MATHS 4 - The ILS Hybrid and Practical Issues

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The INGRAM SCHOOL is a new school of thought - it provides a refreshingly practical and down to earth new theory of business cycles and how to manage them.


When it comes to marketing a new financial product there can be a lot of expense and anxiety. Educating the public can be a a torturous process. With that in mind it is suggested that in countries where inflation is low and the public is afraid of interest rate increases one way forward is to offer the usual familiar Level Payments Model with an additional option - to switch over to the ILS Model if needs be.

Welcome to the ILS Hybrid Mortgage Model

Before reading this, please note that if e% = 0% (the Level Payments (LP) Model), then D% = AEG%, always.

The first and simplest-to-use practical application is to allow the ‘X’, which is usually confined to the Y-axis for a Level Payments Mortgage (zero e% p.a.), to leave the Y-axis, when it seems reasonable to do so. Not forgetting to apply the Safe Entry Cost Equation to determine P% and the amount that can be lent when setting up the mortgage. This will tell you how large a mortgage may be safe - knowing that others may be crossing the safety barrier.

In other words, if your competitors are not joining in with restraint in lending, then you can lend more but your D% will reduce when you need it most. On the other hand, when interest rates rise your competitors will crash out and possibly go out of business unless you take them over...

FIG 4.1 - A sketch using straight lines (they should be curved) illustrating how over-lending will reduce D% and cost borrowers more.

The sketch was originally created to illustrate the relationship between the slope D% p.a. and the rate of true interest I%.

The sketch is the same in this case because if too much is lent when nominal interest rates are low, then when interest rates rise the amount of wealth that has to be repaid in the same 25 year period will increase. This leads to a shallower slope.

The other danger that your competitors will bring is those inflated property prices.

I have seriously suggested that a commission of enquiry be set up to deal with all of the issues (page 10 as per the link) and this is high on the agenda because in many nations property prices are inflated because P% is too low.

On the agenda is the proposition that the value of P% can be left where it is but gradually increased as incomes rise. This will allow the economy to recover without an interest rate related economic squeeze costing jobs.

The alternative that has been proposed by policy makers is to raise the level of deposits and / or to raise the capital requirements for lenders yet again. The intention is to prevent inflation from taking off.

But if inflation does rise it will speed the recovery process without causing an economic squeeze / dip / crisis as long as we structure all of the debts, and savings appropriately so that the link to AEG% which would then be rising quickly is created and kept. This can bring a soft landing to the economy as interest rates rise.

In the event of interest rates and AEG% rising very high then lenders can offer a rent-to-buy alternative which hides the numbers but repays the mortgage and manages the cash flows in the same way as the maths predicts.


During an economic/business cycle, interest rates rise to offset inflation and they rise further to slow inflation. If AEG% p.a. is rising the AEG% line is moving to the right. D% is growing larger. Why not move the ‘X’ to the right instead of increasing P%?

If this is permitted under the mortgage contract and by the regulations, we have a HYBRID ILS Mortgage Model.

The mortgage starts off as an LP Mortgage at an appropriate P%, but there are ILS Options, meaning that the ‘X’ does not always have to be on the Y-Axis.

The chances are that interest rates will be rising because the demand for money (borrowing demand) has risen and incomes have been rising faster, leading to rising prices. The AEG% line has moved to the right and interest rates have risen forcing the LP Model to jump up the payments by 12% or so per 1% raise in the nominal rate of interest.

FIG 4.2 - Risk Management in ILS Hybrid Mode

But the move to the right of the AEG% line opens space for the ‘X’ to move to the right without even reducing the value of D%, which is always equal to AEG% for an LP Mortgage.

Thus, in this example, as shown, if borrowers are looking stressed because the lender was going to jump the 'X' up the Y=Axis, the increase in the payments can be postponed without having to reduce ‘C%’ (or even D% if we are lucky). This means that the mortgage will be repaid on time and the borrowers will feel no significant stress.

As long as P% starts high enough, this strategy has a lot of merit. If AEG% was very low taking interest rates low, and the LP Model lent too much, (with P% too low to give a good value to D% even on ILS), there is not so much scope for moving the ‘X’ sideways. Then both lenders and borrowers are in trouble. The solution is NOT to lend more as interest rates fall and to keep the ‘X’ higher, as if interest rates had not fallen.

P% = C% + D% + I% and I% tends to revert to mean value so a low P% reduces D%.

But as already explained, there is a problem What if the other lenders are lending more? Let them do that. You can also lend more if you wish because when interest rates rise and put them into difficulties you will still be able to move to the right, albeit with a smaller value of D%. Not nice for borrowers but they are better off with you. And now you can pull deposits from those other lenders because much more (than before) of the interest that they are earning will go in risk costs, which will not happen so much to you. You can pay more for deposits and savings. Your profits will be higher. Your ROI better.

In normal times it is better if there are agreed guidelines for all lenders to follow, keeping the value of P% nearer to the long term average level and stabilising property values, (collateral and wealth), then everyone would be safer, and the need for high reserve ratios more questionable.

Let’s look at some other problems and solutions.

Starting again with:
P% = C% + D% + I%
For the LP Model we can go back to the expanded equation. Remember,  I% = r% - AEG%:
So when D% = AEG% and e% = 0%, this equation becomes:
P% = C% + D% + r% - AEG%
Which reduces to:
P% = C% + r%
This looks very familiar.

The payments do not escalate and the only margin of safety to protect the value of P% is that very small value of C%. If the interest rate r% rises by C% then we get a standing loan. If r% rises just a little C% reduces and we get a very extended repayment period. A 25 year loan quickly becomes a 30 year, then a 50 year loan. A bit more and C% = 0% and we are on the standing loan line:
P% = r% interest only.

r% may rise for one of two reasons:
FIRSTLY, Because the level of inflation of incomes (AEG% p.a. has been growing), leaving I% untouched. This means that r% and AEG% have both risen by the same percentage. Remember: I% = r% - AEG%.

Keeping I% constant during an economic recovery makes some sense if the ILS and other debt structures are in place. Otherwise if AEG% rises and r% does not rise, then I% will fall, stimulating the borrowing sector further when it is already moving well in the right direction. 

Remember, the ‘wealth transfer’ effect of I% is felt by all forms of borrowing. It may be argued that people do not think this way - at present. That can change. I% p.a is the rate of transfer of wealth from borrower to lender that is determined by the true interest rate and that is important to everyone. 

The rate of transfer of wealth from all economic activities is important to policy going forward. How much wealth has moved, from where and to where, and how much has 'paper wealth' (the value of tradeables like Equities and Bonds and Property) has gone or increased and how much is still left behind for spending by the borrowers will shape the economy going forward. It is a factor.

SECONDLY, I% may rise to slow the rate of inflation when the economy over-heats, “getting ahead of the curve” as some people call it, and in our words, by making the wealth transfer rate faster (making the true cost higher) by raising the true rate of interest on all forms of borrowing.

The LP Model does not understand the difference between rising r% and rising I%. By the time the true interest rate needs to rise to slow inflation and borrowing in all borrowing sectors, the LP Mortgages are already in trouble.

The LP Model responds only to rising r% and so it will slow an economic recovery by distorting the whole lending and borrowing sector. The property sector becomes an instrument of economic policy instead of being just another part of the economy.

I have explained the feedback effects in my online school as the Low Interest Rate Trap.

So with the equation
P% = C% + D% + I%,
what we have is a general equation for any kind of mortgage in which the usual Level Payments (LP) model is just a special case where we are putting D% = AEG% whether that is justified or not.

Remember, D% = AEG% for the LP Model.

During a recession AEG% can be low and the numbers could look like this in the first year:
Here, P% = 2.401% (C%) + 1% (AEG% = 1% = D%) + 3% (I%) = 6.401%

This gives a mortgage size of 4.69 times income, potentially inflating property values. I% may not have fallen because AEG% p.a. has fallen and the interest rate did not fall so far. It did not have to fall much because the low P% was already increasing the demand for mortgages.

But when AEG% rises back to the more normal 4% p.a., if r% is not raised we will get a true interest rate of zero% and still the mortgages will cost 6.401% p.a. of the sum borrowed. That is unsustainable and inflationary.

To return (post-recession) to a true interest rate of 3% - the average long term rate for the UK (or similar) – we could then be seeing this for a first year mortgage:

Payments have risen from 6,401 p.a. to 8,581 p.a. and the size of new loans has dropped from 4.69 to 3.50 times annual income.

In percentages these figures are a 34% increase in entry cost payments, and a 25% fall in property values / mortgage sizes. So lenders are faced with a huge rate of arrears and they have to repossess properties that may be worth 25% less. Poor borrowers – did anyone think of them?

It would be better to always start with P% closer to 8.5% by shortening the repayment period as the nominal rate of interest falls. This will raise the value of C% a lot, and keep the value of properties (the collateral security and the wealth of the nation) more stable at the same time. Here are the figures for an 18 year mortgage at 4% interest:

FIG 4.3 – An 18 year LP Mortgage

The payments are slightly lower and the mortgages are slightly bigger at 3.80 times income, or 8.6% higher. That is enough to stimulate the economy in this sector, and it has the advantage that people will not worry about interest rates rising during the recovery, nor will they worry a lot about property values falling. It is much safer for the lenders and everyone else, including the economic recovery. There is no multiplier effect on spending and borrowing through the reduced entry cost or through a bubble of wealth, causing panic buying of property.

If we then allow the ILS HYBRID Mortgage Model we get this:

FIG 4.4

The interest rate rises from 4% to 7% taking the standing loan line up with it as arrowed (near the X-Axis).

The usual LP Model starts the ‘X’ too low and leaps upwards along the Y-axis as shown by the curved arrow, causing havoc.

The 3% rise in AEG% p.a. from 1% p.a. to 4% p.a. triggers a 3% rise in r% raising the standing loan line by 3% - both changes are as shown.

The ‘X’ now has space to move to the right by 1% giving D% = 3%, the distance to the new AEG% line.

FIG 4.5 below shows the way that the new position of the ‘X’ might work out in figures.

 FIG 4.5 – ILS HYBRID Adjustment

D% is still a comfortable 3% p.a. The mortgage payments rise every year, but as a percentage of income they are falling by 3% p.a. to end at 14.29% in the final year, down from 30%.

The above spreadsheet generated this picture of the bar chart.

FIG 4.6


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