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In this module we're going to discuss Prepayment risk and Mortgage

pass-throughs. Prepayment risk is a particular type of

risk that mortgage backed securities are exposed to.

Prepayment risk refers to the ability of homeowners to prepay their mortgages.

So mortgage holders or homeowners often have a option to prepay their mortgage

early. And that creates prepayment risk for

investors in mortgage-backed-securities. We're also going to discuss Mortgage

pass-throughs securities. A Mortgage pass-throughs is the simplest

example of a mortgage-backed security, and so we're going to spend some time as

well on this module, in this module, discussing pass-throughs.

Many mortgage holders in the US are allowed to prepay the mortgage principal

earlier than scheduled. Payments made in excess of the scheduled

payments are called prepayments. Now, there are many possible reasons for

prepayments. Number one, homeowners must prepay the

entire mortgage when they sell their home, and there are many reasons why

somebody might need to sell their home, maybe they're moving for a new job, maybe

they're getting divorced, and so on. Homer, homeowners can also refinance

their mortgage at a better interest rate. So for example say a homeowner took out a

mortgage when the interest rates were very high on mortgages, and maybe five or

six years later, they'd see that interest rates are much lower.

Well the ability to prepay allows the homeowner to pre-pay their mortgage and

then take out a new mortgage at a much lower level of interest.

A third reason is the homeowner may simply default on their mortgage

payments. Maybe they're behind on their payments,

they can't catch up and they smiply default.

In this case, if the mortgage is insured then the insurer will pre-pay the

mortgage as well. And finally, for another example, the

home might be destroyed by floods or fire or by some other catastrophe and

insurance proceeds in this case will pre-pay the mortgage.

So there are many possible reasons for pre-payments.

The second reason we've highlighted here is a very valuable reason.

It's the prepayment option that mortgage holders have.

In particular they can benefit when interest rates go lower.

And so this is a prepayment option and like options it has a positive value to

the owner of the option, in this case the US homeowner typically.

So prepayment modeling is therefore an important feature of pricing

mortgage-backed securities. And the value of some mortgage-backed

securities is extremely dependent on prepayment behavior.

Again, we'll come to some examples of mortgage-backed securities in later

modules. For now, we're going to consider the

simplest type of mortgage-backed security, and that is the Mortgage

pass-through. Now before I go on I should mention that

pretty much everything I'm going to be saying here is very US centric.

The mortgage markets are the markets from mortgage bank securities originated in

the US in the 1980s. And that's where most of the the modeling

and the if you like action in the mortgage market is taking place.

So I'm going to be focusing mainly on the US but that's fine.

Because pretty much everything I say will apply in some form or another to mortgage

markets generally. Also the bigger picture that I want to

get at here is the general idea of securitization and how mortgage-backed

securities and indeed asset-backed securities can be created.

How are Mortgage pass-throughs constructed.

Well in practice mortgages are often sold on to third parties who can then pool

these mortgages together to created mortgage-backed securites.

In the US, the third parties are either government sponsored agencies such as

Ginnie Mae, Freddie Mac or Fannie Mae, or other non-agency third parties such as

commercial banks. Mortgage-backed securities that are

issued by the government-sponsored agencies are guaranteed against default.

It is not true of agency mortgage-backed securities.

What do we mean by default here? Well what I mean by default here is just

that the homeowner might be default on their mortgage payments.

They just may not make their mortgage payments and, and therefore the mortgage

can go into default. Well, in that situation, if the

mortgage-backed security was issued by Fannie Mae or Freddie Mac, for example,

then the agency will step in and guarantee the payments.

This is not true in general of non-agency mortgage-backed securities.

So the modeling of mortgag- backed securities therefore depends on whether

they are agency or non agency mortgage-backed securities.

The simplest type of MBS is the pass through MBS, where a group of mortgages

are pooled together. Investors in this MBS receive monthly

payments representing the interest and the principal payments of the underlying

mortgages. So, here's a diagram explaining how this

works. We saw this before in the last module.

We've got 10,000 mortgages, of course the number doesn't have to be 10,000, it

could be 5,000 or 20,000 mortgages. We've got mortgage number one, mortgage

number two, up to mortgage number 10,000. All of these mortgages are pulled

together into one mortgage pull and from that mortgage pull we can create new

securities. These new securities are mortgage-backed

securities and maybe they've got names like Tranche A, Tranche B down to Tranche

D and Tranche E and so on. For now let's not worry about these

tranches. In fact, in the case of the Mortgage

pass-through security we don't have any tranches.

But we will some examples later on where you can have tranches.

So these 10,000 mortgages formed the collateral for the mortgage-backed

security. and so when we create these new

securities out of the underlying pool of 10,000 mortgages, this process is often

called securitization. And as mentioned earlier, the economic

reasons for securitization is that the desire of people to spread risk.

Most people most agents most investors do not like risks.

They need to be compensated for holding risky securities.

So, one could view these 10,000 mortgages, individually, as being very

risky. If you hold any one of these mortgages,

there will be a substantial chance that the homeowner will default, for example,

or pre-pay, and so there will be risk associated with these mortgages.

But by pulling them together, creating new securities, we can sell these new

securities on to investors who want the particular type of risk.

And so that is the economic or financial motivation behind securitization.

The pass-through coupon rate, and we're referring now to our Mortgage

pass-through is strictly less than the average coupon rate of the underlying

mortgages. Now this is due to fees associated with

servicing the mortgages. Somebody has to collect the mortgage

payments every month and do the book work and bookkeeping to make sure that the

homeowners are up to date on their payments, and so on.

We're going to assume that our mortgage-backed securities are agency

issued, and are therefore default free. Now, I'm going to give you a couple of

definitions here. You'll find when we discuss

mortgage-backed securities that there are many definitions.

The weighted average coupon rate, WAC, is a weighted average of the coupon rates in

the mortgage pool with weights equal to the mortgage amounts still outstanding.

Similarly, the weighted average maturity is a weighted average of the remaining

months to maturity of each mortgage in the mortgage pool with weights equal to

the mortgage amounts still outstanding. Now there's no need to worry about the

specific details of these definitions. I just want to mention that there are

many definitions associated with mortgage-backed securities.

We also need to discuss some important prepayment conventions, that are often

used by market participants, when quoting yields, and prices, of mortgage backed

securities. But first we need some definitions.

One definition, is the following, the conditional prepayment rate, the CPR, is

the annual rate at which a given mortgage pool prepays.

It is expressed as a percentage of the current outstanding principal level in

the underlying pool, to this is the so called conditional prepayment rate.

I very related definition is the single-month mortality rate.

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The SM and the SMM is the CPR converted to a monthly rate assuming monthly

compounding. And so therefore the SMM and CPR are

related as follows. Now the CPR is expressed as an annual

rate, and so it is probably the rate that makes most sense to us.

We like to think in terms of annual rates.

We think of interest rates expressed as annual rates, and so likewise we might

think of a conditional prepayment rate as an annual rate.

However, when modeling the payments of a mortage-backed security we typically need

the coresponding monthly rate and that's because payments in mortgage-backed

securities typically take place monthly and so we wont be able to convert our CPR

to SMM, and that's what we do here. We'll also see how the SMM and CPR are

used in the spreadsheet that is associated with these modules to

calculate the various cash flows underlying the Mortgage pass-through and,

indeed, other mortgage-backed securities. In practice, of course, the CPR is

stochastic, it is random, and it depends on the mortgage pool and other economic

variables. We saw, for example, earlier that

prepayments tend to go up when interest rates go down.

And that's because it is more attractive to homeowner's to prepay their entire

mortgage and then refinance at a better rate which is possible when interest

rates have gone down. So the prepayment rate for a given

mortgage pool will certainly depend on the economic variables.

That are present at any given time. That having been said, market

participants, that is, people who work with mortgage-backed securities in the

marketplace. They often use a deterministic

pre-payment schedule as a mechanism to quote mortgage-backed security yields,

and so-called option adjusted spreads. Now we're not going to discuss option

adjusted spreads it all in this course that's fine so you don't have to worry

about what they are. The standard benchmark is what is called

the Public Securities Association benchmark or the PSA benchmark.

The PSA assumes the CPR is equal to 6% times t over 30 if t is less than or

equal to 30 and I should mention here that C is now measured in months.

Here and then after 30 months, CPR is equal to 6%.

So the assumption here is that the conditional prepayment rate of a mortgage

is 60% if it's more than 30 months old. If it's less than 30 months old, the

conditional prepayment rate is 6% times t over 30.

So basically the CPR grows linearly, for 30 months and then is flat.

So this is time t in months, this is 6%, and this is the CPR.

And then slower or faster prepayment rates are given as some percentage or

multiple of PSA. So, for example 2 times CPA refers to

mortgage pool that repays at twice this rate.

A 50% CPR refers to a mortgage pool where the condition of prepayment is half of

this CPR. Giving a particular prepayment assumption

the average life of a mortgage-backed security is given as the following.

Sells equal to the sum from k equals1 to capital T, k times Pk divided 12 times

TP. Where Pk's the principle scheduled and

projected prepayment paid at time k, TP's the total principle amount, capital T is

the total number of months. And, we also divide by 12, so that

average life is measured in years. It should be clear that the average life

decreases as the PSA speed increases. And that makes sense, because if the PSA

speed increases, well then you're going to get more of your principle payments

earlier in the life of the mortgage. So the Pk's for k small, will actually be

larger when the PSA speed increases. And so average life gives you a measure

of the average life, or how long you have to wait to get the payments associated

with the mortgage or mortgage. Implicit in the calculations of the

average life is some assumption regarding the speed of prepayments.

In practice the price of a given mortage-backed security is observed in

the marketplace and from this a corresponding yield to maturity can be

determined. This yield is the interest rate that will

make the present values of the expected cash flows equal to the market price.

So if you recall what a yield to maturity is in the case of a fixed income bond

where the cash flows are fixed, well, it'll be some quantity that satisfies the

following. So it will be n, i equals 1, ci over 1

plus lambda to the power of i. Now if lambda, if the payments are made

semi-annually and we're compunding semi-annually then I should divide lambda

by 2 here and multiply the i by 2. But basically lambda is the quantity that

makes this equation correct. Where P0 is the value of the fixed income

security in the marketplace and Ci is the cashflow that you receive at time I when

you own this fixed income security. The problem with mortgages is, and

mortgage-backed securities, is that the Ci's are uncertain.

You don't know what they're going to be and that is because of prepayments.

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So when you are calculating a lambda or yield maturity for mortgage-backed

security, you have to fix the ci's, and the way to fix the ci's is to make some

assumption about prepayments. So that's what market participants do.

So the expected cash flows are determined, or based on some underlying

prepayment assumptions such as 1 PSA, 300 PSA, etcetera.

So any quoted yield must be with respect to some prepayment assumptions.

When the yield is quoted as an annual rate based on semi-annual compounding, it

is often called a bond-equivalent yield. Yields actually are very limited when it

comes to evaluating a mortgage-backed security.

And indeed, fixed income securities in general, that don't take account the term

structure of interest rates. They don't take the prepayment option

into account. so yields are very limited, and indeed

the, the market place typically uses option adjusted spreads as the market

standard for quoting yields in mortgage-backed securities, and indeed

other fixed income securities with embedded options.

But, as I mentioned before, we're not going to be discussing option-adjusted

spread so there's no need to worry about that in this course.

An investor in a mortgage-back, backed security pass-through is, of course,

exposed to interest rate risk in that the present value of any fixed set of

cash-flows decreases as interest rates increase.

However pass-through investors also exposed to prepayment risk, in particular

contraction risk and extension risk. When interest rates decline prepayments

tend to increase and the additional prepaid principal can only be invested at

lower interest rates. So this is contraction risk.

So if you think about it. When interest rates fall if you own a

home and therefore have a mortgage, it is in your interest to prepay that mortgage

early and then re-finance the mortgage at a much lower level of interest.

If you do this then the people who have invested in these mortgage-backed

securities. They're going to get payments sooner than

they expected, and these payments can only be invested at the lower interest

rates. So this is called contraction risk.

The opposite also provides a risk, which is called extension risk.

In this case, when interest rates increase, the prepayments tend to

decrease, and that makes sense. After all, why would I want to prepay a

mortgage early when I'm going to have to re-finance it at higher interest rates.

So therefore, interest rates increase implies prepayments tend to decrease, and

therefore I'm getting less prepaid principals than I expected.

And so I'm not going to invest that principal, that prepaid principal at the

higher interest rates that might now be prevailing.

This is called extension risk. So, to summarize, in addition to the

regular interest rate risk that fixed income securities have Mortgage-backed

securities and Mortgage pass-throughs are also exposed to prepayment risk, in

particular contraction risk and extension risk.