Page revised on 30th October 2013

I saw a comment on LinkedIn which stated that interest rates should be about equal to AEG% p.a - the rate at which Average Earnings / Incomes are growing.

Here is what I wrote in reply: -

Connel - I used to say that the most neutral interest rate would be one that is equal to AEG% p.a. - the rate at which average earnings were growing, and without taxation or tax relief of course. No tax because that rate of interest simply preserves the wealth of the lender and ensures that the borrower repays the wealth that has been borrowed.

But this rate of interest would allow people to borrow and invest in property whose value would be propelled by AEG% p.a. plus they would get rentals on top. For one example.

Anything less than AEG% interest would mean that a person could borrow three years' average income and only need to pay back two and a bit years' income, or less, depending on the actual marginal interest rate, called the true interest rate. If the nominal interest rate is less tahn AEG% then the true rate is negative and wealth flows from lender to borrower.

True interest is not real interest. It is the marginal rate above AEG% p.a. and which rate of growth carries with it the real rate of economic growth, or  similar.  

True interest rate is added on top, and typically averages around 3% for Housing Finance in the UK.

Here is an example of a traditional Level Payments Mortgage being repaid when the true interest rate s zero  because the nominal interest rate is at the same leve, 7% a - s average incomes are rising - also 7% p.a.

FIG 1 - Zero true interest

The loan starts at 100,000 and interest of 7,000 (7%) is added at year end. A repayment of 8,581 (8.581%) is made at the same time reducing the debt to 98.419. This payment is made after incomes have risen by 7% so it represents 28.04% of the then income of borrowers.

The debt of 98,419 is carried down to the next kine and the process repeats. This continues until the debt is repaid in year 25.

Adding up the total amount of % of incomes paid we find that it comes to 350% or 3.50 years' income, which is the same amount of income that was borrowed.

Now if we alter the rate at which average incomes are growing to 4% p.a. then we still get a loan of 3.5 years' income but it takes 4.69 years' income to repay. See FIG 2.

FIG 2 - 3% true Interest

And if we raise AEG% p.a. to 11% so that the true rate of interest is -4% we find that it costs only 2.53 years' income to repay - saving the borrower a full year's income.

FIG 3  -4% true interest

What this means is that the total wealth involved remains unchanged, but the borrower gets to spend 3.5 years' income initially and after repaying 2.53 years' income he/she can then spend the balance of 0,97 years' income however he/she wants to spend it.

The lender lends 3.5 years' income and gets back 2.53 years' income less costs, to spend.

The wealth has not been destroyed. It has been passed around.

The borrower might have bought a property that rose in value at a rate of AEG% p .a. at 11% p.a. and got some rental as well. If AEG% p.a. had been 7% p.a. the lender gets 7% p.a. but the borrower can invest in a property that may rise at 7% p.a. and get some rental income on top - net of costs.

What has this to do with Siegel's Constant? 

Lenders have to compete for funds and if on average they are getting a better return on lending than shareholders can get of that property  owners can get then it makes sense to invest in lending.

What Jeremy Siegel and others have found over decades of stock market performance, even 200 years for the USA Stock market indices is that returns have outpaced prices by a fairly consistent rate - albeit with some decades not performing at all.

Doubt has been thrown on what should be expected in studied of other stock markets which have not performed nearly as well, and all of the studies use the proces index as a basis for comparison.

This is not easy to understand because prices do not create demand for property and they do not drive turnover and share prices. That prize goes to spending and spending and income are closely related as is the amount that you can borrow to buy a proeprty - that is income based not prices based.

As incomes rise people can compete better to buy or to rent a property. And that has a lot to do with how property prices behave.

As incomes rise, people spend more and people cost more to hire. The result is that turnover rises and profits tend to rise proportionately. Dividends then rise similarly.

So if we are going to apply the Siegel analysis to what we can expect to get from an investment in shares we should at least expect a positive true rate of return.

Unfortunately only real rates of return are ever recorded. So we have to subtract an estimated rate of real economic growth to get the true rate of return.

Since we know that if interest rates are zero true rate there is a compelling incentive to borrow and invest in property for example, than we also know that interest rates are too low to be sustainable. Credit will be created, increasing money supply and stimulating demand beyond a sustainable domestic level. 

This sets a lower boundary / bound to sustainable true rates of interest. True rates can and do spike downwards but they must on average be above Zero by a margin to prevent an inflationary take-off.

The upper Boundary,/ bound should logically (if investors are logical) be less than the true rate of return from other forms of investment such as property and equities. Thus we have to take a look at Siegel's constant and we have to take a look at the equivalent data for other nations, which has been done as reported here:

Clearly the upper boundary for true, secured lending interest rates, is not very high.

So we have to conclude that over the medium to long term true rates of interest, when the risk element is low, have to find a place above zero and below the true rate of return to be expected by rational investors which is about the real rate of economic growth below the real rate of return that is expected.

Why is that?

If incomes rise at 4% p.a. AEG% p.a. and prices rise at 1% p.a. the difference of 3% p.a. is approximately the real rate of economic growth. The true rate of interest at 7% say, is also 3% p.a. making a 6% real rate of interest.

AEG% = RPI% or CPI% + Real Economic Growth%

Where the nominal rate of interest is r% we have by definition:

r% = AEG% + True interest I% which now gives us:
      = RPI % or CPI%+ Real Economic Growth + True Interest I%

Studies reported by Fidelity Unit Trust group gave a real rate of return from UK and USA Equities of around 7% p.a. and for UK properties somewhat less. If we allow an estimated real rate of economic growth of 3% p.a. sustainable, then average incomes will be growing about 3% p.a. faster than that at 6% p.a. So the true rate of return on equities comes down to 7^% - 6% = 1% p.a.

This is not consistent with a true rate of interest on housing finance in the UK of around 3% p.a. from 1970 to 2002 - see FIG 4

FIG 4 - The UK True rate of interest 1970 - 2002

This is why I have assumed that there is an expected (if irrational) true expected by investors rate of return from equities of not ore than 5% and less from properties. For otherwise investors would lend instead of buying equities or property. 

That 5% upper boundary and 2% lower boundary would allow true lending rates on low risk housing finance (in those days) to be at least a rental above zero, say 2% above zero and maybe 2% below the expected return on equities, at 3% p.a.

In short, true interest rates on average occupy a narrow range of values between say 2% p.a. and 4% p.a. in those two nations.

Here is another way of thinking it through:
This AEG% p.a. interest (zero true interest) is not enough to discourage borrowing and it would lead to a shortage of funds to lend, or to inflation until the interest rate rose to balance supply with demand. Pre-crisis the USA Mortgages were sold at -1% true or even less, which was 4% below par. This gave rise to swollen mortgages that were going to cost something like eight years' income to repay by the time that the 3% mid-cycle true interest rate was restored. See FIGs 5 - 7 below

FIG 5 - Pre-Crisis Americans were borrowing at 3.5% yet AEG% p.a. was around 4.5% and rising. True interest was -1% Mortgage size even over 25 years could have been 4.94 times income. The cost of repaying at that rate would have been 4.45 years' income.

FIG 6 - Post Crisis with interest rates averaging say 7% had normal rates been restored, and keeping the mortgage size inflated as before, the cost of repayments could have been anything from this at 3% true interest costing 6.63 years' income, to 8.28 years' income shown in FIG 7 below.

FIG 7 The same Mortgage at 5% true interest is supposedly due to a low future rate of economic and incomes growth of 2% p.a. but a fixed nominal rate of 7% interest. This is perhaps an unlikely combination, but it does highlight the risk of a fixed nominal rate of interest when incomes are not rising.

If you read Adam Smith's Wealth of Nations you will find that an economy, to grow fast, has to balance the supply with the demand using the pricing mechanism, which in this case is partly the interest rate and partly the entry cost for a new mortgage or loan.

As I wrote earlier, based on data that I have obtained for the UK this appears to require interest rates to be around 3% more than AEG% p.a. Hence the need for the Fed to raise rates by around 4.5% to get above norm of around 7% nominal interest or to around 4% true interest for housing and proportionately more or less for other forms of borrowing..

A page on Siegel's constant and expected real economic growth:
Finding the Mid-Cycle Rate of Interest - a page on this Blog

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