Mortgage Derivatives and Risk Management

 
REAL ESTATE 410
RMBS II
 
Spring 2017
 
1
 
Topics
 
Mortgage derivatives
Interest Only / Principal Only Structure
Collateralized Mortgage Obligations
Alternative CMO Structures
 
2
Introduction
 
What is a derivative security?
A 
derivative security 
is a security that 
derives its value from the
value of another security
, which is referred to as the underlying
security.
Mortgage derivative securities derive their values from the values of
the underlying mortgages.
MPT and MPTB can be technically viewed as mortgage derivatives.
What about MBB?
3
Introduction
 
To date we have focused on mortgage-backed bonds and
mortgage pass-throughs.
As noted, MPTs and MPTB are technically mortgage derivatives.
However, these can be seen as 
first-generation MBS
.
These are important assets, but they are really only part of the
story of the secondary mortgage markets.
The second part of that story deals with the 
more
technologically-advanced mortgage securities
, i.e., mortgage
derivative securities.
4
 
Mortgage Derivatives
 
Three 
most
 common types of mortgage derivatives:
Interest Only (IO) mortgage strips
Principal Only (PO) mortgage strips
Collateralized Mortgage Obligations (CMOs)
Commercial Mortgage Backed Securities (CMBS) are structured similar
to CMOs but are collateralized by commercial mortgages rather than
home mortgages and therefore have a different risk profile
 
5
Mortgage Derivatives
 
So why were these mortgage derivatives created?
They allow investors to 
more precisely manage risk 
than they
can with the underlying primitive security or the first-
generation MBS.
Remember that investors in MPTs and MPTBs will be exposed to the
same risks present in the underlying mortgage pool.
This is really why all derivatives, including options, futures, and
forwards, exist in the first place.
6
 
Mortgage Derivatives
 
IO, PO and CMOs allow investors to 
control much more
precisely the type of interest rate risk 
that they want to
bear.
We will begin by examining IO and PO securities, and then
CMOs.
We will cover CMBS in the next chapter.
CMBS allow investors to control much more precisely the default
risk that they bear.
 
7
MBS and Risk
 
Our analysis of MBS shows that changes in interest rates can
affect a mortgage pool in two distinct ways:
A 
reduction in interest rates 
will result in increased 
prepayments
,
causing the 
MBS not gaining as much value 
as a non-prepaying
asset.
An 
increase in interest rates 
causes 
extension (interest rate) risk
.
The 
value of the MBS drops 
because you discount the cash flows at
a higher rate, 
for a 
longer time, due to the lack of prepayments.
8
MPT and Risk
Under a normal 
agency
MPT
 pool, 
all investors
receive their proportional
share of the cash flows
each month.
9
 
More importantly, all 
investors bear the same types risks
.
It may be possible, however, to structure (i.e. design) a security
that somehow 
carved up the cash flows 
so that all 
investors
did not have the same risks
.
IOs and POs
 
They change cash flows that the investors were entitled to.
Instead of having a single bond that all investors owned (as is
the case of MPT), we can create 
two classes of bonds
:
IO Bond:
The investors receive all of the interest paid each month, for the
life of the bond, but none of the principal.
PO Bond:
The investors receive all of the principal paid each month, but
none of the interest.
10
 
IOs and POs
 
Now it would seem that stripping payments into IO and PO
should not make that much of a difference, but it completely
changes the risks that investors in each of these securities face.
Remember, more prepayments results in more principal repayments
and less interest payments.
More importantly, this structure makes the risk very
manageable for investors.
 
11
IOs and POs
12
IOs and POs
 
For now, assume that we have a pool with a $1,000,000
balance and a 10% WAC.
Suppose the pool backs two securities: an IO piece and a
PO piece.
PO holder …
Since you only receive principal, the 
total dollars 
that you will receive
over the life of the PO is $1,000,000
.
You are guaranteed to (eventually) receive this cash.
You will receive some principal each month.
13
 
IOs 
and
 POs
 
PO holder …
You will 
pay less than $1,000,000 to buy this PO
, since the
difference between what you pay and the $1,000,000 is, ultimately
how you earn your return on the asset.
Consider if you purchased the PO today for $600,000. The best thing
that could possibly happen would be if everybody in the pool prepaid
their loans next month. You would get your full $1,000,000 in one
month!
The 
worst thing 
that can happen is if 
nobody prepaid 
at all.
 
14
IOs and POs
 
IO holder …
You will 
receive the 10% coupon 
on the principal, but that is it.
If nobody prepaid
, and the loans were outstanding for 30 years, you
would receive 
total payments of $2,159,257
.
  
360*8,775.72 – 1,000,000 = $2,159,257
On the other hand, 
if everybody prepaid after month 1
, you 
would
only earn the interest due for that month
.
15
 
IOs and POs
 
IO holder …
If everybody prepaid after month 1, the total cash flow from the IO
investment would be: $8,333.33.
1,000,000*0.10/12 = $8,333.33
Clearly the IO investor would prefer for there to be very few
prepayments.
 
16
IOs and POs
 
Contrasting the risk profile of the IO and PO investments.
PO Investor:
Wants to recover principal as quickly as possible, so 
loves
prepayment
, 
loathes extension
.
prepayments increase when interest rates fall; you 
buy a PO when you
expect rates to fall
.
PO investor 
bears the risk that rates will rise
. It is this risk that the
market is paying you to bear.
17
IOs and POs
 
Contrasting the risk-profiles of IO and PO investments:
IO Investor:
Is 
devastated by prepayments
. Wants borrowers to hold onto their
loans for as long as they possibly can.
A decline in interest rates will trigger a devastating wave of
refinancing, destroying the value of the IO.
IO investor 
bears the risk that rates will fall
, and it is this risk that
the market is paying you to bear.
18
IOs and POs
 
Intuitively, then, you can tell something about how IOs and POs will
react to interest rate changes:
IOs
 will tend to 
decline in value when interest rates fall
, and
increase, or at least hold their value, when they rise.
POs
 will tend to 
increase in value when interest rates 
fall and
decrease in value when rates rise.
The pricing of the strips and the MPT using a dynamic repayment
model and assuming a return spread of 200 bps for both the IO and
PO pieces will look like this.
19
 
IOs and POs
 
20
 
IOs and POs
 
There are several points you want to take away from this chart.
The 
IO is generally less valuable than the PO 
– holding the
required return the same.
The 
PO has a relatively symmetric distribution of prices
, much
more so than either the MBS or the IO.
The 
IO is highly asymmetric 
in its distribution.
We can clearly see in this how the 
prepayment function is
radically affecting the IO value
.
 
21
 
IOs and POs
 
22
 
Effect of Interest Rates on IO, PO, and MPT Prices
IOs and POs
 
Clearly we can see that we 
have segregated 
out the
prepayment and extension risks
.
A person that was 
convinced that rates were going to go down
(or that wanted to hedge against that risk) would 
buy the PO
.
A person that was 
convinced that rates were going to go up
 (or
that wanted to hedge against that risk) would 
buy the IO
.
23
 
IOs and POs
 
So we can see that just by a simple reconfiguration of the
cash flows already contained within the MBS into IO and
PO, we are able to radically reallocate risk.
Note that 
this is a real economic service
 – it is not just
paper pushing.
An investor can select which risk, prepayment or extension, that they
want to bear, and not bear the other risk.
 
24
 
IOs and POs
 
The 
market is served 
because this structure allows a 
more precise
allocation of risk 
– which is the only reason a financial market
exists.
This makes mortgage securities palatable to investors that would
otherwise never be willing to invest in them.
This 
expands the universe of 
mortgage 
investors
.
This 
helps homebuyers 
because now there is now a much larger
group of people that are willing to lend (indirectly) in the housing
market. This 
lowers mortgage contract rates!
 
25
 
IOs and POs
 
A couple of important notes.
Fannie, Freddie, and Ginnie do not issue IO and PO combinations
directly. An investment bank will buy the MBS (MPT) in the secondary
market, and then create the IO-PO on their own. The investment bank
then  sells the IO and PO bonds to investors.
Note that the investment bank hopes that when they sell the IO and PO
separately that it will total to more than the cost to buy the MPT.
In our example, we kept the return spread for the IO and the PO the
same. In reality the IO is considered much riskier so it will have a higher
required return.
 
26
 
Mortgage Obligations
 
The IO and PO combination is a straightforward method for
separating prepayment and extension risk that are embedded
in a mortgage, but they are not the only way.
In the middle to late 1980s, a number of securities dealers
began to develop a type of security known as a Collateralized
Mortgage Obligation, more commonly referred to by the
acronym CMO, that use a different structure to allocate
mortgage risks.
 
27
 
CMOs
 
CMOs separate out the prepayment and extension risks in a
very different manner from an IO and PO structure.
They do it by assigning 
different priority of principal payments
to different investors.
This not only allows one to separate prepayment and extension risk,
but also allows one to develop some other very innovative uses for
mortgages.
Generally 
CMOs are more flexible than are IOs and POs
.
 
28
CMOs
 
The basic idea behind a CMO is that we 
prioritize the receipt of
principal 
among the investors.
The CMO is formed by a securities dealer purchasing MBS (MPT)
securities either directly from the issuer or on the open market.
The dealer then 
creates multiple bonds
 (tranches) that they sell
to investors.
The 
“senior” tranches receive all of the principal 
(including
prepayments) 
first
.
Once the most senior tranche is paid off, then (and only then) will the
second most senior tranche be paid principal, and so on.
29
 
CMOs
 
Unlike with the IO-PO combination 
(which you can think of
as consisting of two tranches, an IO and a PO tranche), 
CMO
tranches generally receive both interest and principal
,
although the 
timing of principal 
payments will 
depend on
prepayments and
 of course tranche 
seniority
.
Generally 
all tranches receive monthly interest payments
,
until their principal is paid down.
 
30
 
CMOs
 
Let’s take a look at a very simple CMO structure with an
underlying collateral of $100 million with a WAC of 8% and a
WAM of 360 months.
Four tranches, called A, B, C, and D. Each tranche is “assigned”
$25 million of principal, with the “A” tranche being paid
principal first, the “B” tranche second, the “C” tranche third, and
the “D” tranche last.
Each tranche is generally assigned its own coupon rate, but for
now we will assume that these are all set to the same rate as
the collateral.
 
31
 
CMOs
 
The way this works, then, is that each month the principal that
is received is paid to the A tranche, and its balance is reduced
by the amount of the payment.
Once A has been completely paid off, then B begins to receive
principal, etc.
Every tranche is paid interest every month.
 
32
 
33
 
CMOs
MBS Collateral
$100 Million
A Tranche
$25 Million
B Tranche
$25 Million
C Tranche
$25 Million
D Tranche
$25 Million
Monthly
Principal
Monthly
Interest
 
Initially the “A” tranche receives
ALL of the principal generated
by the collateral. The other
tranches only receive interest,
based on their balance and
coupon.
 
34
 
CMOs
MBS Collateral
Now, $75 Million
A Tranche
$25 Million
B Tranche
$25 Million
C Tranche
$25 Million
D Tranche
$25 Million
Monthly
Principal
Monthly
Interest
 
Once the “A” tranche has
received $25 Million in principal,
they no longer receive any cash
flow, and the “B” tranche
receives all of the principal.
 
35
 
CMOs
MBS Collateral
Now, $50 million
A Tranche
$25 Million
B Tranche
$25 Million
C Tranche
$25 Million
D Tranche
$25 Million
Monthly
Principal
Monthly
Interest
 
Similarly, once the B Tranche is
paid its $25 million, it receives
no more cash flows and the C
tranche begins to receive its
principal cash flow.
 
36
 
CMOs
MBS Collateral
Now, $25 million
A Tranche
$25 Million
B Tranche
$25 Million
C Tranche
$25 Million
D Tranche
$25 Million
Monthly
Principal
Monthly
Interest
 
Finally, the C Tranche is paid
off, and then the D tranche
begins to receive all of the
remaining principal and interest
in the pool.
CMOs
 
First, let’s 
examine the cash flows 
that are being generated by the
collateral, and then how they are broken down into payments for each
of the tranches.
Initially we will model the CMO assuming 
constant interest rates and
no prepayments
, but then we will relax each of those assumptions.
Just to limit the number of digits we have to use, we will scale the principal
amount to 100,000, instead of 100,000,000, so all amounts are in units of
$1000.
First, let’s examine the monthly cash flows from the collateral. It will
look almost exactly like a normal mortgage, with C=WAC and T=WAM.
We are also going to assume 
no servicing 
initially.
37
 
CMOs
 
38
CMOs
39
 
CMOs
 
40
 
CMOs
 
41
 
CMOs
 
So we can generally think of an algorithm for determining the
cash flows to be:
1.
Determine interest and principal paid by collateral.
2.
From interest portion of collateral payment, allocate interest to each
tranche based on its balance and coupon.
If not enough interest from collateral, then use principal
.
3.
Give principal to most senior tranche remaining. If principal is more
than amount owed to senior tranche, pay off senior tranche and begin
to pay next-senior tranche.
 
42
43
CMOs
 
Remember that with no prepayments, the monthly cash flows
are level, although the principal and interest proportions
change by month.
 
CMOs
 
First, let’s focus only on the principal portion.
 
44
45
 
Each CMO tranche is paid its principal sequentially. Since
the tranches are also paid interest each month, this leads
to another set of graphs:
CMOs
46
 
Each tranche receives a level cash flow, until its principal begins to
pay down, at which time its cash flow increases, but then stays
constant until its is paid off. Let’s focus on just the “B” Tranche.
CMOs
 
47
 
CMOs
 
So we can see that for the first 15 years, the payment is
perfectly level, followed by a dramatic jump in payment
amount for roughly 8 years.
48
 
If we examine the principal and interest components of the monthly
payment amounts, we can see how the decline in the interest payment is
exactly offset by the increase in principal payments.
 CMOs
 
CMOs
 
This same general pattern holds for any sequential payment
tranche like these.
It is also instructive for understanding what is happening with
the CMO to examine what happens to the balance of the
collateral and the tranches over time.
Let’s begin with the overall balance of the collateral.
 
49
 
50
 
As with any FRM without prepayments, the balance has this rather familiar
shape. Now, let’s decompose this into the balances of the individual tranches:
 
CMOs
 
51
 
Keep in mind that the scale on the Y-Axis is the aggregated
balance of each of the remaining tranches at each time!
 
CMOs
CMOs with Prepayments
 
Of course we really are going to have 
prepayments
, so how do
they affect the cash flows to the tranches?
Prepayments affect the individual tranche’s cash flows dramatically.
We have just seen how the cash flows look like without
prepayments. Let’s begin with a simple 
100% PSA assumption
.
The cash flows now appear as:
52
53
 
First, the cash flows associated with the collateral are
quite different.
CMOs with Prepayments
54
 
If we focus on the principal alone, we still notice a
dramatic shift in the payment pattern.
CMOs with Prepayments
55
 
In this graph we allocate the principal payments by tranche, and we
can see the dramatic effect this has on the timing of the cash flows.
CMOs with Prepayments
56
 
Indeed, if we look at the entire cash flow allocated to each
tranche by month we see a really interesting pattern.
CMOs with Prepayments
 
57
 
CMOs with Prepayments
 
If we focus on just the one “B” tranche, we see that we still get a
shortened period of cash flows, but it still starts off with a constant
payment amount followed by the principal payments.
 
58
 
Recall how the balance of an MBS evolves under the PSA model…
 
CMOs with Prepayments
 
59
 
then this demonstrates how the aggregated balance outstanding
by month, per tranche, evolves.
 
CMOs with Prepayments
 
CMOs with Prepayments
 
So one question that we might really want to examine is, how
do our tranches change given different PSA rates?
First, let’s look at a graph of Tranche B under different Scenarios.
Clearly as we increase PSA, the tendency is for the cash flows to occur
sooner.
 
60
 
61
 
This raises the inevitable question, what happens to the WAL of the
tranches as prepayments increase?
 
CMOs with Prepayments
 
CMOs with Prepayments
 
Obviously, prepayments will accelerate cash flows received by
investors, thus reducing WAL.
Its probably easiest to see this by simply plotting the WAL
values for each tranche as a function of the PSA level.
Note that we have not yet said what the discount rate For each
tranche should be. Therefore, so we cannot talk about duration
yet.
 
62
 
63
 
We have to be careful in interpreting this – as we raise PSA we reduce
WAL, but the ranking remains.
 
CMOs with Prepayments
CMOs with Prepayments
 
First, we notice that if we assume that we will have at 
least 
100%
PSA 
(a very reasonable assumption), then the 
A tranche is not
particularly sensitive 
to increasing the PSA.
At 100% PSA, WAL = 2.97 years, at 300% PSA it is 1.72 years, that is it still has
58% of the original WAL. The WAL is only reduced by 1.25 years.
Compare this with the C tranche:
At 100 PSA, WAL = 13.9 years, at 300% PSA, it is 6.39 years, this is, it still has
only 46% of the original WAL. The WAL is reduced 7.51 years.
Although not as “clean” as with an IO-PO structure, clearly the
prioritizing of cash flows affects
 
how sensitive individual
tranches are to prepayments
.
64
 
CMO Structure
 
Of course, normally we will not find a CMO with all of the tranches having
the same coupon and balance.
Usually the 
A tranche 
is considered the least volatile and will tend to have a
lower coupon
, with the coupon going up with the loss of seniority – 
What is
important off course is the investors’ required rate of return
.
Similarly, 
spreads will vary across the tranches 
of CMOs.
Obviously, it must be the case that the 
aggregate coupon of the
tranches cannot exceed the aggregate WAC of the collateral
, or the
CMO will not have the cash flows necessary to make the promised
payments.
 
65
CMO Structure
 
Generally, at some point there will be 
cash generated by the
collateral that will not be owed to any of the tranches
.
Who gets this?
This is part of the compensation of the deal sponsor!
Usually there is a 5
th
 tranche, known as the 
Residual (equity)
tranche
, that will receive any cash flows that are not owed to
any of the other tranches.
The 
residual has no principal assigned 
to it, it simply receives
any cash not allocated to anybody else, i.e., interest payment
and overcollateral leftovers.
66
 
CMO Structure
 
Originally residual tranches were held by the company that put the CMO
together. The residual piece represented then their “
skin in the game
”, a
sort of credit insurance against their having created the CMO incorrectly.
They later realized that they could sell the residual: the yields tended to
be very high on them and they were then “out” of the deal.
But the Dodd-Frank regulations adopted following the recent financial
crisis required MBS issued to keep at least 5% of the deal (
risk
participation/retention 
requirement), which may force then to keep this
tranche.
 
67
CMO Structure
 
A CMO with 
sequential tranches and a residual 
is known as a 
“Plain
Vanilla” CMO
, meaning that it has no fancy tranches associated with it –
most CMBS deal use this structure.
More complicated CMO structures include other types of tranches, such
as:
Accrual or “Z” tranche
IO/PO combination tranches
Planned Amortization Class (PAC)
Targeted Amortization Class (TAC)
Floater and Inverse-Floater Tranches
68
 
Z Tranche
 
A “Z” tranche is an accrual junior tranche, usually the most junior tranche,
and it starts off with a very, very small balance.
It 
earns a coupon like any other tranche
, 
but that coupon payment is
accrued 
rather than paid in cash and the 
money is used to pay down the
most senior tranche
.
Once the principal paydown on the tranche starts then the coupon is paid
in cash.
Why do this? Frequently Z’s are 
used to “support” other tranches
. The
deferred cash can be used to insure cash flows that are paid to the more
senior bonds (tranches).
 
69
Residual vs. Z Tranche
 
Obviously the Z tranche will have tremendous variance in terms of both its
cash flow and its balance.
The 
lower the prepayments 
early in the life of the CMO, the 
higher the Z
Tranche total payments
, although these are received later in time.
Similarly, the residual will have tremendous variation, but if anything will
be accentuated.
Realize that 
the later the residual starts to receive payments, the fewer
dollars it will receive
.
Early 
prepayments
 actually 
help the residual 
holder.
Again, prepayments differently affect the Z tranche and the residual.
70
IO-PO CMO Tranches
 
You can take any CMO tranche and split it into IO and PO two sub-
tranches. One sub-tranche receives interest only and the other
receives PO only.
Why do this instead of a simple an IO and PO combination for the
whole deal?
1.
One reason is that the 
market for pure IO/PO tranches may not be big
enough 
to handle the entire collateral amount.
2.
More importantly, however, is that 
if the IO/PO is not a senior tranche,
the IO holder has some protection against prepayments
.
Essentially the senior tranches absorb first prepayments.
The PO holder will also face more upside if prepayments are larger than initially
projected.
71
PAC Tranche
 
A 
Planned Amortization Class 
(PAC) tranche 
guarantees a specific cash
flow stream
 as long as prepayments remain within an upper and lower
PSA band, i.e., levels of prepayments.
PAC is a 
“companion” tranche 
to the normal sequential payment bonds.
As you can imagine, a 
PAC tranche would make the other tranches
riskier
 since their cash flows will become more volatile because of the
PAC. At the end of the day, this is just another way of parsing risk.
Generally, the PAC gets paid first
, until its scheduled cash flows are
made, and then the cash flows are sent to the sequential bonds.
But it also possible that a PAC be paid down simultaneously with the
sequential bonds. It depends on the size of the PAC
Again, a 
PAC reduces prepayment and extension risks
.
72
TAC Tranche
 
A 
Targeted Amortization Class 
(TAC) tranche is a 
variant of
the PAC
 tranche.
Unlike the PAC which guarantees a specific cash flow stream,
irrespective of prepayments in the pool, the principal of the
TAC will follow a single “targeted” prepayment rate 
(e.g.,
100% PSA).
This 
targeted prepayment rate 
is referred to as the 
TAC’s
pricing speed
.
Similar to PACs, TACs attempt to 
insulate the security holder
from the prepayment risk 
of the underlying mortgage pool.
73
 
Floater Tranche
 
A floater tranche 
pays a floating interest rate
.
The coupon adjust periodically to a fixed spread over an index
(similar to ARMs for lenders)
Floaters generally use similar interest rate indices as ARMs (e.g.,
Libor, cost of fund 11
th
 district FHLB).
Floaters are generally 
marketed or structured to meet the
need of institutional investors with floating-rate liabilities
(short interest rate positions).
 
74
 
Inverse Floater
 
The coupon of an inverse floater adjusts in the opposite
direction to its index (i.e., interest rate).
How is this done?
Often created within a CMO structure to 
hedge interest rate
risk stemming from a floater tranche
.
Rather than for portfolio hedging, these securities can also be
used to enhance portfolio yields
.
When would one want to invest in an inverse floater?
 
75
 
Pricing CMO
 
So how do you price a CMO, i.e., the tranches?
Pretty much exactly as we priced an IO/PO combination, except that now
we have to allocate cash flows (both principal and interest) across many
tranches instead of across the IO/PO tranches.
You need to use 
Monte Carlo simulation using a stochastic interest
rate process
 
and a dynamic prepayment model
 to generate the cash
flows, and then allocate them to each tranche.
You then 
discount each tranche by the appropriate rate plus credit
spread 
to get the price of the tranche.
 
76
Pricing CMO
 
Pricing a CMO using a stochastic interest rate process, a dynamic prepayment
model, and Monte Carlo, involves five distinct steps:
1.
Draw your interest rate paths from the stochastic process.
2.
Determine the cash flow generated by the collateral along each interest rate path.
3.
For each interest rate path, allocate that cash to the tranches based on their
seniority and the rules of the CMO.
4.
Discount the cash flows for each tranche back to time 0 for each of the tranches.
5.
Report the average price as the market value of the CMO and of the individual
tranches – of course you can still report standard deviations for each tranche.
As you can see, pricing a CMO (or its near-cousin, a CMBS – coming next), is not
that much more challenging than pricing a standard MPT.
The only real difference is that with the CMO you have the extra work of tracking the
cash flows to each of the tranches.
77
Pricing CMO
 
Remember, security issuers make their money by purchasing
the collateral and selling the A, B, C, and Z tranches.
We are assuming that they retain the residual (although they
could sell it in reality.)
What ultimately determines the profitability of the deal are
these two things:
The value of the residual
The difference between what the amount they pay for the collateral
and what the receive for tranches A, B, C, and Z.
78
Summary
 
Mortgage derivatives (IOs, POs, and CMOs) exist because for many investors
investing in “whole” mortgages is not desirable.
The derivatives allow investors to bear the risk that they want to bear and they
are willing to pay a premium for this.
For mortgage derivatives based on home mortgages, the risks are prepayment
risk and extension (interest rate) risk - default risk is generally not an issue.
The IO/PO combination uses a “brute force” way of separating the prepayment
and extension risk:
The IO holder bears the prepayment risk, the PO holder bears the extension risk.
CMOs provide a number of different mechanisms for tailoring the risks for the
investors.
79
 
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RMBS III
 
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Mortgage derivatives such as Interest Only (IO) and Principal Only (PO) strips, as well as Collateralized Mortgage Obligations (CMOs), offer investors a way to manage risk more precisely than traditional mortgage-backed securities. By allowing control over interest rate and default risks, these sophisticated securities play a crucial role in the secondary mortgage markets, enhancing risk management strategies for investors.


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  1. REAL ESTATE 410 RMBS II Spring 2017 1

  2. Topics Mortgage derivatives Interest Only / Principal Only Structure Collateralized Mortgage Obligations Alternative CMO Structures 2

  3. Introduction What is a derivative security? A derivative security is a security that derives its value from the value of another security, which is referred to as the underlying security. Mortgage derivative securities derive their values from the values of the underlying mortgages. MPT and MPTB can be technically viewed as mortgage derivatives. What about MBB? 3

  4. Introduction To date we have focused on mortgage-backed bonds and mortgage pass-throughs. As noted, MPTs and MPTB are technically mortgage derivatives. However, these can be seen as first-generation MBS. These are important assets, but they are really only part of the story of the secondary mortgage markets. The second part of that story deals with the more technologically-advanced mortgage securities, i.e., mortgage derivative securities. 4

  5. Mortgage Derivatives Three most common types of mortgage derivatives: Interest Only (IO) mortgage strips Principal Only (PO) mortgage strips Collateralized Mortgage Obligations (CMOs) Commercial Mortgage Backed Securities (CMBS) are structured similar to CMOs but are collateralized by commercial mortgages rather than home mortgages and therefore have a different risk profile 5

  6. Mortgage Derivatives So why were these mortgage derivatives created? They allow investors to more precisely manage risk than they can with the underlying primitive security or the first- generation MBS. Remember that investors in MPTs and MPTBs will be exposed to the same risks present in the underlying mortgage pool. This is really why all derivatives, including options, futures, and forwards, exist in the first place. 6

  7. Mortgage Derivatives IO, PO and CMOs allow investors to control much more precisely the type of interest rate risk that they want to bear. We will begin by examining IO and PO securities, and then CMOs. We will cover CMBS in the next chapter. CMBS allow investors to control much more precisely the default risk that they bear. 7

  8. MBS and Risk Our analysis of MBS shows that changes in interest rates can affect a mortgage pool in two distinct ways: A reduction in interest rates will result in increased prepayments, causing the MBS not gaining as much value as a non-prepaying asset. An increase in interest rates causes extension (interest rate) risk. The value of the MBS drops because you discount the cash flows at a higher rate, for a longer time, due to the lack of prepayments. 8

  9. MPT and Risk Under a normal agency MPT pool, all investors receive their proportional share of the cash flows each month. Monthly payments are collected by servicer And sent to FNMA/FHLMC. FNMA/FHLMC then distributes the payments proportionally to the investors in the MBS. More importantly, all investors bear the same types risks. It may be possible, however, to structure (i.e. design) a security that somehow carved up the cash flows so that all investors did not have the same risks. 9

  10. IOs and POs They change cash flows that the investors were entitled to. Instead of having a single bond that all investors owned (as is the case of MPT), we can create two classes of bonds: IO Bond: The investors receive all of the interest paid each month, for the life of the bond, but none of the principal. PO Bond: The investors receive all of the principal paid each month, but none of the interest. 10

  11. IOs and POs Now it would seem that stripping payments into IO and PO should not make that much of a difference, but it completely changes the risks that investors in each of these securities face. Remember, more prepayments results in more principal repayments and less interest payments. More importantly, this structure makes the risk very manageable for investors. 11

  12. IOs and POs Monthly payments are collected by servicer And sent to FNMA/FHLMC. All of monthly principal and prepayments sent to the PO investor. All of monthly interest less servicing and insurance fees is sent to the IO investor. 12

  13. IOs and POs For now, assume that we have a pool with a $1,000,000 balance and a 10% WAC. Suppose the pool backs two securities: an IO piece and a PO piece. PO holder Since you only receive principal, the total dollars that you will receive over the life of the PO is $1,000,000. You are guaranteed to (eventually) receive this cash. You will receive some principal each month. 13

  14. IOs and and POs PO holder You will pay less than $1,000,000 to buy this PO, since the difference between what you pay and the $1,000,000 is, ultimately how you earn your return on the asset. Consider if you purchased the PO today for $600,000. The best thing that could possibly happen would be if everybody in the pool prepaid their loans next month. You would get your full $1,000,000 in one month! The worst thing that can happen is if nobody prepaid at all. 14

  15. IOs and POs IO holder You will receive the 10% coupon on the principal, but that is it. If nobody prepaid, and the loans were outstanding for 30 years, you would receive total payments of $2,159,257. 360*8,775.72 1,000,000 = $2,159,257 On the other hand, if everybody prepaid after month 1, you would only earn the interest due for that month. 15

  16. IOs and POs IO holder If everybody prepaid after month 1, the total cash flow from the IO investment would be: $8,333.33. 1,000,000*0.10/12 = $8,333.33 Clearly the IO investor would prefer for there to be very few prepayments. 16

  17. IOs and POs Contrasting the risk profile of the IO and PO investments. PO Investor: Wants to recover principal as quickly as possible, so loves prepayment, loathes extension. prepayments increase when interest rates fall; you buy a PO when you expect rates to fall. PO investor bears the risk that rates will rise. It is this risk that the market is paying you to bear. 17

  18. IOs and POs Contrasting the risk-profiles of IO and PO investments: IO Investor: Is devastated by prepayments. Wants borrowers to hold onto their loans for as long as they possibly can. A decline in interest rates will trigger a devastating wave of refinancing, destroying the value of the IO. IO investor bears the risk that rates will fall, and it is this risk that the market is paying you to bear. 18

  19. IOs and POs Intuitively, then, you can tell something about how IOs and POs will react to interest rate changes: IOs will tend to decline in value when interest rates fall, and increase, or at least hold their value, when they rise. POs will tend to increase in value when interest rates fall and decrease in value when rates rise. The pricing of the strips and the MPT using a dynamic repayment model and assuming a return spread of 200 bps for both the IO and PO pieces will look like this. 19

  20. IOs and POs Pricing of IO, PO, and MPT using a Dynamic Model Histograms of MBS, IO and PO, 3000 Iterations 600 500 400 Frequency 300 200 100 0 180000 230000 280000 330000 380000 430000 480000 530000 580000 630000 680000 730000 780000 830000 880000 930000 980000 1030000 1080000 Price MBS IO PO 20

  21. IOs and POs There are several points you want to take away from this chart. The IO is generally less valuable than the PO holding the required return the same. The PO has a relatively symmetric distribution of prices, much more so than either the MBS or the IO. The IO is highly asymmetric in its distribution. We can clearly see in this how the prepayment function is radically affecting the IO value. 21

  22. IOs and POs Effect of Interest Rates on IO, PO, and MPT Prices MBS, IO and PO Prices at Various Rates 1400000 1200000 1000000 800000 Price 600000 400000 200000 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Rate MBS Price IO Price PO Price 22

  23. IOs and POs Clearly we can see that we have segregated out the prepayment and extension risks. A person that was convinced that rates were going to go down (or that wanted to hedge against that risk) would buy the PO. A person that was convinced that rates were going to go up (or that wanted to hedge against that risk) would buy the IO. 23

  24. IOs and POs So we can see that just by a simple reconfiguration of the cash flows already contained within the MBS into IO and PO, we are able to radically reallocate risk. Note that this is a real economic service it is not just paper pushing. An investor can select which risk, prepayment or extension, that they want to bear, and not bear the other risk. 24

  25. IOs and POs The market is served because this structure allows a more precise allocation of risk which is the only reason a financial market exists. This makes mortgage securities palatable to investors that would otherwise never be willing to invest in them. This expands the universe of mortgage investors. This helps homebuyers because now there is now a much larger group of people that are willing to lend (indirectly) in the housing market. This lowers mortgage contract rates! 25

  26. IOs and POs A couple of important notes. Fannie, Freddie, and Ginnie do not issue IO and PO combinations directly. An investment bank will buy the MBS (MPT) in the secondary market, and then create the IO-PO on their own. The investment bank then sells the IO and PO bonds to investors. Note that the investment bank hopes that when they sell the IO and PO separately that it will total to more than the cost to buy the MPT. In our example, we kept the return spread for the IO and the PO the same. In reality the IO is considered much riskier so it will have a higher required return. 26

  27. Mortgage Obligations The IO and PO combination is a straightforward method for separating prepayment and extension risk that are embedded in a mortgage, but they are not the only way. In the middle to late 1980s, a number of securities dealers began to develop a type of security known as a Collateralized Mortgage Obligation, more commonly referred to by the acronym CMO, that use a different structure to allocate mortgage risks. 27

  28. CMOs CMOs separate out the prepayment and extension risks in a very different manner from an IO and PO structure. They do it by assigning different priority of principal payments to different investors. This not only allows one to separate prepayment and extension risk, but also allows one to develop some other very innovative uses for mortgages. Generally CMOs are more flexible than are IOs and POs. 28

  29. CMOs The basic idea behind a CMO is that we prioritize the receipt of principal among the investors. The CMO is formed by a securities dealer purchasing MBS (MPT) securities either directly from the issuer or on the open market. The dealer then creates multiple bonds (tranches) that they sell to investors. The senior tranches receive all of the principal (including prepayments) first. Once the most senior tranche is paid off, then (and only then) will the second most senior tranche be paid principal, and so on. 29

  30. CMOs Unlike with the IO-PO combination (which you can think of as consisting of two tranches, an IO and a PO tranche), CMO tranches generally receive both interest and principal, although the timing of principal payments will depend on prepayments and of course tranche seniority. Generally all tranches receive monthly interest payments, until their principal is paid down. 30

  31. CMOs Let s take a look at a very simple CMO structure with an underlying collateral of $100 million with a WAC of 8% and a WAM of 360 months. Four tranches, called A, B, C, and D. Each tranche is assigned $25 million of principal, with the A tranche being paid principal first, the B tranche second, the C tranche third, and the D tranche last. Each tranche is generally assigned its own coupon rate, but for now we will assume that these are all set to the same rate as the collateral. 31

  32. CMOs The way this works, then, is that each month the principal that is received is paid to the A tranche, and its balance is reduced by the amount of the payment. Once A has been completely paid off, then B begins to receive principal, etc. Every tranche is paid interest every month. 32

  33. CMOs Initially the A tranche receives ALL of the principal generated by the collateral. The other tranches only receive interest, based on their balance and coupon. A Tranche $25 Million MBS Collateral $100 Million B Tranche $25 Million Monthly Principal C Tranche $25 Million Monthly Interest D Tranche $25 Million 33

  34. CMOs Once the A tranche has received $25 Million in principal, they no longer receive any cash flow, and the B tranche receives all of the principal. A Tranche $25 Million MBS Collateral Now, $75 Million B Tranche $25 Million Monthly Principal C Tranche $25 Million Monthly Interest D Tranche $25 Million 34

  35. CMOs Similarly, once the B Tranche is paid its $25 million, it receives no more cash flows and the C tranche begins to receive its principal cash flow. A Tranche $25 Million MBS Collateral Now, $50 million B Tranche $25 Million Monthly Principal C Tranche $25 Million Monthly Interest D Tranche $25 Million 35

  36. CMOs Finally, the C Tranche is paid off, and then the D tranche begins to receive all of the remaining principal and interest in the pool. A Tranche $25 Million MBS Collateral Now, $25 million B Tranche $25 Million Monthly Principal C Tranche $25 Million Monthly Interest D Tranche $25 Million 36

  37. CMOs First, let s examine the cash flows that are being generated by the collateral, and then how they are broken down into payments for each of the tranches. Initially we will model the CMO assuming constant interest rates and no prepayments, but then we will relax each of those assumptions. Just to limit the number of digits we have to use, we will scale the principal amount to 100,000, instead of 100,000,000, so all amounts are in units of $1000. First, let s examine the monthly cash flows from the collateral. It will look almost exactly like a normal mortgage, with C=WAC and T=WAM. We are also going to assume no servicing initially. 37

  38. CMOs We can calculate the monthly payment using our normal formula: ??? = $733.76 And we can then determine the interest and principal portions in month 1 in the normal ways: ???????? = 100,000 .08 12= $666.67 ????????? = 733.76 666.67 = $67.09 38

  39. CMOs How to allocate the principal and interest to the four tranches? All of the principal goes to A, reducing its balance next period by the $67.09. The interest is allocated based on the beginning balance for each tranche, and each tranche s coupon rate (which we have made the same for all four of our tranches, 8%.) ?????????= 25,000 .08 12= $166.67 ?????????= 25,000 .08 12= $166.67 ?????????= 25,000 .08 12= $166.67 ?????????= 25,000 .08 12= $166.67 39

  40. CMOs In month 2, we will still have the same uniform monthly payments from the pool (since we do not have prepayments in this example), but the breakdown of principal and interest is different. The balance of the collateral at the beginning of month 2 was 100,000 67.09 = $99,932.91 So the interest portion was: ???????? = 99,932.91 .08 12= $666.22 And the principal portion was ????????? = 733.76 666.22 = $67.54 40

  41. CMOs Once again we allocate the principal by simply giving it all to Tranche A. Remember, however, that the A tranche was paid some principal in month 1, so its month 2 balance is only: ???????2= 25,000 67.09 = $24,932.91 This means that the coupon paid to Tranche A will be less than the coupon paid to Tranches B through D. ?????????= 24,932 .08 12= $166.22 ?????????= 25,000 .08 12= $166.67 ?????????= 25,000 .08 12= $166.67 ?????????= 25,000 .08 12= $166.67 41

  42. CMOs So we can generally think of an algorithm for determining the cash flows to be: 1. Determine interest and principal paid by collateral. 2. From interest portion of collateral payment, allocate interest to each tranche based on its balance and coupon. If not enough interest from collateral, then use principal. 3. Give principal to most senior tranche remaining. If principal is more than amount owed to senior tranche, pay off senior tranche and begin to pay next-senior tranche. 42

  43. CMOs Total Monthly Cashflow, MBS 800.00 700.00 600.00 Dollars (in Hundreds) 500.00 400.00 300.00 200.00 100.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month Principal Interest Remember that with no prepayments, the monthly cash flows are level, although the principal and interest proportions change by month. 43

  44. CMOs First, let s focus only on the principal portion. MBS Principal Cash Flows 800.00 700.00 600.00 500.00 Dollars 400.00 300.00 200.00 100.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month 44

  45. CMOs Principal Payments by Tranche 800.00 700.00 600.00 500.00 Amount 400.00 300.00 200.00 100.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month A B C D Each CMO tranche is paid its principal sequentially. Since the tranches are also paid interest each month, this leads to another set of graphs: 45

  46. CMOs Monthly Cashflow by Tranche 800.00 700.00 600.00 500.00 Cash 400.00 300.00 200.00 100.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month A B C D Each tranche receives a level cash flow, until its principal begins to pay down, at which time its cash flow increases, but then stays constant until its is paid off. Let s focus on just the B Tranche. 46

  47. CMOs Tranch B Total Payment by Month 450.00 400.00 350.00 300.00 250.00 Dollars 200.00 150.00 100.00 50.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month So we can see that for the first 15 years, the payment is perfectly level, followed by a dramatic jump in payment amount for roughly 8 years. 47

  48. CMOs Tranche B Interest and Principal By Month 450.00 400.00 350.00 300.00 250.00 Dollars 200.00 150.00 100.00 50.00 0.00 1 19 37 55 73 91 109 127 145 163 181 199 217 235 253 271 289 307 325 343 Month Interest Principal If we examine the principal and interest components of the monthly payment amounts, we can see how the decline in the interest payment is exactly offset by the increase in principal payments. 48

  49. CMOs This same general pattern holds for any sequential payment tranche like these. It is also instructive for understanding what is happening with the CMO to examine what happens to the balance of the collateral and the tranches over time. Let s begin with the overall balance of the collateral. 49

  50. CMOs MBS Balance By Month 120000.00 100000.00 80000.00 Balance 60000.00 40000.00 20000.00 0.00 1 20 39 58 77 96 115 134 153 172 191 210 229 248 267 286 305 324 343 Month As with any FRM without prepayments, the balance has this rather familiar shape. Now, let s decompose this into the balances of the individual tranches: 50

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