rates, the value of the P0 security rises dramatically. In contrast,

the 10 security falls in value with interest rate decreases, even at rates as

high as 14%. Like the PC, the value of the IC security is most sensitive to

the interest rate near the optimal economic—prepayment point.

     These interest—rate sensitivities are even more evident in Figure 2,

which depicts the durations of the securities as functions of the interest

rate. The duration of the mortgage pool is nearly 3 years at high interest

rates. Without prepayment, it would be about 6 years. The seemingly—large

difference in duration is due both to the incidence of autonomous prepayments

and to the threat of economic prepayment. Even at an interest rate of 147.,

such a threat is not trivial since the interest rate at that point is drifting

downward to its long—run equilibrium value of 10%. The duration of the

mortgage is even shorter at lower interest rates since economic prepayment is

that much more imminent.

    The duration of the P0 security is far larger. For larger values of the

interest rate, it is roughly double that of the mortgage pool. At an interest

rate of 10%, the duration of the PC is 13 years, roughly 5 times that of the

mortgage. From there, duration rises dramatically to 60 years at an interest

rate just above the prepayment point.




                                        —7—
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     The duration of the IC security is, in contrast, negative and of quite

large magnitude at interest rates below 1OZ. At an interest rate of 11

percent, duration Is 52 years; at 10 percent it is 58 years. From there

duration spikes downward even more dramatically. At the optimal economic

prepayment point duration is essentially infinitely negative.5

     These values are more extreme than one would expect to observe in reality

since the valuation model assumes that all outstanding mortgages are prepaid

at the optimal moment, when in practice some homeowners will defer prepayment

for reasons not captured by the model. While the model allows for suboptimal

(autonomous) prepayment, It does not allow for suboptimal non—prepayment.

Nevertheless, the qualitative pattern of strip values Illustrated In Figures 1

and 2 will be observed in practice, and 10/PC strips do empirically exhibit

large durations. Indeed, Figure 5, which traces out estimates of actual 10

and P0 strip values during a period of rising interest rates is remarkably

similar to Figure 1.

     Other (nonreported) simulations replicate the analysis of Figures 1 and 2

for mortgage coupon rates of 8 and 12 percent, thus bracketing the long—run

equilibrium interest rate. While the optimal economic—prepayment points

differed from the analysis of Figures 1 and 2, the qualitative patterns that

emerged were otherwise identical.



3.   Investment Implications



     The peculiar interest rate exposures of the 10/PC securIties create both

opportunities and risks for their investors. The interest—rate exposure of

the P0 security is apparent. Nevertheless, such securities may be useful




                                     —8—
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portfolio tools for investors seeking very—high—duration assets. For example,

pension funds with long—duration liabilities might find PC securities useful

for immunization purposes.

     10 securities offer hedging opportunities for investors holding more

conventional fixed—income securities. For example, a thrift institution with

holdings of conventional mortgages could offset some of its interest rate

exposure by holding part of its portfolio in mortgage—backed 10 securities

with negative duration.



4.   Empirical Evidence



     While the valuation model presented above is useful for analyzing the

properties of 10/PC securities, the particular values derived are dependent on

assumed autonomous prepayment rates and on the posited process for the

evolution of interest rates. One would like a valuation procedure that is

consistent with market information as reflected in prices of other traded

assets. Fortunately, such data do exist, and market assessments of the values

of the lO/PO components of some mortgage poois can be computed directly from

these data. Hence, the "proper" market prices for the lO/PO components of at

least some mortgage poois can be inferred.

     Completely stripped mortgage—backed securities tend to be privately

placed, and to date have been traded only erratically on the secondary

market. Consequently, investment bankers cannot easily rely on market values

of outstanding strips to price newly issued securities. However, FNNA has

issued partially stripped securities that are actively traded that can be used

to infer the market values of IC/PO securities. This inference is made




                                     —9—
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possible because the partial strips allocate principal and interest in

different proportions to different—class securites.

     To illustrate, consider the issues of "B" and "C" series securities by

FtThIA in the letter half of 1986, in which two 9 percent coupon mortgage—backed

securities (MBSs) were divided up so that the premium classes received 2/3 of

the interest and 1/2 of the principal payments, while the discount classes

received 1/3 of the interest and 1/2 of the principal. The premium class,

therefore effectively became a 12% security (   9% x 2/3    1/2) while the

discount class was effectively a 6% security C = 9% x 1/3    1/2). (However,

these synthetic securities would not behave precisely like original—issue 12

or 6 percent coupon mortgage pools since the prepayment behavior of the

"synthetic" securities would be tied to the 9% coupon rate of the underlying

mortgage pools.

     If one were to take a long position in the premium—class security and a

short position -in the discount—class security, the principal payments would

net out to zero, and one would be left with a three percent 10 strip on the

underlying 9% coupon mortgage pools. Therefore, three times the value of the

price difference between the premium and discount securities equals the value

of a pure 9% 10 strip. Substracting the value of that 10 strip from the sum

of the values of the discount and premium securities then gives the value of a

"synthetic" P0 position on the 9% mortgage pooi. The key to this procedure is

that the premium and discount securities are written on the same underlying

MBS and so have identical prepayment exposure. Long and short positions on

different—coupon passthroughs would create Interest and principal—only

securities only until the prepayment behavior of the two passthroughs diverged.

    Goldman Sachs supplied us with price data f or 3 types of partial strips:




                                     —10—
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the B" and "C" series just discussed In which 9% pools were split into 6 and

12 percent securities, the "D" series, in which an 8.5% coupon MBS was split

into 11% and 6% securities, and the "F", "G", "H", and "I" series, in which 9%

coupon MBSs were split into 11.5% and 6.5% securities. Using these data we

created three synthetic 10 strips and three synthetic P0 strips. The inferred

prices of the 10 and P0 strips over time are presented in Figures 3 and 4.

The three 10 and P0 prices all tended to move together over time, which is

gratifying, given that the underlying mortgage coupons are similar and thus

should have similar prepayment behavior.

     The most dramatic price movements took place in April 1987, when the bond

market fell sharply. Prices of mortgage passthroughs (obtained by adding

together the prices of the premium and discount securities) fell as well.

Figure 5 shows that the value of the P0 component fell far more dramatically

than the value of the overall MBS, confirming the extremely long duration of

this asset predicted by the previous sections. In contrast, the value of the

10 security actually rose, also confirming the theoretical prediction of a

negative duration, and indicating that prepayment activity was expected to

decline sufficiently to more than offset the increase In the discount factor

applied to 10 payments.



5. Summary



     We have shown that lO/PO securities are highly sensitive to the

prepayment behavior of the underlying mortgage pooi. Because that behavior

varies systematically with the interest rate, and because prepayments affect

the values of 10 and P0 components in opposite ways, the Interest—rate riàk of




                                     —11—
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strip securities can differ substantially from that of the underlying mortgage

pooi. The P0 component has much longer duratlonthan the underlying mortgage

pool. In contrast, the 10 component typically will have a negative duration,

at least in ranges for which interest—rate movements induce meaningful changes

in mortgage prepayment behavior. The distinct durations of these securities

make them interesting candidates for immunization of long—term obligations or

for hedging the value of fixed income portfolios.

    We've shown how market prices of partially—stripped MBSs that are actively

traded on secondary markets can be used to infer market values of pure lO/PO

strips. This inference method is potentially of value to issuers and

purchasers of such strips. Recent market data is fully consistent with the

theoretical insights offered by our valuation model. When interest rates

spiked last April, P0 values fell far more dramatically than those of the

underlying mortgage pooi while 10 values actually rose.




                                    —12—
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                                  Footnotes




1. Duration is, strictly speaking, the weighted average of the times until

    receipt of each payment from a security, with weights proportional to the

   present value of each payment. For mortgages with possible prepayments,

    such a definition is problematic since the cash flow stream will vary with

   prepayment experience. Throughout this paper, I will use duration in a

   looser, but more common, context as the interest—rate elasticity of a

    security's value, that is, as the proportional change in the security's

   price due to a 1 percent change in its yield to maturity.



2. This simple rule is probably reasonably realistic. Although prepayment

   rates generally are lower in early years of mortgage lives, before they

   ultimately level off, mortgage defaults are generally higher in the early

   years. Because these mortgages are insured, a default is essentially

   equivalent to an autonomous prepayment from the perspective of the lender,

   and the sum of the two sources of autonomous prepayments might be

    relatively stable.



3. This specification can be written formally as,

        E(dr/dt) =   k(.lO—r),
   where dr/dt is the time derivative of the interest rate, E is the

    expectation operator, and k is the proportionality constant, which we set

   equal to .2 in our illustrative examples below.




                                    —13—
FIGURE 1
                                SECURITY VALUES
      100-
                                                      -




       o     Th2rge
(1)
LjJ
-J    60-
>
>-
                                                                      strip
      40-
                                                                 10   strip


      20-
                                               /
                                                                                     Legend
                                                                                      MORTGAGE POOL
                                           /
                                                                                      10 STRIP
                                          1                                                      —
                                                                                      P0 STRIP
       0-           I      I       I             I          I           I       I
                                                                                                      More Mortgage Info




           0.00   0.02   0.04    0.06   0.08   0.10       0.12        0.14    0.16
                                  INTEREST RATE
FIGURE 2
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                                          SECURITY DURATIONS
                     100
                      75
                      50
    z
    (I-)
    0                                                     'S
    F-                25                                       'S
                                                                    5'
                                                                                       —   —            DC'
                                                                                                              strip
    a                  0
                                                                             /
    >-                                                                                     TO   strip
    F-
                     —25
    0
    Ui
    (I)
                     —50
                                                                         /
                                                                         /
                                                                    /                                                   Legend
                     —75                                                                                                 MORTGAGE POOL
                                                                                                                         JO STRIP
                                                                /
                                                                                                                         P0 STRIP
                 —100
                           0.00   0.02   0.04   0.06   0.08                  0.10   0.12         0.14            0.16
                                                 INTEREST RATE
Figure   3


                          Synthetic.              10       Strip Prices
     4-7
     46
     4-5
     44
     4.3
     42
     41

N:
L
     .3a
     —
         I
     ..i ':'



     .34
     .i .1

     .3 1

     3 Ij
               r /r                  .3,' 2                           4/   1   4/22
                                                                                      More Mortgage Info




                                                     r1cT
                      0    (B,c::)            +   ([:t)       4.   (F1c-H,I)
Figure   4
                                              Synthetic              P0          Strip Prices
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                     •7#
                     71
                     7fl
                     69
                     j
                     i_i   j
                     b
                     kD
                     5.3
                     s:jl
                (1
                     59
                     58
                        -r
                     '-'p
                     56
                     54
                     5.3
                     51
                     51j
                               #-,   ,r                  .3/2                              4/1      4/22
                                                                        1987
                                          0    (E4.C:)          +      ID)         >   (F,i31H,i)
Figure 5
                                  10   /'    P0 Strip Prices
More Mortgage Info




                                                      (B 0)
                     75
                     7fl
                     65
                     E;fl
                     55
             L.
             U-
                     50
                     45
                     40
                     35
                     3 Ij
                            "'I             3/2                         4/1   4/22
                                              0     P0
                                                      1   97   +   10
More Mortgage Info
4. Formally, we specify that,

          Variance(dr/dt) =
                              sr,
     and set s =
              0
                   .5.


5.   The value of the 10 srip is zero if the pool is repaid. Hence, a small

     increase in the interest rate from the prepayment point to a value just

     above it, Increases the value of the 10 strip from zero to a positive

     value, which is an infinite percentage increase.




                                     —14—
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                                  References



Michael Brennan and Eduardo Schwartz. "Savings Bonds, Retractable Bonds, and

    Callable Bonds," Journal of Financial Economics, 5 (1977), 67—88.



Kenneth B. Dunn and John J. McConnell. "A Comparison of Alternative Models for

    Pricing GNMA Mortgage—Backed Securities, Journal of Finance, 36 (May

    1981), 471—484.



_____________________________   "Valuation of GNNA Mortgage—Backed Securities,"

    Journal of Finance, 36 (June 1981), 599—616.




                                      —15—

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Nber Working Paper Series

  • 1. More Mortgage Info NBER WORKING PAPER SERIES INTEREST-ONLY/PRINCIPAL-ONLY MORTGAGE-BACKED STRIPS: A VALUATION AND RISK ANALYSIS Alan J. Marcus Arnold Kling Working Paper No. 2340 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 August 1987 We thank Bob Taggart for helpful comments. The views expressed in this paper are not necessarily those of the Federal Home Loan Mortgage Corporation of the Federal Home Loan Bank Board. The research reported here is part of the NBER's research program in Financial Markets and Monetary Economics. Any opinions expressed are those of the authors and not those of the National Bureau of Economic Research.
  • 2. More Mortgage Info NBER Working Paper #2340 August 1987 Interest-Only/Principal-Only Mortgage-Backed Strips: A Valuation and Risk Analysis ABSTRACT We examine the risk characteristics of each portion of 10/PO mortgage strips, present results of a valuation model of these securities, and examine market prices of both the interest—only and principal—only portions of mortgage pools. We show that 10/PC securities are highly sensitive to the prepayment behavior of the underlying mortgage pool. Because that behavior varies systematically with the interest rate, and because prepayments affect the values of 10 and P0 components in opposite ways, the interest—rate risk of strip securities can differ substantially from that of the underlying mortgage pool. The P0 component has much longer duration than the underlying mortgage pool. In contrast, the 10 component typically will have a negative duration, at least In ranges for which interest—rate movements induce meaningful changes in mortgage prepayment behavior. We also show how market prices of partially—stripped MBSs that are actively traded on secondary markets can be used to infer market values of pure 10/PC strips. Recent market data is fully consistent with the theoretical insights offered by our valuation model. When interest rates spiked last April, P0 values fell far more dramatically than those of the underlying mortgage pooi while 10 values actually rose. Arnold Kling Alan J. Marcus Federal Home Loan Bank Board School of Management 1776 G Street, NW Boston University Washington, DC 20013 704 Commonwealth Avenue Boston, MA 02215
  • 3. More Mortgage Info The huge trading losses of Merrill Lynch and other investment bankers recently focused considerable attention on interest—only/principal—only (lO/PO) mortgage—backed securities. These securities are formed by separating interest payments on mortgage pools from principal repayments and selling claims to each income stream separately. The 10 security receives all the interest payments made on the mortgages in the pool. These payments cease when mortgages are prepaid. PC securityholders, in contrast, benefit from early payment of principal. Neither the risk characteristics nor the appropriate pricing of these new securities are yet well understood. Equally important, it is not widely recognized that in some cases market data is available that can be used by issuers to price these securities precisely. In this paper, we examine the risk characteristics of each portion of lO/PO strips, present results of a valuation model of these securities, and show how market prices of traded securities can be used to infer the values of both the interest—only and principal—only portions of mortgage poois. 1. Interest—Rate Risk in lO/PO Securities The major difficulty in analyzing all mortgage—backed securities lies in the analysis of prepayments. A 30—year 10% conventional mortgage selling at par would have a duration of about 8.4 years if prepayments were disallowed.1 In practice, of course, prepayments shorten durations of mortgage pools considerably. For example, a prepayment rate of 5 percent of outstanding mortgages per year would reduce duration to 6.2 years. The peculiarity of IC/PC securities is that the risk of interest—rate increases is borne overwhelmingly by the owner of the principal—only security. The
  • 4. More Mortgage Info duration of the P0 portion greatly exceeds that of the underlying mortgage pool, while the duration of the 10 portion is correspondingly smaller. In fact the IC portion is likely to have negative duration, and thus potentially may serve as a hedging asset for fixed—income portfolios. This disparity in interest—rate exposure derives primarily from the interaction of prepayment behavior with interest—rate movements. When interest rates increase, the value of the P0 security falls for two reasons. First, future repayments of principal are worth less as the discount factor for the time value of money increases. Second, mortgage prepayment rates fall when interest rates rise, thereby increasing the average time until repayment of principal. The increase in the time until receipt of principal payments in conjunction with the increase in the discount rate results in a substantial decrease in the present value of those payments. These factors lend the P0 security a duration substantially longer than that of the underlying pool of mortgages. - In contrast, the 10 portion of the mortgage is affected in offsetting ways by interest rate movements. A decline in interest rates increases the present value of scheduled interest payments, but simultaneously increases the incidence of prepayments of principal. Since these prepayments terminate the stream of interest payments made on the mortgage pooi, they lower the value of the 10 security. The net effect on the value of the 10 security may be either positive or negative. However, for interest rates near the coupon rate of the mortgage pool, prepayments tend to increase enough in response to a fall in the interest rate that the 10 security loses value. In this empirically relevant region, the termination of interest payments dominates the effect of lower discount rates, resulting in a negative duration for the IC security. —2—
  • 5. More Mortgage Info To illustrate these points, consider a 30—year l00,0O0 mortgage with a 10% coupon rate. If prepayments were disallowed, then 84.2% of the present value of the total cash flows on the loan would derive from the interest component of payments while only 15.8% would derive from principal repayments. At the other extreme, if the mortgage were prepaid immediately, an Interest—only claim would become worthless while the value of the principal claim would jump from 15,80O to the principal balance of l00,00O. The effect of prepayment behavior is examined in Table 1 where prepayment per year is assumed to be a constant fraction of outstanding mortgages. The effect of prepayment experience is evident. An unanticipated increase in the prepayment rate from 5% to 7.5% would, even without coincident interest—rate movements, reduce the value of interest payments from 6l to 53.2 per 100 principal balance, inducing a capital loss to an 10 security holder of 12.8%. The corresponding gain on the P0 security would be from 39 to 46.8, for a capital gain of 20%. These calculations are incomplete, of course, because they ignore the interaction between prepayment behavior and changes in interest rates, but they do illustrate the wide swings in the relative shares of the mortgage value that accrue to interest versus principal claimants when prepayment rates change. Market values in practice should be even more volatile than suggested by Table 1 since prepayment rates in fact vary in response to interest—rate swings. The weighted average of the durations of the 10 and P0 securities must equal the duration of the underlying pooi of mortgages. Thus, the great disparity in durations of the component securities are necessary counterparts: the short or negative duration of the 10 security must be matched by correspondingly long durations of the P0 security. —3—
  • 6. More Mortgage Info Table 1: Components of Mortgage Values Prepayment Rate Percent of Value Due Percent of Value Due (per year) to Interest Payments to Principal Repayments 0.0% 84.2% 15.8% 2.5 71.0 29.0 5.0 61.0 39.0 75 532 46.8 10.0 47.1 52.9 15.0 38.1 61.9 20.0 31.9 68.1 25.0 27.4 72.6 —4—
  • 7. More Mortgage Info 2. Contingent—Claims Analysis The right to prepay a mortgage is in essence a call option that gives the homeowner the right to call back the loan from the lender at a price equal to the scheduled balance remaining on the loan. Thus, mortgage—backed securities may be valued using the same techniques that have been developed for other option—valuation problems. In fact, option—pricing techniques have been applied to GNMA mortgage—backed security valuation by Dunn and McConnell (1981a, 198lb), Brennan and Schwartz (1985), and others. Here, we apply similar techniques to the valuation of the IC and P0 components of a mortgage—backed pool. Following their lead, we assume that there are two types of mortgage prepayments: economically—motivated prepayments (and refinancings) that exploit interest rate declines, and "autonomous" prepayments that arise when homeowners change their residences. We will assume that 5% of all outstanding mortgages prepay for autonomous reasons in each year. Such a simplistic specification is arbitrary, but does little harm to the analysis of the interest—rate dependence of these securities, which 2 depends primarily on economically—motivated prepayment. Economically—motivated prepayment will occur when the interest rate reaches a critical point at which refinancing is optimal for the homeowner. This critical point will be determined by the process under which interest rates evolve over time. We will assume that the interest rate is expected to increase when it is below 10% and to fall when above 10%. Hence, 10% is the natural or long—run equilibrium value of the interest rate. The épeed with which rates are impelled toward that long—run value is assumed to be proportional to the difference between the interest rate and its long run 3 equilibrium value. —5—
  • 8. More Mortgage Info In addition to the expected drift in the interest rate, there are continuous shocks to rates due to unanticipated economic events. We model interest rate uncertainty as increasing with the level of rates, specifically that the variance of the interest rate is proportional to the level of the rate.4 In our numerical simulations, we set the proportionality constant equal to .25. At a 10 percent interest rate, this results in a standard deviation of the interest rate of 1.6 percent annually. Using this particular set of assumptions, we can use a valuation model to examine the response of 10, P0, and mortgage—pool values to interest rate changes. Our mathematical approach is modelled after Brennan and Schwartz (1977), which provides a full discussion of the techniques used to value interest—rate—dependent option—like securities. In brief, the valuation methodology uses the dynamics for interest rate movements given in footnotes 2 and 3 to derive the corresponding dynamics for the value-of interest—rate dependent securities. These, together with 'boundary conditions" for the values of the security at extreme values of the interest rate orat optimal prepayment dates, uniquely determine both the value of the security at all points and the optimal prepayment schedule. In our model, we employ a version of the liquidity preference theory, and assume that the expected risk premium earned by each security is proportional to the instantaneous standard deviation of that security's rate of return, with a proportionality constant of 0.1. Such a specification generates a liquidity premium of about 1.5% for an 8—year duration asset. Figure 1 is a graph of the value of the 3 securities (10, P0, and the mortgage pool itself) backed by a mortgage pool with a coupon rate equal to the long—run equilibrium interest rate, 10%, as a function of the current —6—
  • 9. More Mortgage Info market interest rate. The mortgage pool is assumed to have been issued 10 years ago with an original life of 30 years. The current principal value is 90.78 per l00 original principal. Notice that, as anticipated, the value of the PC security falls most dramatically with interest rate increases, especially at interest rates near the optimal prepayment point of about 8 percent. As economically—motivated prepayment becomes more likely at lower interest rates, the value of the P0 security rises dramatically. In contrast, the 10 security falls in value with interest rate decreases, even at rates as high as 14%. Like the PC, the value of the IC security is most sensitive to the interest rate near the optimal economic—prepayment point. These interest—rate sensitivities are even more evident in Figure 2, which depicts the durations of the securities as functions of the interest rate. The duration of the mortgage pool is nearly 3 years at high interest rates. Without prepayment, it would be about 6 years. The seemingly—large difference in duration is due both to the incidence of autonomous prepayments and to the threat of economic prepayment. Even at an interest rate of 147., such a threat is not trivial since the interest rate at that point is drifting downward to its long—run equilibrium value of 10%. The duration of the mortgage is even shorter at lower interest rates since economic prepayment is that much more imminent. The duration of the P0 security is far larger. For larger values of the interest rate, it is roughly double that of the mortgage pool. At an interest rate of 10%, the duration of the PC is 13 years, roughly 5 times that of the mortgage. From there, duration rises dramatically to 60 years at an interest rate just above the prepayment point. —7—
  • 10. More Mortgage Info The duration of the IC security is, in contrast, negative and of quite large magnitude at interest rates below 1OZ. At an interest rate of 11 percent, duration Is 52 years; at 10 percent it is 58 years. From there duration spikes downward even more dramatically. At the optimal economic prepayment point duration is essentially infinitely negative.5 These values are more extreme than one would expect to observe in reality since the valuation model assumes that all outstanding mortgages are prepaid at the optimal moment, when in practice some homeowners will defer prepayment for reasons not captured by the model. While the model allows for suboptimal (autonomous) prepayment, It does not allow for suboptimal non—prepayment. Nevertheless, the qualitative pattern of strip values Illustrated In Figures 1 and 2 will be observed in practice, and 10/PC strips do empirically exhibit large durations. Indeed, Figure 5, which traces out estimates of actual 10 and P0 strip values during a period of rising interest rates is remarkably similar to Figure 1. Other (nonreported) simulations replicate the analysis of Figures 1 and 2 for mortgage coupon rates of 8 and 12 percent, thus bracketing the long—run equilibrium interest rate. While the optimal economic—prepayment points differed from the analysis of Figures 1 and 2, the qualitative patterns that emerged were otherwise identical. 3. Investment Implications The peculiar interest rate exposures of the 10/PC securIties create both opportunities and risks for their investors. The interest—rate exposure of the P0 security is apparent. Nevertheless, such securities may be useful —8—
  • 11. More Mortgage Info portfolio tools for investors seeking very—high—duration assets. For example, pension funds with long—duration liabilities might find PC securities useful for immunization purposes. 10 securities offer hedging opportunities for investors holding more conventional fixed—income securities. For example, a thrift institution with holdings of conventional mortgages could offset some of its interest rate exposure by holding part of its portfolio in mortgage—backed 10 securities with negative duration. 4. Empirical Evidence While the valuation model presented above is useful for analyzing the properties of 10/PC securities, the particular values derived are dependent on assumed autonomous prepayment rates and on the posited process for the evolution of interest rates. One would like a valuation procedure that is consistent with market information as reflected in prices of other traded assets. Fortunately, such data do exist, and market assessments of the values of the lO/PO components of some mortgage poois can be computed directly from these data. Hence, the "proper" market prices for the lO/PO components of at least some mortgage poois can be inferred. Completely stripped mortgage—backed securities tend to be privately placed, and to date have been traded only erratically on the secondary market. Consequently, investment bankers cannot easily rely on market values of outstanding strips to price newly issued securities. However, FNNA has issued partially stripped securities that are actively traded that can be used to infer the market values of IC/PO securities. This inference is made —9—
  • 12. More Mortgage Info possible because the partial strips allocate principal and interest in different proportions to different—class securites. To illustrate, consider the issues of "B" and "C" series securities by FtThIA in the letter half of 1986, in which two 9 percent coupon mortgage—backed securities (MBSs) were divided up so that the premium classes received 2/3 of the interest and 1/2 of the principal payments, while the discount classes received 1/3 of the interest and 1/2 of the principal. The premium class, therefore effectively became a 12% security ( 9% x 2/3 1/2) while the discount class was effectively a 6% security C = 9% x 1/3 1/2). (However, these synthetic securities would not behave precisely like original—issue 12 or 6 percent coupon mortgage pools since the prepayment behavior of the "synthetic" securities would be tied to the 9% coupon rate of the underlying mortgage pools. If one were to take a long position in the premium—class security and a short position -in the discount—class security, the principal payments would net out to zero, and one would be left with a three percent 10 strip on the underlying 9% coupon mortgage pools. Therefore, three times the value of the price difference between the premium and discount securities equals the value of a pure 9% 10 strip. Substracting the value of that 10 strip from the sum of the values of the discount and premium securities then gives the value of a "synthetic" P0 position on the 9% mortgage pooi. The key to this procedure is that the premium and discount securities are written on the same underlying MBS and so have identical prepayment exposure. Long and short positions on different—coupon passthroughs would create Interest and principal—only securities only until the prepayment behavior of the two passthroughs diverged. Goldman Sachs supplied us with price data f or 3 types of partial strips: —10—
  • 13. More Mortgage Info the B" and "C" series just discussed In which 9% pools were split into 6 and 12 percent securities, the "D" series, in which an 8.5% coupon MBS was split into 11% and 6% securities, and the "F", "G", "H", and "I" series, in which 9% coupon MBSs were split into 11.5% and 6.5% securities. Using these data we created three synthetic 10 strips and three synthetic P0 strips. The inferred prices of the 10 and P0 strips over time are presented in Figures 3 and 4. The three 10 and P0 prices all tended to move together over time, which is gratifying, given that the underlying mortgage coupons are similar and thus should have similar prepayment behavior. The most dramatic price movements took place in April 1987, when the bond market fell sharply. Prices of mortgage passthroughs (obtained by adding together the prices of the premium and discount securities) fell as well. Figure 5 shows that the value of the P0 component fell far more dramatically than the value of the overall MBS, confirming the extremely long duration of this asset predicted by the previous sections. In contrast, the value of the 10 security actually rose, also confirming the theoretical prediction of a negative duration, and indicating that prepayment activity was expected to decline sufficiently to more than offset the increase In the discount factor applied to 10 payments. 5. Summary We have shown that lO/PO securities are highly sensitive to the prepayment behavior of the underlying mortgage pooi. Because that behavior varies systematically with the interest rate, and because prepayments affect the values of 10 and P0 components in opposite ways, the Interest—rate riàk of —11—
  • 14. More Mortgage Info strip securities can differ substantially from that of the underlying mortgage pooi. The P0 component has much longer duratlonthan the underlying mortgage pool. In contrast, the 10 component typically will have a negative duration, at least in ranges for which interest—rate movements induce meaningful changes in mortgage prepayment behavior. The distinct durations of these securities make them interesting candidates for immunization of long—term obligations or for hedging the value of fixed income portfolios. We've shown how market prices of partially—stripped MBSs that are actively traded on secondary markets can be used to infer market values of pure lO/PO strips. This inference method is potentially of value to issuers and purchasers of such strips. Recent market data is fully consistent with the theoretical insights offered by our valuation model. When interest rates spiked last April, P0 values fell far more dramatically than those of the underlying mortgage pooi while 10 values actually rose. —12—
  • 15. More Mortgage Info Footnotes 1. Duration is, strictly speaking, the weighted average of the times until receipt of each payment from a security, with weights proportional to the present value of each payment. For mortgages with possible prepayments, such a definition is problematic since the cash flow stream will vary with prepayment experience. Throughout this paper, I will use duration in a looser, but more common, context as the interest—rate elasticity of a security's value, that is, as the proportional change in the security's price due to a 1 percent change in its yield to maturity. 2. This simple rule is probably reasonably realistic. Although prepayment rates generally are lower in early years of mortgage lives, before they ultimately level off, mortgage defaults are generally higher in the early years. Because these mortgages are insured, a default is essentially equivalent to an autonomous prepayment from the perspective of the lender, and the sum of the two sources of autonomous prepayments might be relatively stable. 3. This specification can be written formally as, E(dr/dt) = k(.lO—r), where dr/dt is the time derivative of the interest rate, E is the expectation operator, and k is the proportionality constant, which we set equal to .2 in our illustrative examples below. —13—
  • 16. FIGURE 1 SECURITY VALUES 100- - o Th2rge (1) LjJ -J 60- > >- strip 40- 10 strip 20- / Legend MORTGAGE POOL / 10 STRIP 1 — P0 STRIP 0- I I I I I I I More Mortgage Info 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 INTEREST RATE
  • 17. FIGURE 2 More Mortgage Info SECURITY DURATIONS 100 75 50 z (I-) 0 'S F- 25 'S 5' — — DC' strip a 0 / >- TO strip F- —25 0 Ui (I) —50 / / / Legend —75 MORTGAGE POOL JO STRIP / P0 STRIP —100 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 INTEREST RATE
  • 18. Figure 3 Synthetic. 10 Strip Prices 4-7 46 4-5 44 4.3 42 41 N: L .3a — I ..i ':' .34 .i .1 .3 1 3 Ij r /r .3,' 2 4/ 1 4/22 More Mortgage Info r1cT 0 (B,c::) + ([:t) 4. (F1c-H,I)
  • 19. Figure 4 Synthetic P0 Strip Prices More Mortgage Info •7# 71 7fl 69 j i_i j b kD 5.3 s:jl (1 59 58 -r '-'p 56 54 5.3 51 51j #-, ,r .3/2 4/1 4/22 1987 0 (E4.C:) + ID) > (F,i31H,i)
  • 20. Figure 5 10 /' P0 Strip Prices More Mortgage Info (B 0) 75 7fl 65 E;fl 55 L. U- 50 45 40 35 3 Ij "'I 3/2 4/1 4/22 0 P0 1 97 + 10
  • 21. More Mortgage Info 4. Formally, we specify that, Variance(dr/dt) = sr, and set s = 0 .5. 5. The value of the 10 srip is zero if the pool is repaid. Hence, a small increase in the interest rate from the prepayment point to a value just above it, Increases the value of the 10 strip from zero to a positive value, which is an infinite percentage increase. —14—
  • 22. More Mortgage Info References Michael Brennan and Eduardo Schwartz. "Savings Bonds, Retractable Bonds, and Callable Bonds," Journal of Financial Economics, 5 (1977), 67—88. Kenneth B. Dunn and John J. McConnell. "A Comparison of Alternative Models for Pricing GNMA Mortgage—Backed Securities, Journal of Finance, 36 (May 1981), 471—484. _____________________________ "Valuation of GNNA Mortgage—Backed Securities," Journal of Finance, 36 (June 1981), 599—616. —15—