The previous discussion noted how liquidity constrained borrowers will be concerned with the tilting of real mortgage payments towards the early years of the mortgage. Other households may not be so constrained by considerations of affordability, and be more concerned with cost minimisation over the life of the debt (Breslaw et al. 1996). Both of these choice dimensions involve the rate at which debt can be, or actually is, amortised, an important aspect of mortgage design. This still involves a discussion of imperfect capital markets because even for borrowers for whom the underwriting criteria do not bind, variations in the amortisation rate can be used to hedge portfolios. In a perfectly competitive no arbitrage economy the rate of amortisation would be of little interest. There is now a body of literature on this topic, involving both theoretical and empirical work (Brueckner 1984; Plaut 1986; Goodman & Wassmer 1992; Leece 1997).
How fast, in theory, can we expect borrowers to repay their mortgage debt and accumulate equity in their property? In a sense this is a return to the theory of mortgage demand. The discussion in Chapter 2 demonstrated the critical relationship between net of tax mortgage rates and the net return on savings, in addition to the risk characteristics of these costs and returns. The US typically has a net of tax mortgage rate lower than the rate of return on savings. This implies that mortgage debt will be maximised. However, Brueckner (1994a) has theoretically demonstrated how the riskiness of the rate of return to savings might explain the observed rapid accumulation of equity in a property, that is mortgage demand in situ. The Canadian and now the UK cases are different, with no tax subsidy to mortgage borrowing in the former case and its recent removal in the latter. When the mortgage rate is comparatively expensive we would definitely expect an emphasis upon faster rates of amortisation. The discussion which follows considers two major theoretical models that offer insights into both the implications of flexible amortisation, and the key influences upon amortisation behaviour.
Seminal work by Plaut (1986) has indicated the importance of the ability to vary the rate of amortisation for liquidity constrained households. With constant payment scheduling, and no access to non-mortgage finance, increases in interest rates require a cut in consumption. An equivalent to this restriction is created by tax subsidies on mortgage interest payments that encourage the use of mortgage debt rather than consumer credit. Flexible amortisation scheduling could facilitate the smoothing of consumption over time. Variations in the rate of amortisation also assist hedging against house price falls, and adverse interest rate movements. If households are given flexibility then liquidity constrained consumers choose the rate of amortisation according to the mortgage interest rate, the opportunity cost of equity in property, house prices, and the risk attached to housing and non-housing assets. The actual structure of the model very closely follows mortgage demand under uncertainty presented in Chapter 2, but the amortisation rate is now identified as the dependent variable. Also, the modelling explicitly covers two periods, so for example c1 and c2 are non-housing consumption in periods 1 and 2 respectively. A bar, as in c1, represents expected consumption.
Equations (4.2) and (4.3) correspond to equations (2.5) and (2.7), which were presented as the general form of the demand for mortgage finance under uncertainty. The equations follow Plaut, but the notation is changed to be commensurate with that used elsewhere in this book. Equation (4.2) is the utility function and equation (4.3) is the expression for expected wealth from which a budget constraint can be derived. The interest lies in the use of the additional arguments z and lv, which are the payment in the first period (the rate of amortisation) and the chosen loan-to-value ratio respectively. Also, note that expression (4.3) contains the argument (1 + E(rh)2)H which represents the expected increase in the price of housing, and A is the alternative risky asset to housing. The decision problem for the borrower is the choice of z, given optimum values of other variables. The modelling assumes that a prior decision has been made on the desired quantity of housing services to be consumed.
E( W2) = A(1 + E(rA) )2 + (71 - C1 - z)(1 + E(rA)) (4 3)
Table 4.1 shows the first order comparative static results for the Plaut model with respect to the rate of amortisation. The results indicate that a household with higher income, facing a risky alternative investment to housing, and not subject to mortgage rationing is likely to choose a large direct investment in their property, i.e. a high rate of amortisation in the first period of the two-period model. Plaut has an interesting note on the implications of varying amortisation rates for housing demand. The impact of a change in the amortisation rate depends upon the covariance between house price and the price of the alternative asset. If the covariance is positive then an increase in amortisation reduces the hedging possibilities
Table 4.1 The predicted signs on key variables from the Plaut model1
1 Plaut also considers the effects of price covariance, changes in mortgage limits and risk aversion. See Plaut (1986, p. 236).
of the consumer and housing demand falls. Negative covariance is ambiguous in its effects, higher amortisation can reduce housing demand because the borrower wishes to reduce the risk of a cash flow squeeze. Alternatively, housing demand can increase with increased amortisation due to the reduction in portfolio variance. The links between the choice of mortgage design, the tilt and housing demand will be discussed further in Chapters 7 and 8 where a number of key covariances will also be seen to be critical.
Plaut's model has an interesting focus on the circumstances under which a balloon payment would be considered optimal. A balloon payment is a one-off payment of the mortgage debt on the date of maturity, and corresponds with an interest only mortgage. This can be formally represented in a two-period model by determining when zero amortisation would be optimal for the first period. The model predicts that this option will be preferred when the household has a small mortgage, and when there is little risk attached to the mortgage interest rate, or the rate of return on the alternative asset to housing.
One strongly intuitive result is that a balloon payment will be preferred when there is a comparatively large rate of return on the non-housing asset, and the mortgage interest rate is comparatively low. This corresponds nicely with the case of the UK endowment mortgage where there have been periods of time when the expected rate of return on the endowment was higher than the net of tax mortgage interest rate (Lamb 1987, 1989). This was the basis of the mortgage demand estimates for endowment mortgage holders presented in Chapter 2. In the US, balloon mortgages may have maturities of 30 years but the final payment can be due after 3, 5 or 7 years. Thus these mortgages match the needs of mobile households and provide another interesting perspective on amortisation.
The Goodman & Wassmer model
The work of Plaut has been significantly extended by Goodman & Wassmer (1992). This is a multi-period model that demonstrates the advantages of a fully flexible mortgage instrument. That is the contribution to the economic welfare of the borrower deriving from the ability to vary the rate of amortisation of debt period by period. Optimum life cycle decision making requires that the marginal utility of income is equalised between periods. Liquidity constrained households will have difficulty in achieving this equality because of restrictions on their borrowing, and because conventional mortgage designs require constant payment scheduling. Flexible amortisation is one way of overcoming liquidity constraints and smoothing expenditure and saving between periods. This differs from the work of Plaut in that it is a model based upon certainty, and does not incorporate an alternative risky asset to housing, but it does offer important insights into mortgage design and life cycle planning. The discussion here is a broad brush presentation of what is a rather complex model.
Goodman and Wassmer formulated both a multi-period and a two-period model. The multi-period model is less tractable, hence the alternative formulation, but an inspection of the conditions for multi-period optim-ality where variable repayment is allowed, and where it is not, is instructive. Following Goodman & Wassmer, equation (4.4) gives the consumers' optimal decision with a constant repayment schedule. Expression (4.5) gives the consumers' multi-period optimal conditions when variable payments are allowed. The expression MUitnc is the marginal utility of income in each period (t), MRSt is the marginal rate of substitution between housing and a composite consumption good per period, p is the price of housing relative to the price of consumption with the latter used as a numeraire, and F is the discount factor.
Both expression (4.4) and expression (4.5) aggregate the period by period conditions over time periods. Both represent the equality of the price ratio with the marginal rate of substitution, multiplied by the marginal utility of income. The key difference is that the non-variable payment requires this equality to be achieved on average, that is with respect to an average price over all periods p*, while the variable payment mortgage allows period-by-period equality by equating the marginal rate of substitution multiplied by the marginal utility of income to the current price ratio pt. Removing the constant payment constraint increases the borrower's utility, with the size of this effect depending upon the form of utility function, prices and incomes (Goodman & Wassmer 1992).
Summary of the theoretical models of amortisation behaviour
The above discussion of the Plaut and Goodman & Wassmer models demonstrates the optimality of being able to vary the rate of amortisation
of debt. Though this perspective on mortgage design does not directly address the tilt, it does indicate the importance of repayment flexibility for overcoming constraints on the ability to borrow to finance non-housing consumption (or the effects of a tax subsidy on mortgage interest rates), a factor that adds to the impact of the tilt. The theoretical work of Plaut in particular emphasises the link between amortisation and the theory of mortgage demand under conditions of uncertainty. For example, the role of portfolio characteristics and key covariances such as that between the house price and the price of the alternative asset.
Goodman & Wassmer's model also has implications for housing, and thus mortgage demand. Simulations were carried out to assess the potential effect of a variable payment mortgage (VPM)15 compared to an FRM on housing demand in the US. Not only was there a significant positive impact upon housing demand, but there was also substantial capacity for a lender to charge insurance to cover the risk of attracting borrowers with an high propensity to default (adverse selection). These offer interesting perspectives on the recent growth of more flexible mortgage instruments. Whether VPMs can and do boost UK housing demand, reduce sensitivity to changes in the mortgage interest rate, or lengthen the planning horizons of borrowers are interesting questions for further research.
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