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

Â pass-throughs. Prepayment risk is a particular type of

Â risk that mortgage backed securities are exposed to.

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

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

Â early. And that creates prepayment risk for

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

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

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

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

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

Â earlier than scheduled. Payments made in excess of the scheduled

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

Â prepayments. Number one, homeowners must prepay the

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

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

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

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

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

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

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

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

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

Â payments. Maybe they're behind on their payments,

Â they can't catch up and they smiply default.

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

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

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

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

Â So there are many possible reasons for pre-payments.

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

Â It's the prepayment option that mortgage holders have.

Â In particular they can benefit when interest rates go lower.

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

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

Â So prepayment modeling is therefore an important feature of pricing

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

Â securities is extremely dependent on prepayment behavior.

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

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

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

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

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

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

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

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

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

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

Â markets generally. Also the bigger picture that I want to

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

Â securities and indeed asset-backed securities can be created.

Â How are Mortgage pass-throughs constructed.

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

Â these mortgages together to created mortgage-backed securites.

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

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

Â commercial banks. Mortgage-backed securities that are

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

Â It is not true of agency mortgage-backed securities.

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

Â that the homeowner might be default on their mortgage payments.

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

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

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

Â then the agency will step in and guarantee the payments.

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

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

Â they are agency or non agency mortgage-backed securities.

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

Â are pooled together. Investors in this MBS receive monthly

Â payments representing the interest and the principal payments of the underlying

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

Â works. We saw this before in the last module.

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

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

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

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

Â securities. These new securities are mortgage-backed

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

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

Â tranches. In fact, in the case of the Mortgage

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

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

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

Â security. and so when we create these new

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

Â called securitization. And as mentioned earlier, the economic

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

Â Most people most agents most investors do not like risks.

Â They need to be compensated for holding risky securities.

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

Â risky. If you hold any one of these mortgages,

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

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

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

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

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

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

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

Â mortgages. Now this is due to fees associated with

Â servicing the mortgages. Somebody has to collect the mortgage

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

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

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

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

Â definitions here. You'll find when we discuss

Â mortgage-backed securities that there are many definitions.

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

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

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

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

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

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

Â many definitions associated with mortgage-backed securities.

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

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

Â securities. But first we need some definitions.

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

Â the annual rate at which a given mortgage pool prepays.

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

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

Â 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

Â compounding. And so therefore the SMM and CPR are

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

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

Â We like to think in terms of annual rates.

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

Â think of a conditional prepayment rate as an annual rate.

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

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

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

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

Â used in the spreadsheet that is associated with these modules to

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

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

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

Â variables. We saw, for example, earlier that

Â prepayments tend to go up when interest rates go down.

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

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

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

Â mortgage pool will certainly depend on the economic variables.

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

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

Â marketplace. They often use a deterministic

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

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

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

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

Â the Public Securities Association benchmark or the PSA benchmark.

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

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

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

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

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

Â conditional prepayment rate is 6% times t over 30.

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

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

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

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

Â mortgage pool that repays at twice this rate.

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

Â this CPR. Giving a particular prepayment assumption

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

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

Â TP. Where Pk's the principle scheduled and

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

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

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

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

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

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

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

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

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

Â average life is some assumption regarding the speed of prepayments.

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

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

Â determined. This yield is the interest rate that will

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

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

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

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

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

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

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

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

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

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

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

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

Â 13:10

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

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

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

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

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

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

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

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

Â comes to evaluating a mortgage-backed security.

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

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

Â into account. so yields are very limited, and indeed

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

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

Â other fixed income securities with embedded options.

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

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

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

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

Â cash-flows decreases as interest rates increase.

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

Â contraction risk and extension risk. When interest rates decline prepayments

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

Â lower interest rates. So this is contraction risk.

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

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

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

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

Â securities. They're going to get payments sooner than

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

Â rates. So this is called contraction risk.

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

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

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

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

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

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

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

Â higher interest rates that might now be prevailing.

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

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

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

Â particular contraction risk and extension risk.

Â