## The tilt and cash constraints

The discussion of mortgage demand presented in Chapter 2 and Chapter 3 briefly noted the importance of the so called tilt, that is the tilting of the real value of mortgage payments towards the early years of the debt. The presence of the tilt meant that borrowers might experience cash flow problems, and a case was made for using the nominal, rather than the real mortgage interest rate when estimating mortgage demand equations. The tilt is likely to be particularly problematic at times of high and volatile inflation when borrowers using variable rate debt are exposed to adverse interest rate risk, that is, sudden unanticipated increases in their mortgage costs. Existing fixed rate mortgage holders face the risk of a fall in the prevailing inflation rate which front loads real payments even more, though the eventual impact of this depends very much on the ease of refinancing.

Though house price inflation can reduce user costs by generating capital gains on residential property, the tilt may offset any such benefit. A number of alternative mortgage designs have been suggested to overcome, or to minimise this problem; for example the graduated payment mortgage or GPM. The tilt owes its importance to other capital market imperfections, such as liquidity constraints that prohibit borrowers taking out additional loans to overcome their temporary cash flow difficulties. This has led to suggestions that mortgage payments should be indexed, so they remain equal in real rather than nominal terms over time (Friedman 1980; McCulloch 1982; Houston 1988, Buckley et al. 1993). These arguments and the proposed alternative mortgage instruments are discussed below, but firstly it is important to understand exactly what the tilt is, and when it is a significant problem.

The basic annuity formulae determines a constant mortgage payment, at a given interest rate, that is just sufficient to pay off the principal sum borrowed plus all interest due by the end of a given term. This is the standard formula used in mortgage repayment calculation.3 The annuity formulae front loads, or tilts, the real value of payments towards the early life of the loan. This is the inevitable result of keeping payments constant in nominal terms. In a static economy with a constant and fully predicted inflation rate, constant nominal payments will fall in value in real terms over time. So the tilt occurs even with steady state inflation. Now, if the inflation rate, increases, the aim of the lender will be to preserve the present value of the cash flows attached to a mortgage. If interest rates rise to match new inflation expectations then the mortgage payments in the early years will have to increase more than proportionately to compensate for the higher rate at which payments fall in value in future years. Of course, the increase in the inflation rate must be unanticipated or it would be priced into the original mortgage contract, a further obstacle to afford-ability. Thus the tilt is exacerbated when inflation is not in a steady state and unexpectedly increases.

Figure 4.1 illustrates the tilt problem from the lenders' point of view, and is based upon an illustrative method used by Brueggeman & Fisher (1997).4 The line labelled NVP represents the nominal value of payments on a 25-year term, £50,000 mortgage (that is £263.90 per month). The interest rate generating these payments is 4%. The line labelled NVP assumes that inflation is zero, so that the 4% is the real rate of return to the lender. Now consider the effect of the rather dramatic occurrence of inflation at a rate of 6%. Assuming that the lender wishes to earn the same real rate of return

Months

Figure 4.1 The tilt problem.

Months

### Figure 4.1 The tilt problem.

(4%), then the nominal interest rate charged on the mortgage must be approximately 10% (that is roughly 4% real rate plus 6% inflation). The line INP represents constant nominal payments after including the compensation for the 6% inflation rate, that is £454.40 per month. It is worth noting the effect of the additional 4% here, which is to raise payments by 72%, from £263.90 to £454.40 per month. Though for heuristic reasons the example is rather extreme, it is clear that the cash constrained household is vulnerable to mortgage interest rate changes (Kearl 1978; Friedman 1980; McCulloch 1982; Houston 1988; Buckley et al. 1993).

Figure 4.1 includes a third curve (RV) representing the real value to the lender of the constant monthly payments that they will receive after charging the 10%. Not surprisingly the payments fall in real terms over time, reflecting their constant nominal value. In the early years the deflated payments are above the 4% real payment line, in the later years they are below. The objective of the lender is to sustain the real rate of return of 4% over the life of the loan. To offset the declining real value of the nominal payments, the real payments must be front loaded. This front loading applies to any mortgage instrument where payments are constant in nominal terms.5 From the borrower's point of view nominal incomes may be growing with inflation, but they are unlikely to offset higher real mortgage payments. Equally, younger households who might anticipate rising incomes are disadvantaged by high initial and constant payments rather than facing a gradually increasing payments' profile.

Kearl (1978) presented another interesting way of viewing the tilt that represents this bunching up of real payments in time. He used a measure of duration typically applied to evaluating and immunising bond portfolios. This formula emphasises the weighting given to early years of debt repayment.6 Duration is time weighted (multiplied) by the present value of the debt repayment due at that time. So the maturity or life of the debt is not viewed in calendar years, but according to the significance of these years in terms of the present value of the cash flows associated with them. The upshot of this calculation is that when the nominal mortgage interest rate rises then the duration of the debt falls (future payments are discounted more heavily). This means that in real terms more of the debt is paid off more quickly. Duration changes though the contractual time to maturity of debt payments remains the same.

Miles (1994) utilises a comprehensive calculation to demonstrate and contextualise the tilt, and to demonstrate the effects of various levels of inflation and corresponding nominal interest rates on the mortgage payment burden that a household faces. A slightly modified version of this equation, presented below (4.1), highlights the characteristics of mortgage contracts which impact upon the debt service burden facing the borrower. For clarity the subscript for time period t, is generally suppressed.

The arguments are the loan-to-value ratio lv, the house price-to-income ratio hi, the rate of growth in income g, and the rate of price inflation p. The burden of debt is measured by m / y where m is a period t mortgage payment and y is the value of disposable income at t. The formula is based upon the assumption of a constant nominal interest rate r. This formulation places the tilt in a wider economic context, for example by including rates of income growth and the chosen loan-to-value ratio. The intuitive picture here is that the mortgage burden increases with gearing, inflation (including house price inflation), and the interest rate, but falls with rising incomes.

m/y = (lv)(hi)[(1 + p)(1 + gy]-t/[1 - (1/(1 + r)T+1)] (4.1)7

Using typical UK values to parameterise the equation, simulations by Miles for various rates of inflation (maintaining a constant real interest rate) indicate that even at low rates of inflation the proportion of income taken up by mortgage payments is significant. Thus at 2% inflation the debt burden was over 14.5%, falling to 10% of income after nine years. Miles notes that the greatest difficulties for borrowers arise when there is both high inflation and a policy response by the monetary authorities involving raising the real rate of interest. However, the tilt and affordabil-ity problems can be important even at low mortgage interest rates. Low inflation and corresponding low interest rates slow the erosion of the real value of mortgage payments and expose the borrower to interest rate and credit risk for a longer period of time. Also at low interest rates rapid house price inflation could impose stresses on affordability, and ration entry into owner occupation.

There can be confusion when reading the literature regarding whether the tilt refers to the level payments determined at the outset of a mortgage contract (a steady state model), or to the effects of changes in the mortgage interest rate on the profile of the real payment burden (unexpected changes in inflation). In fact, as suggested above, it relates to both of these considerations. US books and papers typically associate the tilt with the fixed rate mortgage, where payments are fixed in nominal terms for the period of the contract. Clearly, adjustable or variable rate debt can see a fall in the immediate payment burden if interest rates fall. However, mortgages with adjustable or variable rates of interest do face interest rate risk, and potential cash flow problems. Prospective homeowners might also face difficulties in entering owner occupation as a result of adverse changes in the mortgage interest rate and its effect on the real burden of debt repayment (Brueckner 1984). Fixed rate debt holders also face the risk of a fall in inflation and interest rates which will bring real payments forward in time (see Miles 1994), a significant effect in the UK where prepayment can be attended by penalties.

Why does the tilting of mortgage debt emerge as such a problem? With perfect capital markets consumers would be able to borrow more money to offset any increased real debt burden. Alternatively, a mortgage instrument could be designed that allowed consumers to pay off their debt at a constant level in real rather than nominal terms. There have, in fact, been a number of mortgage designs that have been introduced to overcome this difficulty. These range from graduated payments giving first time buyers lower initial outlays, to actual price level adjusted mortgages. However, these mortgages have not always been prevalent, and the cash flow problems remain for some households. In periods of low inflation affordability problems can still arise if house price inflation is not neutral in its effects on the value of the asset (the property) and the burden of the liability (the mortgage).

So what are the effects of the tilt on economic welfare? House price inflation, leading to capital gains on property, can lead to falling user costs of owner occupation, even at times of rising nominal interest rates (Diamond 1980). Tax subsidies on mortgage interest rates also add to this effect (Rosen 1979). However, increasing mortgage interest payments exacerbate cash flow difficulties arising from the tilt. This raises the interesting question of which has the greater effect on consumer welfare, reductions in user costs or the negative impact of the tilt?

Alm & Follain (1984) presented a model of constrained lifetime utility maximisation using a constant elasticity of substitution (CES) utility function, with housing and non-housing consumption as arguments. Simulations were used to evaluate the impact of the tilt. They also assessed the efficacy of various forms of mortgage design. Three types of mortgage were considered - the graduated payment mortgage (GAP), the shared appreciation mortgage (SAM) and the price level adjusted mortgage (PLAM). They concluded that at high rates of inflation the negative impact of liquidity constraints offsets the lower user costs. The three alternative mortgage instruments did confer significant benefits to consumers, but these might have been overstated by using a model based upon certainty.

## The Debt Beater System

Learn How You Can End the Fear and Worry Created by Bad Credit and Debt Collectors. Get Out of Debt Quickly and Easily, Right Now. I am going to show YOU how to become a

## Post a comment