This paper tries to briefly explain various methods of valuation of mortgage backed securities (MBS). We have started with the background of MBS and their history. The later sections cover the growth of the MBS market and how the mortgage backed securities have made this market highly liquid. We have also tried to cover the MBS and securitization market in India.
In the later sections, we try to describe the process of valuation of MBS and why it is different from valuation of other fixed income securities due to prepayment and its path dependent character.We have discussed interest rate, prepayment and OAS models. Different models within these three broad types have also been discussed.
Our main emphasis will be on understanding the valuation of securities having uncertainty and variability in cash flows as opposed to our knowledge of valuation of bonds with fixed cash flows. The focus of the paper will be to develop a conceptual understanding of the valuation of more complex fixed income securities in terms of the factors and models involved.
Mortgage Backed Securities
Mortgage Backed Securities (MBS) are instruments which represent ownership of a number of mortgages grouped together. MBS is usually treated as a method to fund capital pool by lending mortgages.
The history of MBS dates back to the great depression of the US in early 1930's. The United States government created the Federal Housing Administration (FHA) in 1934 to assist in the construction, acquirement, and/or rehabilitation of residential properties. At the time, the only other mortgage payment option was the balloon payment scheme. The FHA therefore helped develop and standardize the fixed rate mortgage that is prevalent today. It also helped in insuring the mortgages, thereby making the whole mortgage market popular.
To create a liquid secondary market for mortgages, in 1938, the US government created the government-sponsored corporation Federal National Mortgage Association (FNMA or Fannie Mae). The purpose was to free the loan originators to originate more loans. Fannie Mae was split in 1968 into the current Fannie Mae and the Government National Mortgage Association (GNMA or Ginnie Mae) to support the FHA-insured mortgages, Veterans Administration (VA) and Farmers Home Administration (FmHA) insured mortgages. The full faith and credit of the United States government made these transactions virtually risk free. Fannie Mae was later authorized to purchase private mortgages (not insured by the FHA, VA, or FmHA), and created the Federal Home Loan Mortgage Corporation (FHLMC), colloquially known as Freddie Mac, to do much the same thing as Fannie Mae. Ginnie Mae does not invest in private mortgages.
The key process behind MBS is securitization. It is a fairly complicated process, and is dependent upon the jurisdiction. The securitization process follows the following steps -
First of all, the mortgage loans are purchased from the originators. These can be banks, mortgage companies etc.
After this, these loans are assembled into collections or "pools".
Third step is to securitize these pools through various legal methods dependent upon the type of MBS and jurisdiction. Government agencies, government sponsored enterprises and private entities do this securitization.
In US, most MBS's are sold by Fannie Mae and Freddie Mac. Ginnie Mae guarantees that investors receive timely payments.
Types of Mortgage Backed Securities
MBS sub-types include -
A pass-through mortgage-backed security or the simplest MBS which can be further classified as:
A Residential mortgage-backed security (RMBS) - backed by mortgages on residential property.
A Commercial mortgage-backed security (CMBS) - backed by mortgages on commercial property.
A collateralized mortgage obligation (CMO) is an MBS in which the mortgages are ordered into tranches by some quality (for example, repayment time). Each tranche is then sold as a separate security.
A stripped mortgage-backed security (SMBS) just like the bond STIPS, are securities where each mortgage payment is partly used to pay down the loan's principal and partly used to pay the interest on it. This is of further 2 types:
An interest-only stripped mortgage-backed security (IO) is a bond with cash flows backed by the interest component of property owner's mortgage payments.
A principal-only stripped mortgage-backed security (PO) is a bond with cash flows backed by the principal repayment component of property owner's mortgage payments.
The mortgages in the pool can be classified as -
Prime mortgages - with prime borrowers, full documentation (such as verification of income and assets), strong credit scores, etc.
Alt-A mortgages - generally prime borrowers but non-conforming in some way, often lower documentation.
Subprime mortgages - have weaker credit scores, no verification of income or assets, etc.
Growth of the MBS Market
The Federal Reserve publishes the figures for the mortgage debt outstanding. The figures for other countries are difficult to obtain. According to the Federal Reserve, as of June 2010, the total mortgage debt outstanding was $ 14.15 trillion. Out of this, about $ 10.7 trillion was with one to four family residences. Non-residential segment comprised of about $ 2.4 trillion.
Of this total pool of mortgages, major financial institution held about $ 4.7 trillion, Federal and related agencies held about $ 5.6 trillion of mortgages while mortgage pools and trusts held about $ 3.1 trillion.
The figure below shows how the holdings of MBS have changed with major financial institution, Federal and related agencies and mortgage pools over the years.
Figure : Holding of MBS
Uses of the Mortgage Backed Securities
There are many reasons because of which the MBS market has flourished -
MBS provide liquidity. They transform relatively illiquid, individual financial assets into liquid and tradable capital market instruments.
They act as a source for the mortgage originators to replenish their funds.
They provide a more efficient and lower cost source of financing in comparison with other bank and capital markets financing alternatives.
They can be used as alternatives to more traditional forms of debt and equity financing for the issuers.
They are used in off-balance sheet activities by removing assets from balance sheet.
Risks Associated with MBS
Mortgage Backed Securities suffer mainly from the Interest Rate/Prepayment Risk and Credit Risk.
Interest Rate and Prepayment Risk: Mortgage prepayments most often happen when a home is sold or the homeowner refinances to a new mortgage, to get the advantage of a lower rate or shorter term. Although the investors receive the money in case of prepayments, but prepayments usually occur when floating rates drop. Due to the drop in floating rates, the fixed income would be more valuable. Hence the term - prepayment risk. To compensate the investors of this risk, the MBS are generally traded at a spread to government bonds. Besides the fall in floating rates, other drivers for prepayment are economic growth, home prices inflation, unemployment, regulatory risks and demographic trends.
Credit Risk: The credit risk depends on the borrower's regular payment at promised intervals. If the property owner should default, the property remains as the collateral, but this safety can be eroded if the property prices fall below the value of the original loan, which happened in the recent sub-prime crisis. Even with these issues, the MBS have fairly high ratings if the mortgages are of high quality and they are insured by the government agencies.
MBS and Securitization Market in India
Securitization in India began in the early nineties. Initially, securitization of auto loans drove the market. But since 2000, Indian market has been driven by the residential mortgage backed securities.
Securitization in India has potential in the following areas:
Mortgage Backed Securities
Infrastructure Sector
Other Asset Backed Securities (ABS)
While mortgage backed securities and activity in infrastructure market is usually financed in India mainly by mortgage originating financial institutions (like NBFC's) and banks, asset backed securities sector is increasingly becoming popular among financial institutions. To facilitate more projects and to stimulate the growth of infrastructure, securitization of projects in housing and infrastructural sector is necessary. This will take the load off from financial institutions and facilitation of more projects by helping them concentrate on their core competency like loan origination.
In India securitization is generally done using the special purpose vehicle (SPV) as a trust structure, created to take the assets off from the balance sheets of the parent firms. The SPV's issue two types of securities:
Pass through Securities: Investors acquire interest in the underlying asset held by the trustee.
Pay through Securities: Investors acquire beneficial interest in cash flows realized from the underlying asset held by the trustee.
Key Originators include Birla Home Finance, HDFC, HSBC, ICICI Bank, Standard Chartered Bank and Cholamandalam DBS while the key investors Key Investors include Insurance companies and Banks.
Valuation of Mortgage backed securities
The price of any security can be calculated using the present value of all the future cash flows discounted at an appropriate rate. In contrast to the valuation of non- callable bonds or non-prepayable mortgages, valuation of MBS is different due to the option of prepayment and the path dependent character of prepayments.
PREPAYMENT MODELS - The cash flows of a mortgage are not fixed owning to the prepayment option. For example when the mortgage rates have fallen, the value of an existing mortgage exceeds the principal outstanding and when the rates have risen, the value of an existing mortgage is less compared to the principal outstanding. This is similar to the mortgager having an American call option where the strike of the option is the principal amount outstanding. So, valuation of MBS should include the price of this prepayment option. This is adjusted by a higher mortgage rate to be payable by the home owner. This mortgage rate is known as the current coupon rate.
INTEREST RATE MODELS- There are various models for prepayment and they depend on various factors which will be discussed later. This necessitates the knowledge of interest rates or a future term structure since prepayment depends to a large extent on the current interest rates and how interest rates have evolved over a period of time i.e. the value of these securities are path dependent. Once the term structure is predicted and an appropriate prepayment model selected, pricing models like binomial recombining tree model, Black Scholes pricing model and Monte - Carlo simulations can be used.
OAS MODELS - both of the above mentioned models are integrated and interest rate paths and corresponding cash flows are simulated using Monte- Carlo simulation to arrive at an option adjusted spread which describes the intrinsic value of an MBS relative to its market price. This model is further exploited to obtain option adjusted duration and option adjusted convexity.
Interest Rate Models
Equilibrium interest rate models are based on the assumption that bond prices, and yields, are determined by the market's assessment of the evolution of the short-term interest rate. For these models, the short rate is assumed to follow a diffusion (continuous time stochastic) process. The general form of these models is described in terms of changes in the short rate, as follows -
Where = infinitesimal change in over an infinitesimal time period, is a standard Weiner Process, is the speed of mean-reversion, is the long run mean of the interest rate process, α is the proportional conditional volatility exponent,and σ is the instantaneous standard deviation of changes in .
There are three models - Vasicek, Dothan and Cox-Ingersoll-Ross (CIR). The difference in these models is mainly in the parameterα. Vasicek assumes it to be 0; CIR assumes it to be 0.5; while the Dothan model assumes it to be 1.0.
Vasicek Model
The Vasicek model is often used for simple interest rate processes. It is based on Ornstein-Uhlenbeck stochastic process for the spot interest rate rt. It is a one-factor model, where all interest rates ultimately depend on the short term interest rate. Interest rate follows the following Weiner process -
In order to simulate interest rate using this model, a discrete form of the equation is used
Since term structure models are additive, sport rate at time t + can be expressed as follows -
If negative interest rates are simulated, absolute values are used.
CIR model
In the CIR model, the only change from the Vasicek Model is in the volatility function. It considers an interest rate process of the type -
Volatility now depends on the level of interest rates.
Dothan Model
This model increases the volatility exponent to 1. Therefore, it considers an interest rate process of the type -
Due to the higher exponent for volatility in this model, it relates the volatility of interest movements more strongly to the level of interest rates. Unlike the previous models, this model does not include a mean reverting term in the drift.
Prepayment Models
In order to arrive at a prepayment model, we need to understand the reasons that lead to a prepayment. The most important reasons are defaults, housing turnovers and refinancing.
Defaults- Defaults become payable in full when the borrower fails to make a payment. If the home owner is not able to make the payment towards the outstanding principal, the originator can sell the house and raise as much amount as possible. Most of the issuers of MBS often guarantee payment of principal and interest and so the investors in MBS get prepayments in case of default.
Housing Turnover-The most important reason for prepayment that is not directly related to interest rates is housing turnover. Most mortgages are due on sale i.e. any outstanding principal must be paid when the house is sold. Since the behavior of home owners to move out of a house or to sell a house does not have much to do with the current interest rate, prepayment resulting in this fashion is not much related to interest rates. Some of the factors that predict housing turnover are -
Age of a Mortgage - home owners are not likely to refinance their loans right after their purchase or when it is close to maturity. The behavior increases as age of the mortgage increases and falls as it approaches maturity.
Lock-in effect-while turnover does not primarily depend on interest rates, there can be some interaction between them. A home owner who has a mortgage at a relatively low rate would be reluctant to prepay the mortgage which is pretty much like paying par amount for a bond trading at discount. This interaction between turnover and interest rates is known as lock - in effect.
Geography - housing turnover also depends on the state of the economy and hence on geography where stable conditions are prevalent.
Season of the year - It has been noted that home owners are more likely to move in certain months than in others.
Refinancing-this is the main cause of prepayment relating to the interest rates. Homeowners can exercise their prepayment options in low interest rate situations by paying off the principal outstanding. Since most of them don't have the cash, they opt for refinancing.
Based on the factors discussed above, various prepayment models have been developed, the important ones being the following:
12 year life method
According to FHA (Federal Housing Administration), a 30 year mortgage will be fully prepaid in the 12th year. Based on this data, GNMA priced MBS' by assuming that a 30 year mortgage will have normal payments till the 143rd month and there will be a prepayment i.e. payment of total outstanding principal in the 144th month.
FHA experience method
FHA has a database of historical 30 year mortgages and based on this a pattern of prepayments is observed. This reveals a tendency to prepay less in the initial period of the mortgage, reaching the maximum at a period of 5 to 8 years. The prepayment rate tapers off after the 8th year. The disadvantage of this method is that it does not take current interest rates into account.
Conditional prepayment rate method
CPR expresses the prepayment behavior in percentage form. The prepayment rate is defined as the rate equal to the proportion of principal that is assumed to be prepaid in every period say a month. It is an annualized expected rate of prepayment for a pool of mortgages and MBS. There are many CPR models, the most used of which are:
PSA standard method-according to PSA, the prepayment is 0.2% in the first month and increases by 0.2% every month until the 30th month. There after it remains constant for the rest of the period.
Schwartz and Torous's proportional Hazard Model- this model divides the mortgage prepayment risk into 2 parts - aging effect and mortgage specific risk. The aging effect illustrates the baseline risk at any time of mortgaging period. The mortgage specific risk is defined by a set of vectors:- difference between mortgage rate and the current long term treasury rate, cube of the vector mentioned before that represents the accelerating effect when treasury rates are much lower than the mortgage rates, the burnout effect which represents the tendency on the part of home owners to refinance less owing to heavy refinancing in the past and finally the vector representing the seasonal effect of prepayments.
Richard and Roll's Modified Goldman Sachs Model-According to Richard and Roll,
Each of the factors can be in turn determined as follows: refinancing incentive by spread between weighted average mortgage coupon rate and mortgage financing rate. Seasoning means that older or seasoned loans have more tendencies to be prepaid. The industry standard for measuring this is the PSA prepayment model discussed before. Month factors measures prepayment behaviors during various times of the year. This is due to increased turnover in some months of the year. The Burnout factor is the tendency of the prepayment to diminish over time. This is measured by how much the prepayment option is in the money. More the pool is deep in the money, higher is the burn out factor.
MBS pricing Models
The attempt at pricing mortgage backed securities has evolved starting from simple static cash flow models. The various models used are:
Static cash flow models
These models assumed that prepayment rates are a function of the age of the mortgages in a pool. The prepayment rates follow various models like the PSA model where the prepayment rate grows gradually and remains constant after some time. Some other models include using historical data on mortgage survivorship to predict future behavior. In the static cash flow model, since the prepayments depend only on the age of the mortgage, cash flows of the mortgage pool over time can be easily predicted. This also helps to determine the yield of the MBS. But this approach is plagued with 2 problems:
Any pricing model should have a means to determine price in the first place. But this model assumes the current price and cash flows to determine the yield of the MBS. The price is arrived at by using a proxy for yield like a 30 year bond yield. But clearly the cash flow pattern of this security is quite different given the nature of prepayments in an MBS. So dependence on interest rates is not taken into account in Static cash flow models
Static cash flow models provide misleading price- yield and duration-yield curves. Since these models assume that the cash flows remain constant, the predicted interest rate behavior will be similar to that of bonds with fixed cash flows. This does not account for the negative convexity of these securities which resemble more of callable bonds.
Implied models
These models attempt at estimating the interest rate sensitivities instead of pricing the MBS. The assumption is that the sensitivity of the mortgage changes slowly over time. So using the recent data on price sensitivity, interest rate sensitivities are determined. So for any two interest rate levels and prices, the difference of past MBS prices divided by difference in interest rate levels would result in the interest rate sensitivity. Using these interest rate sensitivities, future MBS prices can be determined given that these interest rate sensitivities reflect the market conditions of the past data from which they were calculated.To add more accuracy, we can look for a historical period which closely matches current situations. These models also suffer some drawbacks:
These are also not pricing models like static cash flow models.
The assumption of slowly changing mortgage sensitivities may not hold true and may in fact change rapidly over time. We know that the sensitivity of MBS is similar to that of a callable bond and the duration of a callable bonds changes rapidly relative to a non-callable bond. Mortgage durations change rapidly depending on whether prepayments are more or less likely.
Prepayment Models
These are the most popular and sophisticated models which take into account the turnover and refinancing behaviors into account. These have already been discussed above.
Once the cash flows are predicted, the prepayment functions can be integrated with pricing trees as in binomial recombining trees to value a mortgage backed pass through security. The payoffs can be written in the form of a tree. The figure below takes a hypothetical example.
The cash flows can then be discounted using the interest rate models that we have developed. We should observe the difference between pricing bonds and MBS using binomial trees. The key feature is that prepayments depend on previous or historical interest rates whereas in a bond, the price would depend only on the current discount rate. Hence the valuation of mortgage backed securities is path dependent. This can be done by using Monte Carlo simulation.
OAS model
The OAS model or the option adjusted spread model accounts for the prepayment option in an MBS to discount the security to calculate its price. In order to calculate this option adjusted spread we equate the observed market price to the present value of all the simulated interest rates paths and their corresponding cash flows. There are 2 sources of path dependency in a CMO tranche's cash flows.
Collateral prepayments are path dependent since the current period's prepayment rate depends on whether there were prepayment opportunities in the preceding months after the mortgage was issued.
The cash flow to be received in this period by a CMO tranche depends on the outstanding principal of the other tranches. So a history of prepayments is needed to calculate these balances.
The interest rates paths which are generated should be random paths and have to be generated in an arbitrage free model of term structure of interest rates. Many scenarios of monthly interest rates are generated and a corresponding monthly mortgage refinancing rate is generated. The monthly refinancing rate is used to determine the cash flows and the monthly interest rates are used to discount these cash flows.
Prepayments are then projected based on the mortgage financing rate and other factors like age of the mortgage, burnout factor; seasoning effects etc. these have been discussed in the prepayment models. This results in a series of cash flows along a particular interest rate path. These cash flows along a particular path are discounted by the simulated monthly interest rate plus the option adjusted spread to arrive at a present value.
A number of interest rate paths and cash flow predictions using a prepayment model lead to a number of present values. An average of these present values is equated to the observed market price. This equation is solved for the option adjusted spread. Most OAS models use variance reduction to minimize the number of paths necessary to get a good statistical sample.
The OAS model helps in finding the value of a security in the form the option adjusted spread, how much is the security valued over the treasury spot rate at a particular moment. The option adjusted spread can be used to obtain option adjusted duration and convexity which describes these measures for an MBS better.
Duration and Convexity of a Mortgage Backed Security
Unlike holders of conventional fixed income instruments which primarily deal with interest rate risk affecting their portfolio's market value, mortgage backed securities have additional unique risks associated with them. One such unique risk is the risk of prepayment or extension which affects the life of the security. Hence investors holding Mortgage backed securities bear additional uncertainty in the cash flows as they depend on the actual prepayments. The borrowers have the incentive to prepay their loans before they mature by selling the property or by refinancing the loans if the interest rates decline or the real estate market value appreciates. This prepayment risk results in the shortening of the average life of a MBS, also called contraction risk and is akin to the 'call risk' exhibited by callable bonds issued by the corporate or municipal sector and results in a cap on the upside price potential of the security. Similarly increasing interest rates or declining real estate values tend to slow down the prepayments leading to a lengthening of the average life of a MBS, commonly referred to as an extension risk.
Owing to the factors mentioned above Mortgages and MBS exhibit price-performance characteristics known as negative convexity. The behaviour of MBS is non-linear in nature and underperforms those assets which do not exhibit negative convexity like conventional bonds. Although investors are generally compensated for this underperformance by higher yields, but managing negative convexity has ramifications that dictate active management of MBS portfolios. In particular this has led to the various interest rate and prepayment models that are used by the investment industry to model the fluctuating interest rates and associated prepayment rates for the valuation of MBS.
Duration of a fixed income security is the discounted, dollar-weighted average span of time to receive the cash flows. It is an indicator of the price volatility of the security relative to changes in interest rates. Contraction risk and Extension risks also have implications for duration of MBS investments. For a MBS when mortgage rates increase, due to extension risk duration also rises similarly when mortgage rates decline, the duration falls due to contraction risk. Accurate measurement of duration is critical for the process of risk management of MBS portfolios. MBS universe includes securities as interest-only (IO), principal-only (PO) investments and various CMO tranches such as accrual, support and inverse floaters. Investors use treasury securities and derivatives like swaps to hedge their duration exposures on MBS investments. Owing to the huge size of mortgage securities market the hedging requirements of MBS has implications for the treasury and swap rate yield curves.
Issues in Valuation of MBS
Size of the Mortgage backed securities market has outgrown other markets over the years, and is a significant part of the portfolio of US insurers. Investment in MBS is considered an attractive asset allocation to diversify the fixed income portfolios of government and corporate bonds. Although we have witnessed a surge in mathematical modelling techniques, there are various challenges that are faced in valuation and risk management of MBS portfolios. There are tens of thousands of different agency issues available that are modelled using a relatively small number of pooled characteristics. The diversity of the MBS universe in terms of its various tranches and forms give rise to new complications in their valuation. Further interest rate modelling is a key challenge as it depends on exogenous factors like monetary policy. Further we have seen a paradigm shift in various parameters over time like the dominance of the earlier extension risk being replaced more by contraction risk, increasing volatilities of the markets etc. Prepayment modelling is again very dynamic as it hinges on a number of factors apart from interest rates like mortgages seasoning, burnout effect, borrower's heteroskedasticity, real estate appreciation etc.
Conclusion
US mortgage market is the largest debt market in the world, more than half of which is securitized. Mortgage securitization has enhanced liquidity and improved the pricing of the market. We have witnessed risk based pricing where prices are discovered after incorporating the various risk factors. The market's explosive growth has catalysed the need to understand the primary value drivers of the MBS securities. This has, in turn, generated a vast amount of interest in explaining and forecasting term structure of interest rates and prepayment rates. In this paper we have tried to present a holistic discussion about Mortgage Backed Securities while focussing on the valuation of the securities. Our main emphasis has been on understanding the valuation of fixed income securities without fixed cash flows as opposed to our knowledge of valuation of bonds with fixed cash flows. We understood the various factors which contribute to the value of these securities and the simulation techniques necessary to implement them. Working for this paper has provided us a primer in understanding the valuation of more complex fixed income securities in terms of the factors and models involved.
