3.3.1 PREPAYMENT RISK
Prepayment risk is seen as a major risk in good times when the economy is doing well and the interest rates may not be too high. The investor does not want his money not being paid at all but he also does not like being paid too soon either because of reinvestment risk. The rate at which borrowers in a pool prepay their mortgages is defined as prepayment speed.
What causes prepayment?
Home salesHomes that are on a mortgage loan, when sold will lead to the prepayment of the mortgage.
RefinancingsAnother major cause of prepayments refers to mortgagors taking advantage of lower rates by refinancing out of an existing loan into a new one.
This factor is the most volatile component of prepayment speeds, and causes the bulk of prepayments when speeds are very high.
DefaultsA prepayment caused by a foreclosure and follow up liquidation of a mortgage. This is a minor component in good times, averaging less than 0.5% per year in US in normal times for moderately seasoned loans, and is close to zero for very seasoned loans; however it may become a major component during periods of market downturns and recessions.
CurtailmentsSome borrowers may occasionally pay more than the scheduled monthly payment in an effort to increase their equity in their property. These extra payments, called partial prepayments or curtailments, contribute in the aggregate to the prepayments of principal and, for fixed rate loans it will shorten the loan maturity.
Full payoffsHistorical evidence suggests that many borrowers pay off their mortgage in full when the loan is very seasoned and the remaining loan balance is small. Full payoffs may also occur because of insurance related payments to natural disasters such as hurricanes and earthquakes.
Refinancing IncentiveRelated to the difference between the current mortgage rate and the prevailing loan rate. Although some believe that the larger the difference the greater the incentive to prepay, the ratio between the two rates seem to be more determinant.
Burnout effectThis is the tendency for prepayment to decay over time even when refinancing is possible.
• If the mortgage rates decrease below a given threshold then rise up and then go down below this threshold again, the burnout effect means that there would be fewer prepayments second time round because the bor- rowers with highest likelihood to prepay have done it first time.
0 0.2 0.4 0.6 0.8
Seasonality factor
1 1.2 1.4
1 2 3 4 5 6
Month of the year
7 8 9 10 11 12
Figure 3.2.Seasonality as used by Richard and Roll in the Goldman Sachs model.
Notes: The graph is constructed from the numerical values detailed in Richard and Roll (1989).
• The pool factor defined as the total mortgage balance outstanding divided by the original mortgage balance is an important ratio for assessing the level of prepayment; a lower ratio means that prepayments have already occurred.
SeasoningThis means that new loans will prepay slower than older ones. Over time, prepayment rates are low immediately after issuance and increase after some seasoning . Fixed rate mortgages season quicker than adjustable- rate mortgages slowing down prepayments. At the end of the fixed rate period the remortgage rate is close to the market rate and this prevents prepayments.
SeasonalityHouse trading is higher in the spring and peaks in late summer, so there are higher prepayments in those months. There are fewer sales in autumn and winter with lower prepayment rates then.
3.3.2 DEFAULT RISK
Default is easy to define for corporates but it is not so straightforward for home- owners. In general we have default when the lender has already repossessed the property. This can only be done following:
• a court order
• the borrower informing the lender that he is no longer paying and is prepared to hand over the property
It takes time to repossess and for risk management calculation purposes the timing of actual default is difficult to be determine. The main factors influen- cing default are
Ability to payThis factor is generated by common reasons such as divorce, disability or increase in family members, which are more idiosyncratic. The other common reason is unemployment and this is a systematic risk related to the economic cycle.
Willingness to payIf a borrower gets into negative equity then he/she has a strong incentive to default on the mortgage and let the lender take over the house. This is a put option that is in the money once the loan-to-value (LTV) exceeds 100%. Thus LTV is a major indicator of default.
3.3.3 ARREARS
A borrower may be in arrears by any number of months. Arrears are measured by the number of overdue monthly payments. From the risk management perspective, there is a cutoff point after which the loan is considered in default.
In practice, the loan can be in arrears for a few months, then clear, then in arrears again, and so on.
For modelling purposes it is best to define a transition matrix for the arrears, with two states (prepayment and default) as absorbent states. The transition matrix technique is similar to the rating transition matrix estimation used in credit. Arrears are signalling that the loan is on its path to default. Very little has been done for efficient modelling of arrears and defaults.
The Office of Thrift Supervision (OTS) classified loans as being in arrears (delinquent) as follows
• payment due date up to 30 days late: current
• 30–60 days late: 30 days delinquent
• 60–90 days late: 60 days delinquent
• more than 90 days late: 90+ days delinquent 3.3.4 LOSS SEVERITY
Upon failure to make the monthly payments the property that is the collateral to the loan will be repossessed. The outstanding debt has three components
1. the remaining mortgage balance 2. the overdue interest payments
3. any fees incurred in connection with arrears servicing, property repos- session and property sale.
If the sale proceeds are greater than the outstanding debt the excess is returned to the former home owner. However, if the opposite is true then the lender
has a loss The loss severity can be measured as expected loss divided by the remaining mortgage balance.
3.3.5 DRIVERS OF LOSSES FOR NONCONFORMING MORTGAGES There are several drivers of losses for nonconforming2mortgages. Firstly, sup- ply and demand is very important. An indicator of housing market demand is the number of loans approved by lenders, as reported by the Council of Mortgage Lenders (CML). Secondly, property markets are known to exhibit a mean-reversion effect, so the longer a residential market has been on a bull run the higher the probability of a downturn. The geographic location also plays a role since in many developed economies there is a clear north/south or west/east divide. The vintage of the borrowers, their location and their LTV at origination also plays an important role. High inflation or deflation can both lead to losses, reflecting major problems in the real economy. Interestingly, mass-media (always referring to nominal prices!!) and market sentiment (if my neighbour is safe then I am safe) can also skew the views of borrowers and trigger default decisions.
Lenders apply to court for a possession order, which will legally enable them to repossess and sell the property used as security, once a mort- gage is three months in arrears. Usually there is a period that can reach even 12–18 months from the mortgage falling into default to the property being sold.
Individual voluntary arrangements (IVAs) are similar to bankruptcy: the borrower is protected from unsecured creditors and interest stops accruing if she/he pays an agreed amount for a limited period (usually five years). IVAs are not the same as bankruptcy because the primary residence can be retained.
Thus, IVAs do not crystallize losses as opposed to bankruptcies, they only impair the credit quality of the borrower.
3.3.6 RISK MANAGEMENT CONSIDERATIONS FOR MORTGAGES Since the risk drivers for the main options embedded in mortgage portfolios are interest rate risk and house price risk, one may think that buying some options or entering into futures contracts on these two markets would be enough to offset the risks of early prepayment option and default option. How- ever, mortgage portfolios have different maturity and rates characteristics and they are very large. In order to manage interest rate risk related to prepayment the investors in mortgages would have to buy thousand of options with differ- ent strikes and maturities. Buying a basket option is not feasible either because of the large number of mortgages (in thousands). A similar rationale occurs for
2 Nonconforming is the term used in the UK for subprime mortgages in US.
house price risk. Combine that with the fact that for one amortizing mortgage there is a pre-specified vector of strike prices at monthly dates and it becomes clear that it is not feasible to use bespoke options. Furthermore, the options are not exercised as in capital markets because the holders of those options may exercise them following a mixture of rational decisions and forced events.3
As discussed in detail by Case and Shiller (1996) a better solution to risk management of prepayment risk and default risk is to use futures contracts.
The first interest rate futures market was established in 1975, the Government National Mortgage Association (GNMA), in order to cover prepayment risk and interest rate risk. The GNMA futures market perished because the delivery option in the contract led to poor hedging of prepayment risks.
Any GNMA bond is collateralized by a pool of mortgages. There is no default risk because it is guaranteed against default by the full faith and credit of the US government, but actually what this means practically is that if there is a default the GNMA will prepay the mortgage. Hence, for GNMA bonds, the government guarantee transforms default risk into prepayment risk.
The subprime crisis has highlighted that default risk can lead to catastrophic losses, well beyond the losses caused by prepayment. As house prices fall the losses to mortgage lenders increase non-linearly. There is ample evidence4 that the main predictor of default is the LTV ratio. As emphasized by Case and Shiller (1996), regional house prices can exhibit large swings, making it difficult to hedge mortgage default risk in the absence of national and regional derivatives markets on house price indices.
Prepayment and default risks are competing risks and perhaps the state of the art modelling in this area should consider modelling these two risks jointly. Even better, by analogy with rating transition matrices, a total view on risks would be obtained by modelling mortgages in several states: a normal paying state, several arrears states (up to six or twelve months), a prepayment state and a default state. The last two states are absorbent state in the sense that when a mortgagor enters this state they will never leave it. This approach would be data intensive but it will provide early warnings for both prepayment and default.