Economic Myths - The Money Multiplier

Please note, this myth is quite different to the government spending multiplier myth, which I debunked here.

Wiki's take on the money multiplier is here. The article includes a clue (itself flawed) as to why it is flawed here:

In the ["Loans first"] model of money creation, loans are first extended by commercial banks – say, $1,000 of loans (following the example above), which may then require that the bank borrow $100 of reserves either from depositors (or other private sources of financing), or from the central bank. This view is advanced in endogenous money theories, such as the Post-Keynesian school of monetary circuit theory, as advanced by such economists as Basil Moore and Steve Keen.

This myth is based on a misunderstanding of how banks work. The traditional somehow static model makes the following basic mistakes:

a) There is a limited amount of "money" in circulation.

b) Banks can only raise a limited amount of "share capital".

c) Banks take deposits first, and then they lend them out.

d) The amount of "money" which people would like to borrow is unlimited.

Therefore, they conclude, if the Basel Ratio, the total amount of share capital is set at 20% of total assets, banks will lend out five times as much as their total capital. If the Basel Ratio is reduced to 10% (i.e. leverage increased from five to ten), banks will be able to lend out ten times as much as their total capital.
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If you remember The Golden Rules, clearly this is nonsense as the assumptions are contradictory. The Golden Rules are...

e) As far as banking is concerned, "money" is not a thing in itself. It is a unit of measurement, and what it measures it indebtedness between 'borrowers" and "depositors" with the bank acting as middleman. So total financial assets always equal total financial liabilities, down to the last penny. It all nets off to nothing.

f) A bank's capital structure is not particularly important, i.e. how the "financed by" or "liabilities" side is split up between share capital, bonds and deposits. Building societies traditionally were 100% funded by deposits, for example. The old textbook example of the goldsmith who lends out customers' gold at interest also assumes that the entire operation is funded by deposits. A bank could easily be 100% share capital financed, the bank would simply have to have a rolling operation whereby shares are constantly being issued and redeemed at very close to net asset value per share, which would be close to par value.

f) Loans create deposits, not the other way round. When you take out a £10,000 personal loan, a bank "splits the zero" by creating a deposit account for you with £10,000 in it which you can withdraw and spend, and a personal loan account which means you owe the bank £10,000.

g) Clearly, there is an upper limit to the amount of money which people, collectively, want to borrow at prevailing interest rates and conditions, because a bank, however reckless and well or badly funded will adjust the interest rate and conditions depending on people's ability to repay.
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So even if (b) were correct (it is not entirely incorrect, to be honest, but this is market psychology at work) the conclusion above is clearly nonsense.

If a bank has a fixed amount of share capital £100 and the Basel Ratio is 20%, they can lend out £500. If the Basel Ratio is reduced from 20% to 10% (i.e. permitted leverage increases from five to ten), then they can lend out £1,000.

But where does the extra £500 come from? It comes from "deposits" of course. The model does not dispute that for one second, but that makes a mockery of the notion that the amount of "money" sloshing around is limited (a) and also makes a mockery of the notion that banks take deposits first and then lend them out (c).

This is where Wiki's brief description of the "loans first" model is incorrect. If a bank lends out $1,000 (i.e. creates it out of thin air), then it has to increase its share capital by $100 and take new deposits of $900.

Assumption (d) is clearly nonsense. There is an upper limit, even in the worst credit bubble of all time. Yes, some people will take out 100% mortgages if they can, a few people took out 125% mortgages, presumably there are a very few people would have taken out 150% mortgages if they'd been on offer. And when the credit bubble goes too far, it usually pops very quickly.

Despite the best efforts of the UK government to reflate the housing bubble (and they are doing disappointingly well), the total amount of mortgage loans outstanding has remained stubbornly close to the £1,200 billion mark for the past six or seven years.
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The other fatal flaw in the traditional model is that if the Basel Ratio were set to zero (which is perfectly plausible) then the amount of "money" sloshing around would tend to infinity, which is clearly not true.

In fact, you could easily argue that if the Basel Ratio were set to zero, this is tantamount to saying that banks are not allowed to issue shares at all and they have to be funded entirely by deposits (like the traditional building society model).

How would such a bank behave - more cautiously, or more recklessly? You can easily argue that it would be more "cautious", i.e. it would make fewer loans. the reason for this is psychological/behavioural as much as anything.

If you take over a bank with $1,000 loans, $1,000 deposits and no reserves or share capital whatsoever and know that if the bank goes bust your name will be mud and you'll never work in banking again (again, not realistic assumptions - nowadays, you might be stripped of your knighthood but you'd get a massive great pension payoff), then any hint or rumour that the bank has problems collecting in all the mortgage repayments would trigger a bank run and it would be all over within hours.

Therefore, you would be as cautious as anything with lending, you'd only grant 60% mortgages to people who'd been in the same steady job for years and had a good record of regular savings towards the 40% deposit (like the traditional German Bausparkasse).

You'd charge the highest interest rates and pay the lowest interest rates you could get away with to try and build up a bit of a cushion if things get sticky, and so naturally, your bank would not find as many willing borrowers and willing depositors as other more "reckless" banks - in fact, the only people who'd deposit with you would be people trying to save up that 40% deposit.

At any one time, you would have (say) 1,500 savers with an average deposit of 20% of the price of a house each and 1,000 borrowers with an average mortgage of 30% of the price of a house each.

(Of course, this is still a bit of a Ponzi scheme, because the borrowers would have to be repaying their mortgages quicker than they build up the original deposit (which is just about plausible, as the borrowers have more spare cash as they no longer pay rent as well), which is why, as soon as a government lifts the restrictions on what a building societies or a Bausparkasse can do, they pelt headlong into disaster. But let's gloss over that.)

What's the difference between the "fractional reserve banking" ratio and the "Basel capital adequacy " ratio?

The answer is, they are a mirror image of each other (but lead to much the same outcome).

* The FRB ratio restricts the ratio of liabilities (deposits) to a specific category of assets (gold coins in the safe) to a certain maximum (let's say ten) and

* Basel ratios restrict the ratio of assets (loans made to customers) to a specific category of liabilities (paid up share capital and retained profits - the bank, as an entity is under no obligation to repay them except as dividends or on a winding up) to a certain maximum (again, let's say ten). Remember also that "share capital and retained profits" are nothing in themselves - the assets are real, the liabilities are real and this is just a balancing figure (in the same way as "equity" in a house is nothing tangible, the house is real, the mortgage is real and your "equity" is just a mathematical or legal concept).

Which is why it is best to avoid the word "reserve" completely, as it can mean two completely opposite things. The FRB banker keeps ten gold coins "in reserve" and the Basel banker has "capital reserves"; the former is an asset and the latter is a liability.

In either case, the banker starts off with "ten" (call it gold coins, millions of pounds, cockle shells, sickles, galleons, whatever) and lends them out. The borrower spends them and the recipient deposits them back in the bank, so they can be lent out again and will be re-deposited and so on until the upper limit is reached.

The idea that banks lend out ten for every one taken as a deposit is a nonsense. Once the dust has settled, under FRB the bank has lent out ninety pence for every one pound taken as a deposit, and under Basel rules, the bank has lent out £1.11 for every one pound taken as a deposit, as the diagram shows (click to enlarge):

Oh yes you can.

Adam Collyer left a comment on Markets Work. The Other Thing Doesn't:

All agreed, except for the passing mention of "ever increasing quantities of credit, based on fractional reserves to inflate economies and buy votes". You can't have banks really without fractional reserve banking - you certainly can't have loan finance.

Consider if you insist on 100 percent reserves. So you put £100 in the bank. They can't lend it out because they need to hold 100 percent of it in reserve. And that's it. No loans - banks become just a safe place to store money - like a fortified version of your mattress.

1. Although nobody in his right mind suggests banning FRB entirely (i.e. insisting on a 100% ratio), it would not be the end of the world. When you go to the bank with your £100, you can either:

a) Invest it as share capital (or buy existing shares to the value of £100), or
b) Invest it as a debenture or bond (or buy existing bonds to the value of £100), or
c) Invest in an interest bearing current or deposit account, or
d) Pay it over as a pure deposit or current account for safe-keeping for a small monthly or annual charge.

With a) to c), it is implicit that your money is lent on at interest and you expect a share of the profits (the more risk you accept, the higher your return). With d) there is neither risk nor return.

2. FRB is like most things - it's good up to a point and 'too much' is a bad thing. So whether we measure the old-fashioned reserve ratio (ratio of liquid assets to total deposits) or the more modern Basle ratio (ratio of share capital-plus-retained profits to total assets) is neither here nor there. A ratio of anything above fifteen per cent appears to be, in practice, more or less rock solid. Anything below ten per cent usually leads to disaster.

3. Even without FRB, businesses can still borrow from the public directly without the bank as an intermediary (although admittedly it is much easier for very large companies to borrow in this way than it is for small, medium or quite-large ones).

4. To really get a credit bubble going, you also need an asset price bubble (usually land and buildings), because then the debits and credits more-or-less create themselves (nearly every penny that the banks lend to Mr Purchaser as a mortgage gets deposited back with the banks by Mr Vendor). Sorting out land price bubbles once and for all is dead easy of course - by shifting taxes from income and output to land values - provided we can first wean the general public off the idea that rising house prices = increased wealth.

More banking fun

Captain Ranty left this comment on Another crash course in banking:

You don't appear to understand fractional reserve lending practices.

My £100k is not shown as a liability on the banks' books. A liability indicates a risk, it indicates that the bank has offered something of equal value in the contract and they have not. They do not take an equal risk. Dig a little, my friend, a mortgage contract is easily defeatable in court. Actually, it is fraudulent, as full disclosure is never, ever given by the bank.

The simple indisputable facts of the matter are that the new loan which the bank "creates" is shown as an asset on the bank's balance sheet (because it is an asset, the precise valuation thereof is another matter); the borrower takes the money, buys a house, gives the money to the vendor; the vendor deposits the money back in the bank and the vendor's deposit is shown as a liability (from the bank's point of view).

So a split second after the transaction, the bank's net asset position is unchanged - it has additional assets and an equal and opposite additional liability. That is how FRB works. I am not saying it is a good thing or a bad thing, I am merely describing what happens.

If you do not believe me, I invite you to download the balance sheets of a bank or building society and look for yourself - customer deposits are shown as liabilities (because that is what they are).

Sorting out the 'credit crunch'

I am, as you may have noticed, an accountant, so I like to look at both sides of every equation - for example; for every reckless borrower there is a reckless lender; and for every overstretched buyer there is a vendor laughing his or her way to the bank. Similarly, the credit bubble was the cause and the effect of the property price boom; and the credit crunch is the cause and the effect of the property price crash. It's not just correlation; they are two sides of the same coin - you can't have one without the other.

MSM reporting of the whole credit crunch debacle - and the politicians' response thereto - has been muddled to say the least. I suspect because they haven't bothered to understand things properly, which are, if you follow the logic through, quite simple. But - be warned - like all simple things, it has to be explained and understood step-by-step.

The basic, fundamental, simple problem underlying all this Lehman Brothers/Northern Rock nastiness is that first-time-buyer households with an income of £30,000 have overstretched themselves with a mortgage of five-times-income to buy a home costing £150,000 at the peak of the market last year. Once the mortgage market returns to normal, the lending multiple will fall to three-times-income and property prices will fall by 40%, so in this example, the price of the first-time-buyer properties will fall to £90,000. (These are UK figures, but similar principles apply in the USA, Spain, ANZ or anywhere else that's had a credit/property price boom/bust).

In a simple world, without interbank lending, the building society lent an FTB £150,000 for a 100% mortgage in mid-2007 and credited the vendor with a deposit of £150,000. By the time house prices have fallen 40% from their peak, the poor FTB will be kicking himself, as he has overpaid by £60,000. Unless he wriggles out of that debt by declaring himself bankrupt, he will end up paying £977 a month until 2032 (assuming 6% interest, 25-year repayment mortgage), unlike a canny buyer who will wait until the bottom of the market in five years' time, use the money he has saved by renting not buying to pay a 20% deposit and pay £523 a month until 2032 (6% interest, 20-year repayment mortgage).

So last year's FTB has made a £60,000 notional capital loss, kicks self. His mortgage lender in turn, would be prudent to write down (more accurately, "make a general bad debt provision against...") the value of the mortgage advance on the basis that £60,000 of it is unsecured. Sure, that's not the sort of security that I'd want, but the chances of last year's FTB losing his job; falling behind on payments; being repossessed and declaring himself bankrupt is quite small. Even a rabid pessimist would look at a large sample of such mortgage advances and write off fifty percent of the unsecured portion, in our case, that would be £30,000 per FTB, or a write down of 20% of the initial advance.

Using my negative-equity-o-meter, a 40% fall from peak will see just under 3 million households in the UK in nequity. Let's assume average mortgage £150,000, average bad debt provision 20% = £30,000, £30,000 x 3 million = £90 billion (or about one-sixteenth of outstanding mortgages in the UK - which is three times my previous worst-case estimate and so probably wildly overstated).

So we are straight into the realms of double-counting - we have 3 million households kicking themselves that they overpaid by £60,000 (=£180 billion) and banks/building societies kicking themselves that they have to write off £90 billion of mortgage advances.

But it is the same loss! The losses do not add up to £270 billion; the losses are £180 billion. If - taking an extreme example - banks did the decent thing and sent recent FTBs credit notes for £30,000 each on the strict condition that borrowers kept up with repayments in future, that would still leave the banks' losses at £90 billion, but would halve FTB losses from £60,000 per property to £30,000 per property.

And it does not stop there.

The original mortgage lender packaged up those mortgages on overpriced properties to people who couldn't really afford them on a semi-recourse basis to an SIV in the Channel Islands. So the SIV is also booking a potential loss of £30,000 per mortgage.

And some investment bank invested in that SIV, so the investment bank is also booking a loss of £30,000 per mortgage.

And some highly leveraged hedge fund may have borrowed further to buy shares in that investment bank and enticed investors by promising annual returns of 10%. The hedge fund is booking a loss of £30,000 per mortgage.

And the original vendor may have withdrawn his £150,000 sales proceeds from the boring building society current account paying 5% interest and invested in the highly leveraged hedge fund. So that investor is worried about making a £30,000 loss as well.

So, we have the FTB worrying about a £60,000 loss and the building society, the SIV, the investment bank, the hedge fund and the hedge fund investor/original vendor all worrying about a £30,000 loss each. But the total potential losses on each mortgage do not add up to £60,000 plus 5 times £30,000 = £210,000!! The total loss per mortgage is probably in the order of £30,000 (if that) - this has to be split up between the various parties - if all six parties take a £5,000 actual loss on the chin, then they've all learned a valuable lesson and nobody gets wiped out.

Even better - and this parallels a previous post on the merits of Sovereign Wealth Funds - the ultimate source of all this easy credit and cheap finance is The People's Republic Of China and oil rich countries like Russia and the Middle East. So we in the West can pull a fast one, put our banks into receivership (in a controlled and orderly fashion) and tell the bond holders (the PRC and petro-states) "Oops, sorry! We can't repay the full value of those bonds, but hey, we'll issue you new bank shares to the face value of the shortfall." This would, from the banks' point of view convert a short term liability (bonds) into a long-term non-repayable liability (shareholders' capital), so our banks would be recapitalised on the sly without the need for these messy and embarrassing rights issues.

And if you don't like the sound of Johnny Foreigner running our banks, then just move your mortgage and your deposit account to a good old-fashioned British building society! Johnny Foreigner will end up owning bank buildings, thousands of computer terminals and bugger all else. A bank without customers is worth nothing!

Well, congrat's to anybody who's bothered to read this far. And double congrat's to anybody who understood it all.

"HBOS will attempt to raise £4bn"

As I calculated before, UK banks will have to have rights issues of about £1 for every £5 market capitalisation.

HBOS is now going for a £4 billion rights issue, against a current market capitalisation of £18 billion.

As a rough guide, you can assume that the next to do rights issue will be those with the lowest ratio of market cap-to-gross assets, i.e. Barclays, Alliance & Leicester and Bradford & Bingley.

HSBC and Standard Chartered look pretty 'safe' for now; Lloyds TSB is borderline.

"System no longer works, confirms UN"

From The Daily Mash, h/t John East

"Meanwhile, the banks are borrowing money from taxpayers so that they can then lend the same money back to the taxpayers at a higher rate of interest than they borrowed it from them in the first place. Seriously, is it just me?"

I'm a taxpayer and a tenant. Does that mean I'm paying extra tax to subsidise my landlady's mortgage? Yes?

UK banking 'crisis' in perspective

Total UK personal debt (mortgages, credit cards etc) was £1,409 billion at the end of 2007. That's roughly the same as gross domestic product or nearly £60,000 per household. But there can't be a liability without an asset, rather unsurprisingly, total household bank deposits are around £1,000 billion.

The banks only have to worry about those people who can't afford to pay their mortgage and who are in negative equity. Let's assume that house prices fall by one-third to their long term average price/income ratio (reversing the last three or four years of price rises) and that a fairly catastrophic* five per cent of people lose their jobs. There are about eleven million people with outstanding mortgages so let's assume the banks repossess 550,000 homes** and suffer a loss of £50,000 on each one. That'd be a loss of £28 billion, which sounds like a heck of a lot, but it's only 2% of the total money that banks have lent out.

A brief summary of the main UK banks*** is as follows:


There seems to be a heck of a lot of double-counting (total assets over £5,000 billion!), but even assuming that banks have to write off as much as £50 billion and thus have to raise another £50 billion in cash from their own shareholders, via rights issues, like RBS, this is on average only asking shareholders for another £1 for every £5's worth of shares that they currently own.

In RBS's case, it's more like £1 cash for each £3's worth of shares****, but hey, so be it. And that £50 billion is only one-twentieth of all the money that households have on deposit with banks, so all the bank's shareholders are being asked to do is swap a cash deposit for more shares. Which they can then sell in the market and stick the money back in the bank if they want.

* i.e. one-and-a-half million workers. Unless it's those one-and-a-half million superfluous public sector workers, of course.

** There were 190,000 actual repossessions (not just 'repossession orders') in the years 1990 to 1992. This time is going to be a lot worse.

*** Excluding Nationwide (a building society), Abbey (owned by Johnny Foreigner, so who cares) and Northern Rock. Total assets as at 31 December 2007 per published accounts and market capitalisation is as at today's date from the rather excellent Yahoo finance section.

**** The rights issue is supposed to raise £12 billion, against a current market capitalisation (the total value of all shares in issue) of £38 billion.

Fractional reserve banking for beginners (2)

Maybe it's easier to explain this with balance sheets.

On Day 1, I set up Wadsworth Bank Limited with £50 of my own money, which I stick into the cash-box in coins and notes. On Day 2, WBL lends the money to Mr A who toddles off and buys a house worth rather more than £50 (that house being WBL's security).
By Day 3, I notice that other banks are taking deposits, which enables them to lend out far more than WBL can. I assume that a Tier One Capital Ratio of one-eighth is a sensible figure, and can thus lend Mr B £400 to buy Mr A's house. WBL's balance sheet duly records an asset of £400 (what Mr B has to pay back to WBL), and a liability of £350 (money that Mr A can withdraw at any time, being his sale proceeds of £400 less the £50 that he owed WBL from Day 2).
This is all rather splendid, as Mr B is paying WBL 7% interest (£28 per annum) and WBL is only paying Mr A 6% interest (£21 per annum) so WBL is making a handsome gross profit of £7, or 14% return on the £50 I originally invested.

On Day 4, I take most of the afternoon off to enjoy a splendid lunch at my Club. On my return I am horrified to see that my fresh-faced young mortgage salesman has been rather too enthusiastic in granting new loans. He has financed the sale of Mr D's house to Mr C for £400. WBL's balance sheet looks like this:
"But look, Sir" he enthuses "We can earn £56 a year interest on our loans to Messrs B and C, but we only have to pay £45 interest to Messrs A and D, so our gross profit will rocket to £11 a year, a 22% return on capital!".  I explain the Basel capital requirements to the young fellow and he is briefly crestfallen. "Ah, but Sir" he suggests after a few minutes head-scratching "We could lend the bank's good name to a completely independent company incorporated in the Channel Islands, transfer Mr C's loan to it and invite Mr D to withdraw his deposit and use it instead to finance that company. We could even offer him a slightly higher interest rate of 6.5% to compensate him for the higher risk".

After discussing the matter, Mr D agrees and by Day 5, WBL's balance sheet is again showing a healthy Tier One Capital ratio of one-eighth.
Wadsworth Bank (Jersey) Limited is not licensed as a deposit taker in the UK, and so has no need to comply with such petty requirements.
As WBJL is a totally independent company, WBL is not required to include its figures in its own balance sheet, and because Mr C is paying 7% interest and WBJL is only paying 6.5% interest to Mr D, WBJL is generating a further £2 gross profit each year out of thin air, which my mortgage salesman and I share as an annual bonus. Splendid!

Unfortunately, Mr D's solicitors insisted that under the terms of his loan to WBJL, WBL (as sponsor) have to guarantee any shortfall should Mr C be unable to meet his commitments, or should Mr C's house turn out to be worth less than the £400 purchase price ...

Fractional reserve banking for beginners

A lot of people accuse banks of creating money or printing money, and then a debate ensues about the wisdom of allowing fractional reserve banking, and some of the explanations are really long winded.

It's actually dead simple...
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Mr A agrees to sell his house to Mr B. The bank lends Mr B the money (which it shows as an asset in its accounts) and Mr A of course deposits the proceeds with the bank (which it shows as a liability in its accounts)*. The bank of course is just a middleman, it charges Mr B sufficient interest to cover the interest it has to pay Mr A, plus its running costs and a retention to cover possible bad debts. If there's anything left over, the bank makes a profit.

As soon as the sale goes through, by magic, there's an additional £x00,000 of 'money' in the system. In reality, that money nets off to nothing, mathematically.
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So provided the house is sold for a fair amount that Mr B can afford to repay, all is well with the world. Problems only arise when their is a spiral of easier lending, which leads to higher house prices, which leads to over-confidence and even easier lending and so on. This is how the house price bubble and the credit bubble are self-perpetuating. Until they go *pop* of course, as they do every 18 years or so.

In which case...
Mr B is in a mess, because his house is falling in value and he can't afford the mortgage any more;
Mr B's mortgage lender is in a mess because it has to write down the value of its assets (the irrecoverable part of Mr B's mortgage);
Mr A's bank is in a mess because it might not be able to recover all its money from Mr B's mortgage lender; and
Mr A has to worry about there being a bank run on the bank where he deposited his money.
Somehow or other, the loss will be shared out between the various parties who based their original transaction on an inflated house price/unrealistic expectation of Mr B's ability to service the mortgage.

That's all, really!

See also Banking supervision for beginners; the Bank of England predicted the Northern Rock failure ten years ago!

* You can invent infinite complications to add to this, such as, it might be Bank C that lends the money to Mr B, so Bank C has an asset, and Mr A deposits the money with Bank D, so Bank D has the liability. But Bank C in turn owes the money to Bank D, so it all evens out. The so-called Tier One Basel capital requirements just means that banks have to be able to finance about one-eighth of their total lending out of their own money, i.e. share capital and retained profits. They got round this eminently sensible rule by shifting assets and liabilities off-balance sheet, aka 'securitisation'.