Monthly Archives: May 2010

No move expected by the Reserve Bank

Vale Martin Gardner

I was saddened to hear today that Martin Gardner has passed away at the age of 95. Born in 1914, Gardner was a prolific and gifted writer. He is best known for his mathematical and scientific writing, but he also dabbled in magic and philosophy. His The Annoted Alice is perhaps the ultimate edition of Lewis Carrol’s Alice in Wonderland.

For many years he wrote a column on “Mathematical Recreations” in Scientific American, which I read avidly as a child. These columns gave me endless pleasure, solving puzzles, constructing tetraflexagons and hexaflexagons and pondering probability paradoxes.

I am sure it was reading Gardner that I first came across the peculiar “second child paradox”. While perhaps not strictly a paradox, it is at least a little counter-intuitive and goes something like this. Imagine you bump into an old friend you have not seen or heard from in years who tells you she has two children and one of them is a boy. What are the odds that she has two boys? Since the possibilities are Boy-Boy, Boy-Girl, Girl-Boy, the answer is 1/3. But if she had told you she has two children and the oldest is a boy, the odds that she has two boys are 1/2!

Of his science writings, my favourite is The Ambidextrous Universe (now in its third edition), which explores left and right “handedness”–the difference between an object and its mirror image–and its role in the physics of the universe. In exploring the notion of mirror symmetry, Gardner asks the strangely puzzling question why does a mirror reverse left and right but not up and down?

Gardner also gave me my first exposure to the debunking of pseudo-science. In 1952 he wrote “Fads & Fallacies in the Name of Science”, which takes on an eclectic mix of peculiar beliefs ranging from flat-earthers to UFO-logists, from bizarre beliefs about pyramids to ESP and from Forteans to medical quackery. But the chapter that has really stayed with me since reading Fads & Fallacies almost 30 years ago is the one on dianetics, the “science” behind Scientology.

In this chapter, Gardner describes the notion of an “engram”. According to adherents of dianetics, the unconscious mind has a habit of making recordings of painful experiences. These recordings, particularly those made as a child or even in utero, have a tendency to cause problems later in life. Of course, trained “auditors” can help identify and purge troublesome engrams. As Gardner notes, engrams seem to be susceptible to bad puns:

An auditor reported recently that a psychosomatic rash on the backside of a lady patient was caused by prenatal [engram] recordings of her mother’s frequent requests for aspirin. The literal reactive mind had been feeding this to her analytical mind in the form of “ass burn”.

As a skeptic, Gardner would look askance at anyone claiming to be able to predict the future, but it is a pity his own powers of prediction were not more accurate:

At the time of writing, the dianetics craze seems to have burned itself out as quickly as it caught fire, and Hubbard itself has become embroiled in a welter of personal troubles.

Sadly, Scientology is not only still around, it is probably stronger than it was back in the 1950s.

Science, mathematics and skepticism all continue to be very important to me, and I suspect that Martin had no small part to play in sowing their seeds in my mind many years ago. There are many others like me he has inspired and, along with his enormous catalogue of publications, that inspiration is a wonderful legacy.

Following one link too few…a mea culpa

5 Replies

My last post, Are Australia’s banks about to collapse?, took Steve Keen to task for a presentation on the dire outlook for Australia’s property market and its banks. However, a commenter has pointed out that it was not Steve’s presentation! Moreover, the final slide of the presentation, which is in very poor taste, appears to have been added by Business Insider.

How did I get that wrong? By following one link too few. Here is a quote from the Business Insider article where I found the presentation:

according to this presentation from economist Steve Keen, courtesy of Mish’s Global Economic Analysis

Following the link to Mish’s Global Economic Analysis gets a bit closer to the truth (“on his blog” not “by him”):

Australian economist Steve Keen addresses that question and more in a presentation on his blog How to Profit From the Coming Aussie Property Crash (and Banking Crisis)

At that point I made the mistake of not following the final link to Steve’s blog and instead read the presentation. Slide 3 was a familiar one I had seen in various forms and by then the notion that Steve had written the presentation was firmly implanted. The style should have given me pause for thought as it is extraordinarily hyperbolic.

If I had followed the final link, as indeed I should have done, I would have found a post entitled “Excellent presentation on Scribd on Australian housing” the following on Steve’s blog:

This presentation was noted by a blog member today. Take particular note of slides 21-20 which compare the balance sheets of US and UK banks to that of one Australian bank, the Commonwealth.

How to Profit From the Coming Aussie Property Crash (and Banking Crisis)

So who did write the presentation? Who knows, but it was uploaded to Scribd by someone called Karenina Fay.

In any event, while Steve may think it is an excellent presentation and I clearly do not, he did not write it and hence this a mea culpa. I apologise for following others in incorrectly attributing this presentation to Steve and I have edited the original post. I will also be endeavouring to click that last link in future!

Are Australia’s banks about to collapse?

34 Replies

UPDATE: In this post I repeated Business Insider’s mistake of attributing the presentation I criticise to Steve Keen. While Steve considers it an excellent presentation, he did not write it and I apologise for not confirming the source before publishing this post. I have now struck out the incorrect attributions. My criticisms of the presentation itself still hold, which is why I am leaving the post up in its edited form.

Steve Keen and his forecasts of a property market collapse have received plenty of local media coverage over the years. Now he has come to the attention of the international press as well.

In April, Keen hiked to the top of Mount Kosciuszko after losing a bet about the direction of property prices with Macquarie Bank strategist Rory Robertson. This event was enough to prompt an extensive review of Keen’s concerns in the New York Times. Curiously, Robertson himself did not receive a mention, despite winning the bet.

Now the US business site Business Insider, which has a penchant for drama, has published one of Keen’s presentations a presentation, incorrectly attributed to Keen, under the headline “Here’s What You Need To Know About The Major Property, Debt, And Banking Crisis Brewing In Australia”.

One of Keen’s central concerns is the size of private sector debt in Australia. This is a legitimate concern and should receive more focus than misguided fears about Australian government debt. However, I am far less pessimistic than Keen about the outlook for Australian property prices.

As for the Business Insider presentation, Keen takes his concerns it goes too far, to the point of unsupportable alarmism. The final slide of the presentation is evidence enough of this, not to mention being in extremely poor taste. This slide appears to have been added by Business Insider! If that is not enough to convince you, I will consider just one of the arguments offered by the anonymous author Keen.

On slide 22 of the presentation, he writes:¹

Look at CBA 2009 annual report—Leverage ratio is almost 20 times (total assets of $620.4 billion against $31.4 billion of equity). Of $620.4 billion of assets, $473.7 billion are loan assets. If around 6.6% of CBA’s loans go bad (any loans not just mortgages), 100% of its shareholder equity will be wiped out!!

(the bold italics are not mine, they appear in the presentation). Here the implication is something like “6.6% is not very much. Wow! CBA could easily collapse!”. But, that line of thinking does not stand up to even moderate reflection.

Crucially, we must understand what “going bad” means for a loan. It does not mean losing everything, which is in fact very rare for most types of bank loans.

Over half of CBA’s are home loans and these are secured by the property that has been mortgaged. According to their half-year presentation², based on current market valuations, the average loan-to-value ratio (LVR) for CBA’s portfolio is 42%. This means that, on average, the value of the property is more than twice the loan amount. This gives the bank an enormous buffer against falls in property prices. Of course, this average conceals a mix of high and very-low LVR loans. Even assuming that loan defaults occurred on a higher LVR section of the portfolio, say with an average LVR of 70%, and allowing for Keen’s oft-quoted figure of a 40% decline in house prices, CBA would still only lose 14% on their defaulting loans³. Even then, this does not take into account the fact that, like other lenders, CBA takes out mortgage insurance on loans with an LVR of more than 80%.

But we can be more conservative still. In their prudential standards, the banking regulator APRA considers a severely stressed loss rate on defaulting home loans to be 20%. To suffer actual losses of 6.6% in their mortgage portfolio, CBA would have to suffer a default rate of at least 33%! This would be astonishingly unprecedented. Currently, the number of CBA borrowers late on their mortgage payments by 90 days or more is running at around 1%. Most of these borrowers will end up getting their finances back in order, so for actual defaults to reach 33% is inconceivable. A default rate of a “mere” 2% would be extraordinary enough for CBA.

As for the rest of the $473.7 billion, it includes personal loans, credit card loans, business loans and corporate loans. The loss rates on some of these loans can be higher than for mortgage portfolios, but losing everything on every defaulting loan is still highly unlikely. So to suffer 6.6% in actual losses on these loans, defaults would have to run at a far higher rate. Furthermore, since the dire prognosis for the banks is rooted in the view that the property “bubble” is about to burst, presumably the argument would not simply be based on everything other than the home loan portfolio collapsing.

If property prices do fall sharply and our economy has another downturn, will bank earnings be affected? Of course. Are they teetering on the brink of collapse? Of course not.

¹ While there is a footnote on the slide referencing this post, what is not made clear is that the whole paragraph is a direct quote rather than Keen’s own words. Presumably he agrees with it though!

² Page 84.

³ If property prices fall to 60% of the original value, the loss on a 70% LVR loan would be (70% – 60%)/70% = 14.3%.

Resource Super Profit Tax Everything Correctly Explained (R.S.P.T.E.C.E.)

62 Replies

This guest post from Mule Stable regular Zebra (James Glover) delves into the details of the proposed Resources Super Profits Tax.

The Australian Government (hereby known as the Govt) has proposed a Resources Super Profits Tax (RSPT) for mining companies. Superficially it appears to be a 40% tax on all profits (measured by Return On Investment or ROI) in excess of the Govt Bond Rate (or GBR, the interest rate at which the Govt borrows money, over the long-term).

The key points of this article are:

1. The GBR is the correct threshold level for RSPT,

2. If the Govt increases the threshold above GBR this will represent a subsidy of miners by taxpayers,

3. The RSPT will benefit small and marginal mining projects to get finance through partial Govt backing of risks.

So for example suppose miner Mineral Wealth of Australia (MWA) invests $1bn in the Mt Koalaroo Iron-Ore mine. MWA is a wholly owned subsidiary of Silver Back Mining (SBM). In the year following they make $200m profit or a return on investment (ROI) of 20%. If the GBR = 5.5% then the 40% RSPT means a tax revenue to the Govt of Tax = 40% x (20%-5.5%) x $1000m = $58m.

This seems very straight forward. It appears that the Govt is saying that GBR represents some “fair” level of return and anything in excess of this is a “super profit” to be taxed accordingly. Not at the normal company tax rate of 30% but a “super tax” rate of 40%. This is how it has been presented by both sides in the media. Arguments against the RSPT have focused on whether the GBR as a “risk-free” rate is the appropriate benchmark for a risky profit stream. Indeed it is not but in fact this isn’t what the RSPT is about. For example normally taxes on profits have no negative impact on the Govt if the company loses money. In the case of the RSPT though the Govt has stated that 40% of any losses can either be claimed back from the Govt (as a refund) or carried over to other projects.

So what is the RSPT? A good way to consider it is if the Govt took a 40% stake in MWA as a “silent partner”, leaving SBM with a 60% stake. In this case we would expect the Govt to contribute $400m of the investment costs (raised presumably through issuing bonds at the GBR or equivalent). In return it would get 40% of the profit. The Govt return would therefore be 40% of the profit less the cost of funding its 40% investment ie Tax = ROI x 40% x I – GBR x 40% x I = 40% x (ROI – GBR) x I.

This appears to be the formula that the Govt has presented to calculate the RSPT and in this derivation it is quite straightforward. However the Govt appears to be getting something for nothing since it isn’t actually stumping up the $400m in investment capital. So what’s going on? A clever piece of financial engineering that’s what. The Govt avoids raising the capital itself (and hence have it be counted as Govt debt) by getting the project to raise it on the Govt’s behalf.

(You can easily skip the next paragraph if you aren’t interested in the details of mine financing costs)

Whilst MWA raises 100% of the $1bn in capital the Govt appears to get the upside (and potential downside) as if it has contributed $400m without doing so. Money for old rope you say. However consider MWA not to be the stand-alone mining company SBM, but the joint venture beween the Govt and SBM. Suppose MWA borrows $1bn in capital at its Project Funding Cost (or PFC). This PFC will be lower than the SBM’s Miner’s Funding Cost (or MFC) as the Govt is now backing 40% of all liabilities. In fact in an efficient market we deduce PFC = 60% x MFC + 40% x GBR. If MWA then allocated these funding costs accordingly it would charge the Govt its share, risk-weighted, not PFC, but GBR. If the GBR = 5% and MFC = 8% then we expect PFC = 6.8% not the 8% if SBM was the sole investor. Under this arrangment SBM’s cost of funding (in % terms) its effective 60% share of the joint project is the same as its stand alone cost of funds, as it should be.

An argument against raising the threshold above GBR is that this will effectively lower the miners’ cost of funds, the difference being borne by the Govt and hence us taxpayers. No wonder miners are arguing so vehemently for the threshold to be raised. In fact it can be shown that raising the threshold to 11%, as some propose, and using a GBR of 5.5% would effectively reduce the miners’ cost of funds by a whopping 3.67%! If you want a formula for the Miners’ Taxpayer Subsidy(MTS) it is: MTS = 2/3 x (Threshold – GBR) in terms of the miners’ funding cost discount (paid for by the taxpayers remember); or MTS = 40% x I x (Threshold – GBR) in $ terms. For the Koalaroo mine this would represent $22m of funding cost transferred from the mining company SBM to the taxpayer. That’s you and me. You don’t see that in their ads.

From the Govts perspective the advantage to them is that the investment does not sit on their balance sheet but the project company MWA’s and in effect SBM’s balance sheet. From a financial engineering point of view all this makes perfect sense. Having said that, it was precisely this sort of clever off-balance sheet flim-flammary that got Greece (and Lehman’s et al) in trouble. We need to make absolutely sure it is properly accounted for.

Update: Several commenters have pointed out the effect on mine financing of the RSPT. Specifically with the Govt backing 40% of any losses smaller stand-alone projects will find it easier to get project finance. As discussed above the funding cost will be lower with the Govt’s partial backing. The operating profit (so called EBITDA) of the project is unchanged so this makes them more, not less, viable. This is at odds with what the miners have been saying. Even existing projects with refinancing clauses in their loans should find it easy to convince their lenders to reduce their interest payments. For large global miners such as BHP-Billiton, who issue bonds, it will be harder to disentangle the Australian RSPT benefit to their overall cost of funds and hence spreads. But the market should over time price this in with lower spreads on their bonds. With a reduced cost of funds miners will be able to leverage their existing equity across more projects and make up for the 40% the Govt now takes out of individual profits (and losses) through the RSPT.

Update: Tom Albanese, CEO of Rio Tinto was on Inside Business on ABC on Sunday May 30. It is interesting that in arguing against the RSPT he referred to the unfairness of the Govt coming in as a 40% “silent partner”, and not about the GBR threshold. He clearly understands the true nature of the RSPT. While it was self-serving he emphasised (in my terminology) the determination of Investment or “I” for existing projects. Depreciation comes into it but some of these projects are decades old and it would an accountant’s dream/nightmare to work out the correct value of I to base the Govt’s GBR deduction on. He also questioned the “principle” (his word) of the Govt forcibly coming in as a “silent partner” on projects which are clearly profitable going forward, having survived to this point. After all they are not compensating mining companies for mining projects that failed in the past. I’m afraid I have to agree with this point, though I think it is more complex than I currently comprehend. It is good to see the RSPT being debated for once without the disinformation we have seen from less eloquent opponents. After all the Govt did say at the beginning that it was these sort of aspects of the RSPT they were prepared to negotiate on, not the 40% and not the GBR threshold.

UPDATE: Zebra looks at a fair value approach to the RSPT.

Graphing using R

4 Replies

R Project logo Long-time readers of the Stubborn Mule will know that charts are a regular feature here. Almost all of these charts were produced using the R statistical software package which, in my view, produces far superior results to the most commonly used graphing tool: Excel. As a community service to help rid the world of horrible Excel charts, here is a quick tutorial on charting using R. Since R is a powerful and versatile tool, there is a lot more to it than covered here, so there may be more tutorials to come.

Installing and Running R

The first step is to get R installed on your computer. R is open source and can be downloaded for free from the Comprehensive R Archive Network (CRAN). It comes in many flavours: Mac, Windows and Linux.

Once you have installed R and have fired it up, you are presented with something that looks very different to Excel. This is the first indication that R is an interactive programming environment not a spreadsheet. You will see various messages, including copyright information, some instructions on how to display licence information, how to run a demo, get help, and finally you are presented with a command prompt: “>”. R is now waiting for you to type commands.

As an example, try entering the following command:

getwd()

This will display the current “working directory” (hence “wd”), which is the default folder that R will use for reading and writing data. You can easily change the working directory, either by using the drop-down menus (which menu option varies depending on whether you are using Windows, Mac or Linux) or by using the setwd command:

setwd("/Documents/Mule Docs")

Unless you have a “Mule Docs” folder in a “Documents” folder, you will need to substitute the name of one of your own folders, otherwise you will get an error message. Note that you need to use forward slashes (“/”) rather than backslashes (“\”) even on Windows.

You can see detailed explanations of any R command by prefixing the name of the command with a question mark:

?setwd

This is short for help(setwd). Of course, this assumes you know the name of the command already. To search the documentation for a keyword, use a double question-mark. For example

??median

will show a list of all the commands which feature the word “median” in their documentation. This is short for help.search(“median”). Note the use of double quotes (“) here, not required in the ?? syntax.

Reading Data and Charting

To get started, here is a simple data file in CSV fomat (“comma separated values”). Download it and save it in your working directory (or save it somewhere else and then change R’s working directory to where you just saved the file). You can then load the data into R with the following command:

x <- read.csv("demo.csv")

While the read.csv part is self-explanatory, the “<-” may look a little odd. It is the assignment operator. Whereas most programming languages simply use an “=” to assign to variables, R uses what is intended to look like an arrow. In this case, you should interpret the command as saying “read the contents of the file demo.csv and place the result in the variable x“. To see the contents of x, you can simply type x at the command line and press return, which will display a table with all the data read from the demo.csv file. When dealing with larger “data frames” (to use the R lingo for this type of object), having that much data flash by may not be very useful. Some other useful commands for quickly inspecting your data are:

head(x)
tail(x)
summary(x)

Now you are ready for your first graph. Try this command:

plot(x)

You should see a simple, clean scatter-plot. If you would prefer a line graph, this is easily done too.

plot(x, type="l")

The plot function has many options, which you can explore in the documentation (just enter ?plot). There are also various commands for further annotations for your chart. Try the following commands:

grid()
axis(side=4)
text(2, -4, "Random Walk")

These will add gridlines, put axis labels on the right-hand sides (R numbers chart sides from 1 to 4 starting from the bottom and working clockwise) and finally displays text on the chart.

Using Program Files

Using R interactively like this is useful for familiarising yourself with the system and for performing quick calculations, but if you find yourself wanting to make small changes here and there, it will quickly become annoying re-typing long commands. This is when you should move to using program files. All that this involves is saving a series of R commands to a file using a text editor (you can just use a simple text editor like Notepad or TextEdit, but many fancier applications can help out by automatically highlighting R commands in different colours, a trick known as “syntax highlighting”). Here is one I prepared earlier: demo.R (by convention, R files are given the .R extension). You can download this and save it into the same folder as the demo.csv file. To execute a program file once you have saved it, you use the source command:

source("demo.R")

This example will also produce a chart of the demo data, but this time it saves the result to an image file (using the Portable Network Graphics image format). This is done using the png command:

png("demo.png", width=400, height=400)

The main parameters for this command are the filename of the image you want to produce and the size of the image. After you execute all of your desired charting commands, you must close off the graphics “device” and save the results, which is done using the following command:

dev.off()

To find out more about graphics “devices” in R, including saving to other file formats (such as PDF or JPEG), have a look at ?Devices.

So that’s it. You are up and running producing charts with R. To go further from here, while you wait for further tutorials, you can explore some of the R files I have used to produce charts for the blog. I store quite a few of them here on github.

The Australian Resources Tax

8 Replies

The recent announcement by the Australian Treasurer of plans to introduce a “Resource Super Profits Tax” (RSPT) has led to the longest discussion thread on the Mule Stable yet. A lot of the discussion turned on whether or not share investors can be considered to have lost anything when share prices fall if they have not sold their shares.

Whether or not “unrealised losses” should be considered real losses takes us back to an oft-visited topic: the nature of money. Money has many guises: store of wealth, medium of exchange and, most relevant here, unit of value. Finance has its jargon like any other discipline and when money serves as a unit of value, it is known as a numéraire. Today, however, I will not explore the theory of money any further (although, you can trawl through the Mule Stable discussion to gather some of my thoughts). Instead, I will focus on what has happened to mining stocks.

The chart below shows the performance of the S&P/ASX 300 share price and the Metals and Mining index. While not quite as broad as the All Ordinaries index, the Australian stock market is dominated by large companies and in fact the market capitalization* of the ASX 300 is around 85% of the All Ordinaries, so it does give a very good indication of the performance of the overall market. The Metals and Mining index simply consists of those companies in the ASX 300 that are categorised as being (no surprise) in the business of metals or mining. In order to provide a direct comparison, both of these indices have been scaled to a common base of 100 on 30 April. This was this the Friday before the weekend announcement of the RSPT.

Performance of the Mining Sector following the RSPT announcement*

As the chart clearly shows, the metals and mining index certainly did suffer more than the market as a whole in the first couple of days after the announcement. By the end of Tuesday, resources had fallen 4% more than the ASX 300. Since the RSPT can only serve to decrease not increase profits of resources companies, this fall would seem quite reasonable. Curiously though, this week resources closed the gap once more. In fact, the resources sector has now performed 0.35% better than the overall market!

Of course, one could argue that the sector returns would have been even better over the last two weeks if the tax had never been announced. That may well be the case, but it is hard to argue that the Government had caused a terrible mischief to the superannuation savings of all working Australians when resource have, well, matched the performance of the broader market.

*Data source: Standard and Poor’s

A spam attempt gem

3 Replies

I have been getting a few very enjoyable spam attempts on the blog of late. While the filter captures the usual Russian porn dross, from time to time comments slip through the filter and it falls to me to moderate them. This little gem appeared on a two year old post about wandering the streets of Newtown with my (then) five year-old son looking at the annual “Art on the Streets” displays in shop windows.

Gratitude for posting this posting. I’m decidedly frustrated with struggling to researching out pertinent and intelligent commentary on this issue. Everybody today goes to the very far extremes to either drive household their viewpoint that possibly: everyone else in the planet is wrong, or two that everyone but them does not really understand the situation. Many regards for your concise, pertinent insight.

Touched though I may be to have my insights described as concise (rarely) and pertinent (perhaps), this comment is going into the spam bucket. I will not be giving this particular spammer any free traffic to their website.

More on “Five Down”

2 Replies

Yesterday’s puzzle “Five Down” stimulated a fair amount of discussion both in the post’s comments section and via email. I also exchanged emails on the topic with the author of Futility Closet (which is where I came across the puzzle) and he told me that the puzzle generated a lot of correspondence for him too.

All the commenters on the blog came up with the correct solution, but there are quite a few different ways of looking at the problem, all of which help provide insight into the nature of money. Since that is a common topic for this blog, I will consider some of these perspectives here.

First, the solution itself. The question asked was “What was lost in the whole transaction, and by whom?”. Taking the “whole transaction” to include the banker finding the counterfeit note in the first place, the answer is that no-one lost anything, subject to a couple of assumptions. These assumptions are that the banker actually owns the bank and so the bank’s gains or losses are his gains or losses (otherwise we would have to conclude that the banker was up $5 and the bank was down $5), and that the banker and his wife pool their finances (so we treat her debt with the butcher as his debt).

The first way to think of the problem is a variation of the comment from James. Imagine that the $5 was not counterfeit at all and all the same transactions took place with a genuine note. But then imagine that when the banker closed the bank at the end of the day, taking notes and coins back to his safe, the $5 slips from his hands and is blown into the fireplace. There it is quickly consumed by the fire. Earlier in the day, the banker had a windfall of $5, but then he lost the same amount to the fire. He gained in the morning, lost in the evening and, although perhaps disappointed to have lost the $5 again, he was even on the whole transaction. No-one else involved lost either as they had simply performed legitimate transactions, clearing various debts, using a valid $5 note. The question now is, how is anyone any better or worse off in this scenario than if the note had been counterfeit all along? The answer is, they are not.

Now that approach gives the right overall answer, but it may be unsatisfying to some as it doesn’t take account of the fact that a whole series of “invalid” transactions took place with the counterfeit note. This too can be clarified. If the note had been real, then the banker made a gain when he found the note, but finding a counterfeit note involves no gain, because it is worthless. In that case, the gain for the banker comes when he is able to discharge his debt with the butcher using a worthless note. So, he is still ahead early in the day, but the timing is slightly different. With a real note, the gain is in the finding and the transaction with the butcher is a neutral fair trade (legitimate $5 in exchange for a discharged debt). With a counterfeit note, the gain is delayed to the next step in the sequence. Of course, in receiving the counterfeit note, the butcher makes a loss. But then the butcher makes a gain when he in turn is able to discharge his debt to the farmer with a worthless note. And so on. Each person in the chain loses when they receive the $5 but has an offsetting gain when they use it to settle a debt, leaving them whole on the transaction. The chain continues all the way back to the bank, which loses $5 when the laundry woman settles her debt with the dodgy note. Assuming, as we are, that the bank’s loss is the banker’s loss, this simply offsets the gain the banker had when first paying the butcher. Again, everyone comes out even. Of course, if someone other than the banker had been left with the note, they would have been down $5 and the banker up $5. Having the transactions complete a full circle is a key part of the puzzle.

The final perspective is a more technical one. At the heart of money is the notion of a debt. Money is essentially a more convenient way of managing debts. If I buy a cow from a farmer and sell a meat pie to a patron at my restaurant, we could simply agree to record various debts: I owe the farmer one cow, the diner owes me one cow. Of course, this is inconvenient (not to mention risky) as we all have to maintain records denominated in a whole range of different commodities and I don’t really want to discharge my debt to the farmer by giving him a cow back. He has plenty already. Nevertheless, this points to the origins of money. In the excellent (if lengthy) treatise “What is Money” is it observed that “for many centuries, how many we do not know, the principal instrument of commerce was neither the coin nor the private token, but the tally”. Indeed in the Five Down puzzle, there are a whole string of tallies. Each of the players in the story has kept track of a debt due to them and one they owe to another. If the merchant did not owe the laundry woman but instead owed $5 to the farmer, the merchant and the farmer could simply agree to cancel their debts to one another. It is not so easy when the debts extend in a longer chain. Nevertheless, if one were to assemble all the parties in a single room and ask them all to consider their respective debts discharged, they should all readily agree. After all, they all owe $5 and all are owed $5 and it is much easier for everyone if that effective net zero position could really be zero without the fuss of worrying about chasing debts. It would be different if someone was owed more (or less) than they owed. We might call this simultaneous discharging of all the debts “multi-lateral debt netting”. In theory it is very attractive, but in practice we cannot get everyone in the same room to get it done. Effectively, the counterfeit note serves the purpose of facilitating multi-lateral debt netting. Because everything nets out evenly in the story, the counterfeit note can achieve the netting just as effectively as real money. The extra feature real money offers is that if the netting does not quite even out, those owed more than they owe can hang on to the money and use it for netting again in the future. Not so with the counterfeit money: once it is discovered, it loses its power to work. The solution to the puzzle lies in the fact that no debts were left over.

I will end this discussion by reprinting a very similar story that one of my email correspondents sent to me (as I understand it, it is not new but has been updated to fit the times).

It’s a slow day in a dusty little Australian town. The sun is beating down and the streets are deserted. Times are tough, everybody is in debt, and everybody lives on credit.

On this particular day, a rich tourist from down south is driving through town , stops at the local motel and lays a $100 bill on the desk saying he wants to inspect the rooms upstairs in order to pick one to spend the night in.

He gives him keys to a few rooms and as soon as the man walks upstairs, the owner grabs the $100 bill and runs next door to pay his debt to the butcher.

The butcher takes the $100 and runs down the street to repay his debt to the pig farmer.

The pig farmer takes the $100 and heads off to pay his bill at the supplier of feed and fuel.

The guy at the Farmer’s Co-op takes the $100 and runs to pay his drinks bill at the local pub.

The publican slips the money along to the local prostitute drinking at the bar , who has also been facing hard times and has had to offer him “services” on credit.

The hooker rushes to the motel and pays off her room bill to the motel owner with the $100.

The motel proprietor then places the $100 back on the counter so the rich traveller will not suspect anything.

At that moment the traveller comes down the stairs, picks up the $100 bill, states that the rooms are not satisfactory, pockets the money, and leaves town.

No one produced anything. No one earned anything.

However, the whole town is now out of debt and looking to the future with a lot more optimism.

And that, ladies and gentlemen, is how the Australian Government’s stimulus package works!!!

Five Down

16 Replies

One of my favourite blogs is Futility Closet, which is sadly appropriate given its tagline “An idler’s miscellany”. This week it featured a puzzle called Five Down devised by the English mathematician Henry Dudeney. Since the subject of the puzzle is money, it seems like an appropriate one to share here on the Mule.

A banker in a country town was walking down the street when he saw a five-dollar bill on the curb. He picked it up, noted the number, and went to his home for luncheon. His wife said that the butcher had sent in his bill for five dollars, and, as the only money he had was the bill he had found, he gave it to her, and she paid the butcher. The butcher paid it to a farmer in buying a calf, the farmer paid it to a merchant who in turn paid it to a laundry woman, and she, remembering that she owed the bank five dollars, went there and paid the debt.

The banker recognized the bill as the one he had found, and by that time it had paid twenty-five dollars worth of debts. On careful examination he discovered that the bill was counterfeit. What was lost in the whole transaction, and by whom?

I will not reveal the solutiuon here to give you a chance to think about the puzzle. What I will reveal is that the “solution”, originally published in The Strand in 1917, was re-published on the blog yesterday but it is in fact incorrect! Understanding what is wrong with the original solution (and the blog’s author was quick to provide an update following feedback from his readers) gives some insight into two of the roles money plays: a medium of exchange and a store of value.