The Terrible Risk of Government Bonds


Readers are invited to have a look at this report on the British Banks. Much the same applies to banks around the world. I Quote from The Economic Consequences of the Vickers Commission - Laurence J. Kotlikoff - Professor at Boston, June 2012.pdf.

"...Indeed, today’s safest assets are, according to the market, UK gilts and U.S. Treasuries. But based on long‐term fiscal gap analysis, they are among the riskiest assets in the world. Yet, the Commission would allow good, ring­‐fenced banks, to borrow 25 pounds for every pound of equity and invest it all in gilts. In this case, the Commission’s ring­‐fenced banks would fail if gilt prices dropped by just 4 percent..."

If these assets are so safe then why do they behave with such extreme volatility? See FIG 6.1 below for USA Bonds as traded on a year on year basis:

FIG 6.1 - we will return to this later. The Blue line represents year on year market value changes in USA Treasuries.
Source: Morgan Stanley Research c/o Money Game Chart of the day.

As already explained on other pages, this graph is telling us that America reduced inflation over the period from 1980 to 2010 (the period illustrated), but this was costing USA tax payers 9% p.a. of GDP in interest per GDP of government debt initially and declining over time - see the trend-line. The decline would have been caused by the maturity of exiting bonds and replacement with new bonds at lower fixed rates of interest.

For the markets it was a massive wealth re-distribution machine. Wealth re-distribution happens when people and institutions deal with each other in these bonds or in their derivatives. Looking at the BLUE line which represents the true rate of return on an investment in these bonds on a year by year basis we see as follows:

A fictitious investor that bought and sold these bonds every year and who owned a GDP's worth of them, would see a small loss in the first year, and a massive 27% of GDP (not a 27% money increase) increase in value in the second year. The loser would be the one that sold the bonds at the end of the first year. The winner, the one that bought and sold in the second year.
Having such kinds of re-distribution of wealth both from tax payers and to and from dealers in the market place on such a huge scale in any economy is without question the source of a lack of confidence in the wealth of the nation. Neither the wealth invested nor the cost of servicing the wealth borrowed is safe, never mind the health of the banking and pensions sectors that may be forced to invest in such bonds as a 'risk free' asset. How would they put a value on such bonds? Market value is the only way but it is too volatile to make it the basis upon which to do business. 

The clear assumption made by the law makers is that money has a constant value and all of the interest is income. Yet everyone knows this to be untrue.

The need to reform the structure of government debt is urgent and essential to the future stability of the economies of the world. This is made particularly clear in nations where average incomes are falling as in Europe and as explained in Chapter 5, and in nations like the UK and the USA where there is a Low Inflation / Interest Trap created by the instability of these bonds, which threatens to create havoc as soon as interest rates rise.

Another way of saying this which was liked by a reader is this:


HERE is one main debt pricing problem which lies at the centre of current difficulties - take a few moments to have a look at this diagram and the words on it...

FIG 1 - Fixed Price Bonds v Compounding growth of incomes - what are they worth?

You can see the problem. No one knows what a Fixed Interest Bond is worth.

The result is that traders put guessed prices on the bonds and sell them in the stock market, so as predictions of economic growth and other variables change, the price of bonds varies wildly - like this:

FIG 2: USA Bond returns compared to average incomes / GDP (similar) 1980 - 2010

Source: Morgan Stanley Research c/o Money Game Chart of the day. Figures adjusted by Edward for AEG to reveal the true rates of return 1980 - 2010.
The true rate of interest is the marginal rate above the growth rate of GDP. It is a measure of how fast GDP borrowed gets increased in terms of GDP. A 1% true interest rate adds 1% of GDP p.a. to a GDP of debt. AEG% p.a. has been used here - meaning average incomes / earnings growth. It should give a similar result.

The trend line shows that from 1980 the  government was adding to their own debt (if they were not repaying enough), 9% of GDP p.a. at first and this has reduced to almost nothing now due to Quantitative Easing. This is itself enough to explain the ballooning of USA Debt over that period - just the debt servicing costs alone. It is enough to explain much of the rise of the wealthy class over that period.

The dealers who bought and sold every year would get the returns indicated on the blue line. A fictitious dealer that owned a GDP's worth of the debt might have lost some GDP in the first year, but gained 27% or so of a GDP in the following year. These trades are between winners and losers in the market place. They re-distribute wealth that may have taken a lifetime to save. The trend line averages this out.

Get the picture? No one knows what a fixed interest bond is actually worth. The damage done is immense.

Here is the maths of Fixed Interest and GDP-Linked Bonds - it is derived as a special case of a mortgage bond in which the Payments Depreciation is fixed at zero and the true rate of interest is fixed:

In 'Mathematics Chapter (to be named - but check this link in the meantime MATHS straight in' we derived Ingram's Safe Entry Cost Equation:

P% = C% + D% + I%

If C% falls the total repayment period increases.

If C% falls to zero, the loan is never repaid. 

If C% stays positive but D% falls to zero, the '% of the borrowers' incomes' payable remains the same throughout the repayment period.

It means that the cost rises as fast as AEG% p.a. 

I have used AEG% p.a. here as a proxy for the rate of growth p.a. of government revenues from incomes and other taxes on spending etc, but in practice it may be that some other index is used. The main thing is that it should be similar to some growth rate that attracts investors into the bonds and does not unduly vary the cost (of true interest and capital) to net government revenues. Both conditions cannot be satisfied at the same time by one index so choices must be made. But for now let us assume that there is a perfect index.

If both C% and D% fall to zero, the '% of government income' needed never alters and the loan never gets repaid.

This is a Wealth Bond.

The government / treasury issues a bond paying a fixed level of true interest only and index-links the capital to AEG% p.a. or (maybe) to Nominal GDP - NGDP.

Indexation has the same effect on the capital value of a bond as re-investing the same percentage of interest. For example, if a bond valued at 100 is indexed up by 5% it becomes worth 105 in money terms. If 5% tax free interest is added instead, it still becomes worth 105 in money terms. There is no difference.

A government that is borrowing does not need any D% - it does not get payments fatigue like ordinary people do, and it does not need to plan for its retirement as people do so there is no critical time for the repayment of the debt. Its revenues are likely to correlate fairly well to NGDP over the short term or to AEG% p.a. over the longer term.

If a government has borrowed a lot of money that it may never repay but upon which it pays interest, there will be a shortage of money in the economy. But if the government creates more money then that will prevent the shortage and enable the economy to grow anyway. This is a challenge to those who say that when government borrowing exceeds 80% of GDP the rate of growth of the economy slows. Why, and why 80%?

If it is not the lack of money supply available for borrowing, it must be due to the cost of servicing the debt - paying the interest rate coupon. 1% of 80% of GDP is not a lot. It equates to an addition of 0.8% to the rate of VAT or similar.

The real question to ask is how much government borrowing and then spending will distort the economy if there are no real limits that are clearly defined and that n=have little impact once new money has been created.

I will think about that and maybe write about it later. On second thoughts, if a government has that much power to borrow, then in the market place where there are limited amounts of money seeking a safe place to invest, that is where a heavily borrowing government will squeeze out access to capital to the borrowing private sector for businesses, households, and housing.

It is noticeable that in Europe due to austerity, the population is dropping so this affects NGDP but does not distort AEG% p.a. as far as investor like pension funds are concerned.

However, an index-link to NGDP is likely to suit a government's budgeting plans quite well. The servicing cost will be a fairly constant percentage of tax revenues and the amount of wealth that was borrowed will remain constant in those terms (by that measure) until maturity.

In FIG 6.2 below the spreadsheet writes AEG% p.a. as if it were the base / core interest rate, but readers can substitute the letters NGDP instead if they wish.

As can be seen, the capital value of the debt - the bond shown in the BALANCE column rises at that AEG% p.a. rate. 

FIG 6.2 - A wealth bond offering 1% true interest for 10 years.
Figures in billions
Source: E C D Ingram Spreadsheet
The bond is repaid on the maturity date. It is called a Wealth Bond because by index-linking to AEG it preserves the wealth which is defined as the amount of average income (or GDP) invested in the bond. 

Typically a wealth bond with a 1% interest coupon might be issued by a government to get cheap borrowing. Doing that instead of offering fixed interest bonds also adds to the nation's economic stability, removes the 'wealth redistribution machine' and underpins the reserves and the stability of the banking sector. It enables a government to reduce the level of inflation at no additional true interest rate cost, and it protects the nation's wealth invested in such bonds if inflation rises.

In short, it creates economic and financial stability in major parts of the economy.

Economic stability is increased because not only is the government's call on tax-payers both low and pre-defined, but the wealth invested in the bond is also safe. Even if the bond is traded on the open market its value will not vary wildly as current fixed interest bonds are prone to do.

For simplicity the above illustration shows that the government borrows 10% of annual revenue and repays a total of 11% of annual revenue over 10 years, which is 1% p.a. of the wealth borrowed plus the return of the wealth borrowed at maturity.

If the government prefers to create an index of total national income which is normally thought of as GDP, and if that figure is well defined in that way and is not manipulated,  then a wealth bond can be created with an index link to GDP. It should be about the same as a link to AEG% p.a. There is a discussion on this topic on the MATHS 3 page.

With this index the share of the GDP that a person has earned can be stored in such a wealth bond. The cost to tax payers is the true interest payable of maybe just 1% p.a. as illustrated above in FIG 6.2. The true cost is the 10% (1% p.a.) true interest paid and is the same as the wealth added to / earned by the lender. At maturity the amount of GDP that was borrowed has to be repaid. That costs no additional wealth / share of GDP than was borrowed.

Here is the bar chart. It compares the wealth bond (ILS) paying 1% true interest rate coupon with a 5% fixed interest (LP) bond paying the same 1% true interest. For the LP bond this true rate is due to the 5% interest coupon being payable in a fictitious fixed AEG = 4% p.a. environment.

FIG 6.3  - Index-Linked Wealth Bond payments of 1% compared with 5% Fixed Interest Bond payments. 

Paying 5% p.a. fixed interest means paying more p.a. but results in a maturity value which is less. The maturity value payable is 7.09% of revenues compared to the 10% of revenues originally borrowed / lent using the fixed interest bond whereas the maturity value of the wealth bond is the full 10% of the revenues / all of the wealth that had been borrowed. This shows that the fixed interest payments were eroding the stock of wealth owed at maturity.

Here is the tabulation for the fixed illustration of the above Fixed Interest Bond when AEG% = 4% p.a. in which the 7.09% figure is shown - right hand column, final payment.

FIG 6.4 - Fixed Interest 10 year bond paying 5% at AEG% = 4%
Source: E C D Ingram Spreadsheet
10% of government revenue is borrowed and 10.81% is paid back but the final installment paid on maturity is only 7.09% of revenue including the interest coupon of 5%. 

Why is less than 10% true interest paid? Why is 11% not repaid in total payments? Because the value of the debt reduces as more that just the 1% true interest is being paid. The debt is a reducing debt in true value terms - adjusted to AEG% p.a.

But in reality, neither AEG% nor the true rate of interest is fixed for a fixed interest rate bond. In the case of a fixed interest bond issued when AEG% p.a. is higher than 4% p.a. and repayable when AEG% p.a. is low or negative, the government has to pay out a great deal more of its revenues / wealth. The same thing happens when an economy is in trouble and AEG% p.a. falls as illustrated next.

But the Wealth Bond pays out the same 1% p.a. at any level of AEG% p.a. 

Here is how it would look if that same 5% fixed interest rate bond found that AEG% p.a. suddenly fell to -2% p.a. on account of austerity:

FIG 2.5 - Fixed Interest bond after AEG% p.a. has fallen
Source E C D Ingram Spreadsheet
Now that same bond is costing tax payers 17.84% of revenues instead of 10.81% of revenues for a loan of 10% of revenues. 

The final payment is 12.85% of revenues to repay a debt of 10% of revenues, and the cost of the interest coupon was rising every year as well. See right hand column.

The mathematical reason for this is that based on the equation:
I% = r% - AEG%

The true interest cost is:

5% nominal interest - (-2% AEG% p.a.) = 7% true cost p.a.

But the 1% fixed true interest rate wealth bond is largely unaffected in these terms. The true cost remains at 1% p.a:

FIG 2.6 - Wealth Bond cost / benefit is almost unchanged
Source: E C D Ingram Spreadsheet
In FIG 6.2 with AEG% p.a. = 4% the wealth bond cost tax payers 11% to service a '10% of revenue' bond - exactly the same figure as here in FIG 6.6 with AEG% p.a. = -2%.

The money repaid is less but the investor still gets back the same proportion of GDP as was lent. The government has enough trouble with revenues falling, so the fixed interest bond would be adding a significant additional cost when the economy can least afford it. 

With fixed interest bonds during recession or austerity, wealth moves from the poorer tax payers to the wealthier investment institutions and others, and economic recovery takes longer and is more costly.

Here is the Bar Chart comparison:

FIG 6.7 - % of revenues needed to repay - comparison of fixed interest (LP) and wealth bonds (ILS)

Source: The above spreadsheets
Now as shown, (blue bars), the government is paying out five times as much every year and still has to repay a higher percentage of its (then reduced) revenues on maturity.

In fact in FIG 6.7 it shows that the cost-to-revenue is rising every year with the fixed interest bond.

This is the kind of thing that happened in the 1980s to American tax payers after the great inflation was brought under control. Remember, the following chart shows the return to investors who were trading in government bonds at that time:

FIG 6.8 Cost / Returns on USA Treasuries 1980 - 2010. This needs a little explaining - see below the graph

Source: Morgan Stanley Research c/o Money Game Chart of the day.

Any bond that is index-linked to AEG% or to GDP as defined here, can be called a wealth bond. It does not matter whether the capital is repaid in installments or at maturity, the indexation simply preserves the share of the national income or of National Average Earnings (NAE) that was lent / invested in the bonds.


There is more related reading on these issues in the GLOSSARY page and in the WEALTH BONDS page. Click on those links.

The Glossary discusses true interest rate v real interest rate in more detail.

The Wealth Bond page has some amazing illustrations of wealth bonds as applied to mortgage finance.

More reading of interest can be found in the NEW PRODUCTS RESULTING page. Click that link to read it. It is full of fascinating practical uses for the knowledge that you have gained already.

I will also be adding a lot of back-testing and discussions for the ILS Mortgage model in later pages of this Blog.


Because, for the standard Level Payments Mortgage, D% = AEG% the risk manager has no control over this D% function. This is why this Mortgage Model gets into difficulties when AEG% is low or negative: the downwards slope of the ‘% of income’ can become level or turn upwards as AEG% reaches zero or below zero. The cost may go above and outside of the 30% of income 'box'.

With the LP Model, this means that if I% rises, and D% is determined by AEG% p.a. at all times, then the value of C% is all that remains for the risk manager to mange in order to protect P% from rising or jumping upwards.

FIG 2.5 - This is a bad case of the LP Model going out of control. The blue bars are the LP payments and the other bars are how ILS Model payments might behave with the same interest and AEG rate data.

In practice, the Level Payments (LP) Model nearly always jumps the 'X' up and down the Y-Axis so as to keep C% where it needs to be to repay the loan on schedule.

This is a requirement of the regulators who will treat any deviation with suspicion.

Another way to write the equation for the LP Model is this:
P% = C% + AEG% + (r% - AEG%)
because I% = r% - AEG% by definition. r% being the nominal rate of interest.

This then reduces to:
P% = C% + r%

So if r% rises P% rises, making the payments jump upwards. If C% reduces to zero as r% rises, then we have an interest only payment:
P% = r%

This arrangement is far too inflexible. It is unable to ride out many changing conditions.

Furthermore, when r% falls, P% also reduces and then lenders increase the amount of wealth that they lend.

When (not if)  r% rises again P% rises, but by then too much wealth has been lent and costs rise out of control.

The Level Payments (LP) Model has neither proper control over the slope of the '% of income' (cost) bars nor any proper control over the amount of wealth that may be lent. The interest rate and inflation rate risks and the risk to the value of the collateral security, (property values generally), are simply out of control.

If the mortgage model is released from this straight jacket of always paying all of the nominal interest r% and P% is made to start high enough (by the risk manager) to ensure that F% has a useful value (F% = C% + D%) then both D% and C% can be reduced to help to protect the value of the payments going forward, if I% rises.

If the payments are not enough to prevent the mortgage balance from rising lenders can offer a rent-to-buy contract in place of a mortgage, and the arithmetic remains basically the same except for additional costs which may be small.

In Turkey they have introduced a wages-linked mortgage where D% = 0%, and I% is fixed. It is not very user friendly and the risk of arrears and losses by the lender is made significant by this omission.  The mortgages run for only 15 years.

Do a Google Search on "Kanak Patel" and "Turkey Mortgage"
Various commentaries can be found there.

In fact the Turkish model was first designed by me in 1974 and it was published in the Building Societies Gazette in October of that year.

But on 11th April 1975 my letter to The Times was published asking for funds needed to refine that model. I needed to find the Safe Entry Cost Equation. I needed to add D%.

Click on FIGs to enlarge and read then click back page to return.

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