The Minsky moment in Mary Poppins

The views on saving versus investment expressed in Mary Poppins, released in 1964 when Hyman Minsky was in his prime intellectually, quite nicely presage the coming credit bubble leading up to the great financial crisis of 2008 onwards.  This is the story of a battle between the proponents of a welfare state, gross national happiness, fun and games, care for the elderly, humanity on the one hand, and investment, austerity, asceticism on the other, as represented by the two characters of the childrens' nanny, and the childrens' father.  The fiscally prudent state and the nanny state.  The children are us, the people.  

The key moment revolves around the question of what the boy should do with tuppence (that was set in 1910, which corresponds these days to less than two pounds adjusting for inflation).  Poppins advises him to 'feed the birds'.  Listen for yourself.  How could you refuse?

His father advises him to invest wisely.  But the characterisation of both choices leave it in no doubt where the film makers' hearts lie.  The old woman feeding the birds is a fine enough image of the recipient of social benefits.  The bank head complains that the result of feeding the birds is fat birds.  So there you have it.  We've been dealing with both of these opinions for quite some centuries, and both have validity.  Nothing's been decided or proved any way, the argument moves on.

Here's what the banker would do with the money.  Written down, who could complain?

If you invest your tuppence Wisely in the bank Safe and sound

Soon that tuppence, Safely invested in the bank, Will compound

And you'll achieve that sense of conquest as your affluence expands

In the hands of the directors Who invest as propriety demands

You see, Michael, you'll be part of

Railways through Africa Dams across the Nile Fleets of ocean greyhounds

Majestic, self-amortizing canals Plantations of ripening tea

All from tuppence, prudently Fruitfully, frugally invested

In the, to be specific, In the Dawes, Tomes

Mousely, Grubbs Fidelity Fiduciary Bank!

Now, Michael, 

When you deposit tuppence in a bank account

Soon you'll see That it blooms into credit of a generous amount

Semiannually And you'll achieve that sense of stature

As your influence expands To the high financial strata

That established credit now commands

You can purchase first and second trust deeds

Think of the foreclosures!

Bonds! Chattels! Dividends! Shares!

Bankruptcies! Debtor sales! Opportunities!

All manner of private enterprise! Shipyards! The mercantile!

Collieries! Tanneries! Incorporations! Amalgamations! Banks!

You see, Michael

Tuppence, patiently, cautiously trustingly invested

In the, to be specific, In the Dawes, Tomes Mousely, Grubbs

Fidelity Fiduciary Bank! 

That banker is making a decent case for a well diversified portfolio of investments.

The children refuse the investment offer and inadvertently trigger a spot of financial fragility (no doubt already there in the system) - namely a run on the bank.  Not the first time the people's spending and investment patterns trigger a financial crisis.  Not the first time - nor the last - we have difficulty judging how much to spend and how much to invest.

Adam Curits - YouTube professor of the history of conspiratorial epistemes

Adam Curits thought piece on politics of British market ideology.  Has a British angle but is somewhat broader in goal.  What I'd like to take issue with is the assumption that there's some kind of prior political agenda which effectively determines the choices we make in selecting our economic models (political expectations theory, if you will).  The clip by Tony Benn nicely makes the point.  Clearly this is quite true, to some extent.  But clearly also it is the case that politics itself has evolved over time to reflect the hard won insights (I won't call them truths) of certain sciences.  I'm thinking of the secularisation of modern politics around the time of the early enlightenment (Montaigne, Hobbes), the incorporation of specialist knowledge into key decision making processes and, yes, even some economics is uncontroversial enough to enjoy broad support in many developed economies.  Curtis is right, though, that some other broadly supported key ideas may turn out to be inadequate. I know of no documentary maker who more winningly develops these critiques.   

Foucault has the idea of an episteme which provides a structure within which conceptual argumentation occurs, but beyond which it is much more difficult.  These epistemes surely must have a kind of Hegelian movement to them - I wouldn't say they're inevitably evolving towards Truth, as such, but clearly we're building on some, rejecting others, all the time.  Within that moving context, all thinking people find a certain politics, a certain economic mind-set within which we can wander intellectually.  I don't think it is fair to  denigrate individual intelligences as merely captured birds of some political cage.  Many thinkers the world over, are probably more than comfortable with the ultimate transience of their thought; and they probably have a range of opinions on the acceptance or rejection of their ideas by the current political establishments.  True, ideas, especially economic ones, can pretty soon develop an unshakeable political musk which attracts some, repulses others.  That musk, insofar as it augments or clashes with the major cultural epistemes of the day, will likely determine the fate of the idea in the history of ideas.  But its fate is one thing.  Its value quite another.

Curtis's documentary style and content are so interesting and provocative that I'll always hunt out and consume his output.  But his characterisation of Hayek's key idea that distributed pricing information is too incompressible for any system other than a market is perhaps unfair.  It is quite far from Curtis' characterisation of it as robotic technocracy.  Hayek sees no-one as a robot.  Curtis on the one hand tries to characterise Hayek's ideas a technocratic, and on the other as Machievellian in their committed political drive.  It is hard to see how you can have it both ways.

I often wonder how successful traders operated before the whole concept of the rational man first made an appearance in the history of ideas.  No doubt there were successful traders, industry barons, market manipulators, manipulators of public opinion (or of respected opinion, just as damaging), operators innately sensitive to the business cycle, theorists like John Law and especially Richard Cantillion who could engineer vast personal profit (and lose it again, the former's case).  Is it possible to look at all of these lives in a way which is not simply politically deterministic, but is still sensitive to their political effects as well as determinants?  And can we see how some of these ideas are important and long lasting; which have survived many transformations?  I say yes.  Enjoy the history of ideas, but see that there's nothing inevitable about their direction; there's nothing to say those ideas always move in the direction of truth.  There's nothing to say usurped ideas can't be valuable ones, in the end.

I'll give you twenty chickens for that cow. Barter as the limit of gift exchange in the absence of credit

When I first read chapter 2 of David Graeber's book "Debt - the first five thousand years", I was blown away by the juxtaposition of anthropology and economics and the history of ideas.  I still am.  Now that I'm reading it a second time, I'm less convinced by his first main argument.  

The chapter, "The Myth of Barter" takes Adam Smith and other early economists to task

for founding economics on the idea of the invention of money as an inevitable and necessary improvement to a pre-existing barter economy. The anthropological evidence, Graeber tells us, makes it likely that no such barter economy existed.  

I'd like to criticise this argument.  First, how serious is it really to the foundation of economics that the early economic authors were not anthropologically accurate?  Second, I'd like to argue that we should consider barter in the forms that did exist in ancient cultures, as an end point in that very real and ever-present phenomenon of primitive economic life often referred to as gift exchange.  Thirdly I'd like to point out that for everyday gift exchange to function in any culture, the participants must have been able to get a handle on one of the three great founding elements of money - its role as a unit of account.  Gift exchange cultures, which are really just credit based cultures, didn't use a singular means of echange, nor did they have a singular store of value.  Hence they didn't have money as understood by modern economists.

1.

Adam Smith wasn't just an economist.  He was a humanities guy.  His job required him to give courses on three main disciplines of the humanities - the political/economic perspective of human culture, the ethical perspective, and finally the religious perspective.  Hi died before he could write a book on the religious dimension, but his two masterpieces clearly address the syllabus he worked to.

As such, he probably ought to have been more aware of anthropological thinking (though the academic subject of anthropology had not yet been created).  I guess there's only so much one man can do.  And no doubt he picked up on the barter story from book reading, or speaking to others who read books.  Quite likely too, he operated in a time when the Western world's view of primitive cultures was quite superior.  But we don't throw away the idea of democracy just because it was born in a culture which  endorsed slavery.  The ideas can transcend the context of their birth.

Anyway, how much of modern economics really does hinge on the existence of a barter culture?  Wasn't economics for Smith really an analysis of those cultures where money had already made an appearance?  Did Smith's argument need for there to pre-exist some barter cultures?  No.  At worst, then, Smith is an anthropologist of that subset of cultures where money as a concept had emerged.  I guess we shouldn't be too unhappy with this already wide remit.  The anthropologist of monetary  cultures.

2. 

Graeber's book gives you some wonderful examples of tibal cultural activity.  He's widely read and exploits many of the founding anthropologists' ethnographies  well for his argument.  Graeber makes it clear that within small communities, they operated a credit based system of exchange, often wrapped in the terminology of gift exchange.  These people kept mental accounts of who owed what to them, and to whom they owed.  Graeber also points out that barter, where it did happen, happened in high octane meetings between rival tribes.  Barter was part of the ritual of these exchanges.  These exchanges were often political any symbolic exchanges,  with a view to avoiding real life-threatening conflict.  Not the kind of quotidian asset transfers we often think of when we think of barter.  Indeed, he makes  it clear that our notion of consumerism as a distinct cultural activity, separate from spiritual, political, sexual interaction, just wasn't a distinction primitive cultures made.  Nevertheless, I think it is possible to characterise barter as the limit point of gift exchange in the presence of unquantifiably large credit risk.  If you don't know much about these strangers, and if money hadn't been invented yet, then you'd quite possibly perform barters with them.  That is to say, in modern financial/mathematical terminology, swaps with short duration and matching legs of approximately similar value.  This minimises the effect of the uncertainty caused by you not being able to quantify the credit worthiness of the other. Credit makes more sense if transactions occur between you and the other regularly.  You then get a handle on their credit worthiness.

3.

Graeber raises the question: how do you quantiy a favour?  "One establishes a series of ranked categories of types of thing.  Pigs and shoes may be considered objects of equivalent status; ... ; coral necklaces are quite another matter".  These "spheres of exchange" are of course, primitive, heterogeneous units of account.  In other words the unit of account is the singular limit of these spheres of exchange.

So I argue that you can rehabilitate Smith.  He was the founding father of a particular kind of social science - the study of those cultures who'd unified their spheres of  exchange into a singular unit; and who'd additionally beefed up the consequences of that peripheral state of gift exchange, namely gift exchange in the absence of a handle on credit.  It should not be so surprising that a seemingly marginal and perhaps even questionable cultural activity can later become the centrepiece of another cultural form.  Perhaps barter, that risky, sexually charged encounter with strangers, always on the verge of degeneration into violence, associated with dance rites, free love, nervous laughter, happening on the outskirts, physically and culturally, could have been the beginning of the anonymisation of exchange which heralded the modern age.  If this is so, then most of the juice in Graeber's expose of the myth of barter in the foundations of economics gets diluted.  Great book though - read it.

Anatomy of a convert - reckoning is not paying

In finance there's a useful difference made between the role of a calculation agent and the role of a payment agent.  Think of the calculation agent as the person (or process) whose job it is to digest the terms and conditions of a security, then on certain agreed days, to perform some calculation which can have a material impact on the value of the security, or on the decision to pay certain cash flows.  The security in question can be a convertible bond (among many others) and it is really a contract between the owner and the issuer.  In an ideal world, both the owner and the issuer will have a calculation agent on hand, to make sure no mistake is made in the periodic reckoning which is done.  

Related to this, but separately, is the implementation of any real payments which arise as the result of the monitoring performed by the calculation agent.  Both have synchronised calendars, but distinct calendars nonetheless.  Think of the calculation agent as the in house quant, and the payment agent as the operations department, if you like.

A good word for this calculation activity is to think of it as reckoning.

before 1000; Middle English rekenen, Old English gerecenian (attested once) to report, pay; cognate with German rechnen to compute

A reckoning is done a number of times during the life of the security's contract, and they need to be done on those particular days probably because they need a read or two from reality - perhaps a check on that day's interest rate, perhaps a read on whether that day is an unexpected non-business day.  On those observation dates, reality interacts with the terms and conditions of the security.  The result might change the state of that security, and that change of state may have implications for some transfer to be made - a coupon payment, an issuer call, a dividend payment, a holder's decision to put a bond back to the issuer, a stock price passing through a trigger level, an issuing company having accepted an offer to be bought or merged.  Often a security is observed by an independent, mutually agreed calculation agent, so as to reduce the likelihood of argument.  It is up to the writer of the security's terms and conditions to be as explicit as possible when defining the rules which need to be obeyed on upholding this contract. 

It is a useful thought to have in your mind the idea of multiple known and unknown calendar dates in the future which constitute that security's reckoning dates.  Many of those dates are known from day one, but many others can't.  For example, it may be the case that for a 20 year coupon paying bond, the expected coupon payment date in year 19 has by then become a public holiday.  So you can't write specific dates into such a contract.  You need to provide a set of rules with some flexibility to cope with surprising future states of the world.  We use day count conventions and business day conventions to help with this kind of uncertainty.  The result is a contract which, while seemingly cluttered with legalese and sometimes baffling circumlocutions, provide a robust framework for the calculation agents, the reckoners, to move it through the various stages of its investment life.  Payment is in a sense dependent on reckoning, and itself feeds back into future reckonings.  As we'll see, a convertible will have many many days of reckoning during its trandeable life.

Anatomy of a convert - analytics should facilitate comparison

Bonds, equity derivatives, and therefore convertibles have a number of measures of value and risk which can be applied to them at any one moment in time.  Luckily, for bonds and convertibles, there's a handy monetising fixed point called the face value.  Many of the contract terms of bonds are described in terms of this monetiser (i.e. are expressed as a ratio to the face value or denomination).   The coupon is the most obvious contract feature which is expressed as a ratio to the face value.  Originally, the face value of the bond represented the final 'redemption' payment - where the borrower finally pays back the loan (assumed to be the denomination) made to the company.  These days, this is still often the case, though the final redemption payback amount can accrete to some value above or below the face value.  Even here, the final redemption value is often expressed in terms of a ratio to the face value.

The great thing about expressing all these terms with respect to the face value is that the bond analyst is already beginning the task of facilitating comparisons of one bond with another.  This helps the investor to compare many bonds with each other.

From a cash flow point of view, as a bond holder you need to know which absolute cash flows you'll be getting, and when.  From that point of view, you'll receive, to make up an example, £100 once a year, for 19 years, followed by a payment of £1,100 (made up of the final £100 coupon, plus the redemption amount, equal to the face value, of £1,000).

But from the perspective of an investor who would like to compare these amounts with other bonds, it is great to transform them into a series of 19 annual payments of $0.1 \times D$, where $D$ is the denomination, followed by a final payment of $1.1 \times D$.  More convenient still for us to drop the reference to the denomination, and move to percentages rather than ratios, stating that the bond pays a coupon of 10% annualised for 20 years (and, redeems at face value).  Likewise the traded price of this bond, on the open market can be quotes in currency - for example £960 - or it can be quoted as a ratio of the denomination - $0.96 \times D$.  Again, dropping reference to the denomination and moving to percentage terminology, the bond price is quoted as 96.  This quoting style is referred to as percentage of par quoting or simply the par convention.  Certain bond markets prefer the par convention, others prefer to see a real cash amount quoted for the price - this convention is called the unit trading convention; since it is popular in French markets, you'll often hear of it as French style quoting.  Clearly, this is just a quoting style - for every unit trader price, there's a par quoted number which is its equivalent, and vice versa.

In practice, rarely is a bond actually trading precisely at par, even when it is first issued.  They usually start off pricing not too far away from par.  In the end, though, if the bond is still around by the time of redemption, it'll eventually trader closer and closer to par - to the redemption amount.  An instant before it redeems, when all the coupon payments during its entire life have already been made, then you can see that the fair value ought to converge to par, since that's what it represents at that point - a promise to pay the face value to the bearer in the next instant.

The original terminology for face value comes from coinage, where this number would be printed or embossed on one or two of the faces of the coin.  Denomination captures the sense, again probably originally from the world of coinage, that there is a graded set of related values within a singular system.  This makes more sense with money than it does with bonds, since for any given issue, there usually is only one face value.  But from its original latin, you get the sense that it is an amount which is fully named - and perhaps in a sense fully defined by the arbitrary act of naming its value.  Maybe this term caught on in a world where fiat currencies were being born.  The Chinese in the tenth century first issued fiat paper currency, but it was first attempted in the eighteenth century in the western world, and this lines up quite nicely with the word's entomology, where it took on the monetary sense around the 1650s.  Finally, lurking behind the technical definition of face value is the implication that the value expressed on the face is not the real value.  For coins, movement in inflation, or the price of precious metals, or the degree to which the coin's edge has been clipped, all explain why the face value is not the same as the real price.  Likewise this carries over well into bond terminology where, as I noted earlier, during most of the life of a bond, it won't be worth precisely the face value.

Purchasing Power

Following on from my previous post on liquidity, you can think of a person or organisation's  purchasing power as the sum of currently liquid assets plus the set of liquid assets of other people which you've rented out.  

Your rental charge will compensate them for their foregone risk free rate plus a credit spread reflecting how much confidence they have in your ability to pay any used credit back.  Plus any cut the arranging institution takes (the bank as middle man).  This rental charge can variously appear expressed as a rate of interest, as a fixed fee, as a service commission, or some combination of them all.  From a finance theory point of view, it doesn't much matter.

Liquidity

I'm trying to get it clear in my head just what that slippery financial term liquidity really means.  I've heard it referred to as a synonym for money, I've heard it attributed to classes of security (government bonds being more liquid than convertibles, say), I've even heard it attributed to people themselves.  What is it really?  

To my mind, it is best understood as a property of a specific market.  It is an estimate of how satisfactory  some hypothetical future experience you (or any other putative participant in that specific market) might have with respect to price in-elasticity of order size and with respect to minimal price variance.  Let me take that all bit by bit.

First of all, it is an estimate.  By this I mean not only that individuals can have their own opinion on the liquidity of any specific market, but that there can be a degree of inter-subjective agreement too.  We can as a community reach a kind of consensus on the liquidity of a market.  This is based on experience - namely based on how that specific market, or markets like it, have behaved in the past.  In the recent past especially, but also over longer periods of time.  It is an estimate however which is aimed at the future.  Sure, you measure the past and from that it leads you to your conviction about the future.  But nevertheless, when you come to a specific market, you are interested in its liquidity going forwards.  I could invent some fable about a possible world where a specific market has a clear and measurable history of illiquidity, yet be content that some profound, uncontroversially effective change occurred in the world which leads me to estimate it to be likely to be liquid going forward.  These forward looking estimates which you or the market community might have are clearly time-bound - the further out in time, the less certainty we might have for this belief in the liquidity of a specific market.  I wouldn't really need to invent some fable whereby some profound structural real world chance occurred which made a specific market become almost instantaneously less liquid - you just need to see what happens during periods of financial crisis to see this scenario playing out.  What all this means is that it is an estimate which is usually well-founded - based on many experiences in the past - but it can nevertheless break down (or, less often, break to the upside).  Now, whether you want to say that a community was wrong in their previous estimation (or you yourself were wrong) versus saying that the community reserves the right collectively to change its mind in a dramatically short period is probably a question for the philosophy of economics, not for this post.  Suffice it to say that an individual opinion about some future interaction with an individual market can exhibit quite some volatility dynamics.  Perhaps that opinion stays stable in that person's head for years, across multiple business cycles - with virtually no volatility in their estimate of the liquidity of that market.  That same opinion could dramatically shift, perhaps permanently, perhaps temporarily.  This behaviour may or may not be rational economically - that's a whole different argument also.

Ok.  So now we have a forward looking opinion in one person's head about one specific market.  That judgement can at times exhibit remarkably stability or remarkable instability, and we can put this down to rational expectations or less rational psychological causes.  Remaining neutral on that debate for now, I could say that the stability of this opinion over any time window could range from calm to dramatically different, and all shades in between.  When an observable time series behaves like this we say it has high volatility of volatility (high vol. of vol.).  This simply captures the idea that it can exhibit little or no movement for periods, then exhibits a lot of movement in other periods.  So we have a forward looking, high vol. of vol. opinion in one person's head about one specific market.  What next?

When an individual comes to a market to transact, they have a transaction size (or a range of transaction sizes) they'd like to execute.  In general they might also be looking to sell into that market or buy from that market.  And doubtless there are many elements of that market's structure which the participant would do well to pay attention to - its permanence, it legality, the level of trustworthiness of the co-participants, the homogeneity of quality of the units for sale or purchase at that market, any institution of redress to deal with dispute, convenience of location, and so on.  They're all important, but for now I'm focusing on just two properties of that market - the ability of participants to see a price and know that it'll be the same price even if they decide to buy (or sell) a thousand more.  There are, of course, limits to this price in-elasticity - often that market will quote you a buy price and a sell price, each with a maximum lot size.  That price is good for any quantity up to that maximum lot size.  Leaving aside specifics of individual orders, nevertheless, a market participant  might need to transact in size, over multiple lots, and would like to know that they'll still get to transact at the current market price (or thereabouts - nothing is too guaranteed even in theoretical markets ) even if he decided to buy 10 or 10,000 units.  Turning up at a market with 10,000 units only to find the market can only give you a price on 100 of them can be costly economically, so knowing that this market allows you this freedom is a valuable attribute of that market.

Next up is minimally variant price action.  This is a huge subject and I'll do a lot of simplifying here.  Imagine a market with no price variation.  The price is always nominally $p$ no matter what.  That price action is minimal.  Imagine a market with extraordinarily variable price action.  Clearly each market participant will approach those two markets (and all shades in between) with a different expectation, a different feeling of confidence or dread.  If I know with certainty that would get $p$ for selling a unit into a market and expect $p$ back again tomorrow - then I could use that market a bit like a safe deposit box. If I could likewise drop off 1,000,000 units at $p$ and certainly get it back tomorrow for $1000000p$ then clearly this market has uses.  If I had much less certainty about what I'd get back tomorrow - maybe $p$, maybe $0.9p$, maybe $0.00001p$, maybe $1000000p$ - then I would be wise to treat that market differently to the first one.  So far I haven't talked about money or inflation, but you can imagine quite easily how even the first market, in a hyper-inflationary environment, could appear in real terms to resemble the high variance market.  Inflation is not the focus of this post, so I'll only mention it in passing and also mention that, if inflation was growing steadily, or if we were deflating steadily - by which I mean predictably - then we could as market participants work around these known changes and still find some use in markets.  The worst situation is a highly uncertain inflationary/deflationary environment. So when I talk about minimally variant price action, I really mean unpredictable price action.  Forget inflation, if there is a rule which tells me with certainty how much I'll get for a unit tomorrow if I sell it in to that market today, then that's still minimally variant.  Clearly the least variance is when the nominal price stays the same as yesterday - that way you don't need to apply that extra step and run a simple calculation to see what the price should be tomorrow.

Minimal values for these two properties - the degree of price sensitivity to order size and the degree of unpredictable price action - are seen as positive elements of that market.  This is liquidity.

Now, there are so many markets out there.  Some are quite similar to each other.  Others strikingly different.  And our level of precision may vary with interest and purpose too.  This leads us often to be happy to lump together two or more specific markets and make pronouncements about their average liquidity.  To be specific, we individually (and collectively) might have an opinion on the liquidity of IBM's publicly traded equity, on the liquidity of Google's publicly traded equity, but we might also have aggregated opinions on the liquidity of U.S. technology equity issues, or U.S. equities, or equities in general.  Likewise we may have opinions on this month's on the run U.S. T-bill  and slightly different opinions on any other off the run U.S. T-bills, or we might have a singular opinion on U.S. T-bill liquidity in general, or in U.S. Treasury bond liquidity in general, or in G-20 sovereign bond issue liquidity, or sovereign bond issue liquidity.  Hence we can come (individually or collectively) to opinions about the liquidity of whole asset classes.  We could track how that opinion varies through time.  We could analyse the factors which cause those differences.  We could think through the implications of the stability of these inter-asset class liquidities.  

When used of a person  or company - what this means is simply that the collection of assets and liabilities which that person or company owns (or a subset thereof depending on the focus of the conversation) belong to asset classes (or individual markets) with certain liquidity attributions.  

In any given economic region, money is often considered most liquid, next bank cards and debit cards, then cheques, certificates of deposit, time deposits, Eurodollar futures, short duration highly trustworthy government bonds, longer duration trustworthy government bonds, corporate bonds, equities, and onwards down to highly illiquid assets, including distressed assets, housing stock and so on.  Some assets could experience periods where it is literally impossible to transact in them - their market has seized up completely.

I've said nothing about what causes a liquid market - just how to spot it. But to speak of causation for a moment, I'd say that the stability of price action will have a tendency to make a market to become bigger, which in turn would allow a certain in-elasticity on lot size; so in a sense the core definition of liquidity is in-elasticity of lot size - that's what we see - but this is usually caused by the sheer size of the market, which in turn is caused by the appealing usefulness of low variance on price surprises in that market.  In theory, you could perhaps invent a bizarre story about a world which has the key liquidity element - in-elasticity to lot size - without the other causes, but scale through widely-perceived usefulness is how most markets come to be liquid.  A market which doesn't shock its participants too much is a good candidate for liquidity.  And liquid markets will play some role in the investment perspectives of participants too - but going into that subject of liquidity, investment and money would move me too close to Book 4 of Keynes's General theory for now.

Finally, some people think what I've just described is not liquidity at all, but market fluidity or depth.  They claim liquidity is the property of an asset which allows it rapidly to be transferred from one use to another.  Certainly I would agree with the rapidity of the transaction, which it my mind is a property of the general level of confidence market participants have in particular markets.  Perhaps these two are permutations of the same phenomena - the confidence which must exist in that asset which would allow economic agents to use it so frequently for exchanges, in so many different circumstances is the logical consequence of economic agents coming to realise that it is a better way to run an economy to agree on just one asset - what we call  money - to be the reference asset in many economic transactions.  And that confidence is surely based on the two properties I mentioned earlier.  Money typically is backed by a central authority with an affiliated mandate for price stability or by a real asset, such as gold.  Neither are perfect with regard achieving that stability - consider periods of hyper inflation with fiat currencies, or with moments of discovery of new sources of gold (the Spanish-American experience and the nineteenth century gold rush experience).  To say that liquidity is a property of that asset which we use most frequently in most of our economic transactions is merely to ask the first, and not the most important question about it.

Anatomy of a convert - dirty translators

Sometimes you need yield translators for inter-converting meaningful, mathematically valid yields.  But then again, sometimes you need dirty translators,  which switch away from the realm of valid yields and into the realm of historical convenience.  In other words, sometimes the market convention with some yields is simply mathematically not justified, and perhaps that market had its origin in a time before the real mathematics was widely understood.  Once a convention has a real human practice and history associated with it, it is difficult to make a big-bang switch away from the inferior formalism.  Best just to think of these dirty expressions as market quotes.  And the process of packing/unpacking the market quote as a bit like taking your shoes off or putting them on  when entering a house.  Once cleaned, then the rules on yield translation can be applied for your specific purpose.

When we come to looking at specific markets we'll see some of this going on.  But a second point I'd like to make just now about yield conversions is the possibility that the nominal rate time basis - the time period within which you  understand your $n$ and $r$ - isn't yearly.  It can be any period.  It mostly is nominally expressed as a return for a 1 year period, but it could be a rate expressed for a multiple year period, or a half year period, or quarterly.   Day count conventions, which I'll be getting to soon, can be thought of as a digital-to-analogue signal converter for time, embedded at the level of the market quote (taking your shoes off at the door).

Archaeo-Biography

Dateline 2400.  Peta Cube Inc., this year's most successful IPO, has just announced that it has acquired the entire email and calendar records of struggling Data Font Partners, a private equity firm which has in recent years accumulated the full archive of a popular early twenty first century company Google Inc. said to contain personal email records and calendar entries for over three billion human beings who lived around that time.  Data Font also contains the rival  email archive for that period, hotmail, hosted by a maker of contemporaneous operating systems.  In a earlier deal, Peta Cube had previously acquired and structured the mobile telephone geo-location information of a vast number of global mobile phone companies.

A spokesperson for Peta Cube said work was progressing well on a net space project which interfaces with a number of supra-national government public records offices to allow individuals to surf through their ancestry to identify distant relatives of interest.  A notable feature of the project is the use of proprietary network relevance algorithms and story-driven computational language processing modules to construct an automatically written biography for each person, tapping into the public domain Facebook archives.  Experts believe this could revolutionise the genealogy industry.  In addition, it is expected to prove a valuable resource to more traditional biographers and historians of ideas.

Anatomy of a convert - time and time again

In a previous posting I showed all the ways simple discrete compounded and continuously compounded rates could be inter-converted.  However, now I'd like to state that all these types of rate can really be seen as variants of the discrete compounding $(1+\frac{r}{n})^{nt}$.  It is good that this can be seen as the most fundamental representation, in my mind, since it works so well as a contributory definition of capital as a property which produces other properties.

You already know, thanks to Jacob Bernoulli, that the limit of discrete compounding is $e^{rt}$.  All you need to see is that, when you let $n=\frac{1}{t}$ then the discrete compounding formula $(1+\frac{r}{n})^{nt}$ becomes $(1+rt)^{\frac{t}{t}}$ which is identical to the simple interest formula $(1+rt)$.  Great; so we have a continuum of compounding frequencies, running from 1 to $\infty$.

What are you doing when you set $n=\frac{1}{t}$?  Well, remember $t$ is the term of the loan or bond and $n$ is usually the number of times per year (i.e. per unit t=1) you compound.  So in the general case you will have discretely compounded $nt$ times.  But if you only want to compound once at the end, then setting $n=\frac{1}{t}$ is the way to do it.  Also notice the similarity with geometric and arithmetic means here.  With arithmetic means, between the start observation $t_0$ and the end observation $t_N$ you have a series of in between observations $t_1, t_2,...$ and you can work out a series of returns $t_{i+1}/t_i-1$ and then calculate the arithmetic average of these returns.  Likewise you can calculate the single value $t_N/t_0-1$.

Anyway, back to the fixed income analysis of converts.  As you'd imagine with any loan, both parties probably have in mind some notional loan term.  You can imagine a retail client approaching a bank manager.  One of the first questions is bound to be for how long do you need this loan?  After that some haggling will result in a rate.  Understand that the rate in question is actually the remaining pair $r$,$n$.  You always need to know the $n$ to understand the value of $r$.  If you really wanted to lay this out sequentially, then you could say, in any negotiation about a loan you first set the term, $t$, then set the compounding framework $n$ for understanding finally the rate $r$.  A more prosaic interpretation is to say that $n$ selects the formula you use to plug your $r$ and $t$ into.

Notice the choice of $n$ here doesn't have any implication for actual cash flow transactions - the borrower could actually keep a hold of the interest until a final payment.  Or on the same analysis, he could pay out on the compounding dates into your account and you'd be free to do with the interest anything you wanted, including spending it unwisely.  It doesn't alter the theoretical analysis.   Payment dates are just a best considered on a different schedule to the compounding schedule implied by $n$.  

The world of fixed income is overwhelmingly interested in $n={\frac{1}{t},1,2,4,12,365,\infty}$, namely simple interest, annualised compounding, bi-annual compounding, quarterly, monthly, daily and continuous compounding.  At a pinch you could reduce it further to $n={\frac{1}{t},1,2,\infty}$

But this is not all.  It would be if all fixed income markets quoted securities in one of the rate formalisms covered by $n={\frac{1}{t},1,2,4,12,365,\infty}$.  They don't.  Often they quote some other market variable, and you need to do some unpacking of that market quote.  That unpacking is, naturally, a function of the various fixed income markets themselves - and there is additionally some regional variation in conventions/usage patterns.

In the next posting, I'll talk about the day count conventions, the digital-to-analogue converters of time and the final wrinkle we need to iron out before we can move on to look at real market quotes and begin to get into the details of building a yield curve.

Anatomy of a convert - dates of interest

There are so many things I'd like to say about the interest calculations whose inter-translation I covered.  First up is the step up in complexity when moving from simple interest to compounded interest (discrete or continuous).  I would imagine the maths for simple interest has probably been understood and practised for at least a couple of millennia.  And while compounded loans are surely not much younger, their mathematics, that is, showing what the fair price ought to be, is quite recent.  The definitive book about discrete compounding came out in 1613, by Richard Witt.  No doubt Indian mathematicians probably cracked it 600 years earlier, but in our Western dominated tradition, we like to 'reset the clock' on important intellectual discoveries like this, unfortunately.  There's a nice temporal recapitulation here - the mathematics for fairly valuing certain future cash flows was first published in a Western book a mere 41 years before Pascal and Fermat opened up the way for estimating the fair value of uncertain future events.  Likewise we're spending time on understanding the fixed income side of convertibles before looking at their optionality, which requires more probability theory to understand.  Also, whilst Napier first talked about the exponential constant in 1618 - a mere 5 years after the Witt book -  Jacob Bernoulli, in working on the compound interest problem, identified that $e^x = \lim_{x}(1+{\frac{1}{x})}^x$, namely that if someone came to you and offered you a 100% annualised, continuously compounded rate of return for a year, if you lend them £1, then you'd get back £2.72 approximately.

I've come to realise how Christian, Islamic and Jewish arguments against money generally and the practice of usury in particular (which to many an ancient mind was strongly associated with compound interest, often regarded as grossly unfair) tainted - and still does taint - the Western world's view, so perhaps it is no wonder that we have to wait until 1613 for a full book on the subject. Compare that with a modern definition of capital as a property which creates other properties.  All you need to do is realise the recursive nature of this definition and you have a compelling need to assume compounding as the basis for understanding how capital works.  We've broken through with the mathematics, but we retain much of the moral disgust which accompanies lending and interest generally.  Even those ancient loan makers who only lend out on a simple interest basis, assuming that when they get their payback, they lend it out again (namely lend out their repaid capital).  This practice of a sequence of simple interest based loans it itself a compounding operation when viewed from the perspective of the loan maker's business over time.  So any attempt to distinguish on moral grounds simple versus compound interest must surely be bogus.  It isn't the compounding frequency that's the problem in usury, it is the rate of return.  Any fair simple interest rate has a corresponding fair compounded rate.

There's too great a temptation to rush forwards in my overview of the anatomy of a convert, but I'll hang around a while on the subject of yields.  Remember where we are right now.  I'm seeing how to model the value of cash accruing to us in a future date so that we get a handle on the value now. In this world of rates, I started with so-called risk-free rates.  This allows me to ignore how to model credit, for now.

I'd like to spend some time on the general concept of a yield curve.  But even when I restrict for now my attention to maximum-creditworthiness borrowers, there can still be a confusing jungle of rate forms  (often called rate bases in the financial jargon).  The reason for this is we get those rates from several disparate actual markets.  And each of those markets has its own culture - its own quoting convention, time horizon.  If we ever want to imply anything from real rate market data, we'll need to understand each of those markets' quoting conventions.When you can do that, you can feed the rates into a homogeneous view, the yield curve.  And just as there are multiple conventions for quoting bonds or money market rates, or swap rates for market data quote interpretation, so too there are multiple ways of expressing the output yield curves. 

In the next posting I'd like to develop a general purpose and fairly simple framework for placing rate formalisms in a context which makes the operations seem totally sensible.

Anatomy of a convert - prehistoric rational expectations

I'd love to know the history of the kinds of clause which are typically found in modern day convertibles.  I'm sure each clause would have a fascinating history.  But in the meantime I'd just like to point out first of all that these clauses individually do have a cultural history - somebody invented each and every one, at a specific time, and for a specific purpose.  Either they allowed a potentially failing new issue to go through, or they smuggled in a 'screw you' clause which wasn't well understood by either the issuer themselves, or by the  marketplace.

Second, I'd like to point out just how many of them can be cashed out in terms of algorithms.  Modern convertible pricing systems can turn pretty much every significant clause into a cash-now contribution towards the overall fair value of any convert.  That is quite amazing to me.  

And most interesting of all is that convertibles have existed for quite some time.  Whereas the modern pricing of options traces its origins to the late 1960s only.  How on earth did market participants manage to run that market in the absence of a decent convertible model?  Well, probably profitably.

One way of looking at these 'prehistoric' times for convertibles is to imagine how the disciples of rational expectations would explain what would have been going on back then.  How does a rational agent (or the average rational agent) manage to come up with a market price for a convertible in the absence of a coherent modern convert model.  I guess that the best model available would be the next best target for a prehistoric rational agent?  Certainly it could be the case that the average opinion of prehistoric market participants would be close to the average opinion of current market participants, with perhaps more variance.  But my gut feeling is that this would have been unlikely.  In other words, there was probably some kind of unrecognised persistent bias in the prices of certain prehistoric convert issues.  Really?  Could this be?

And what about the instant that the first step change in convertible pricing occurred?  I guess around the time of E.O. Thorp.  What if he decided not to publish his book on convertibles, but had kept it to himself.   Wouldn't he have an edge?  Wouldn't the market price be inefficient insofar as E.O. Thorp decided to leave money on the table back in the late '60s?  Rational expectations can never be about market efficiency in any absolute sense, but there must surely be an evolution of expectations.  Which means there ought to be a whole series of incrementally more efficient insights and practices when it comes to judging the market's efficiency at any one time, even now.

Robert Lucas attacked by chaos machine

Robert Lucas, a godfather of the rational expectations movement has come in for a lot of criticism recently.  Here's my own brief attempt.

Imagine an artificial economy with just two actors, who each have to guess game theory style at the likely behaviours, economically, of the other.  They both are fully cognisant of each other's economic models.  All they need to do is apply those rules to apply a decent best guess of model parameters - the legendary sloppy assumptions - and we'll sit back and watch well known macro-economic phenomena emerge from their identically specified micro-level models of themselves as economic actors.

Now lets imagine those models shared a similar property (as many many models do) with the logistic function, $X(n+1)=rX(n)(1-X(n))$, namely they are riddled with chaos.  Our two agents might agree perfectly on each other's model and what's more be correct but when it comes to apprximating the model parameters, needless to say, they cannot guess the other's starting value with infinite precision.  The result, over certain wide ranges of the parameter phase space - is utter chaos.  All it takes for rational expectations to be shown to be inadequate is some likelihood of such radical non-linearity in real (no pun intended) sets of micro-founded models of agent interactions within the wider rational expectations movement.

How would a rational exceptions robot respond to the possibility, or even more strongly, the knowledge that their models had 'dark areas'.  I guess the sensible thing to do is to apply probabilistic approximations around those regimes.  And those heuristics too would probably be amenable to the rational expectations approach.  I guess the rational expectations agent can operate under radical uncertainty.  But what if there were clear patterns of information which cry out for some kind of rational expectations model to develop, while an entirely different initial parameter set results in a different rational-seeming system to lure the unsuspecting rational economic agent.  And what's worse, where do you draw the line between uncontroversially certain parts of your model, and the stable-seeming boundaries at the edge of chaos?

Indices of the world, unite!

I'd like to suggest an idea.  Within a short number of years, thanks to Amazon and Google Books, we'll soon be in a position to have available to us in textual format virtually all of the indices of all of the books which have ever been written.  Clearly this is somewhat of an exaggeration, but not too much, especially in the realm of non-fiction.  Imagine a research project which applied the techniques of computational linguistics to automatically link all these indices together, to provide a search and browsing resource between parts of books.  Something like this is already just beginning to happen with citations - but in a sense these are external (but still related) to the content.  Indices get you right in to a particular page.  Once in place, the Big Index, as I'd like to name it, then becomes an intellectual super-highway, a novel way to read (parts of) books, of seeing connections, of hopping, of surfing, of delving freely into the history of a concept, of tracing influence.  On top of this super-highway, us travellers can then leave notes, attach personal commentary (rather like the Amazon kindle shared notes).  In time, we'll be able to follow the paths of great thinkers themselves, what they read and thought about, which connections inspired them.  How they felt about it at the time.  Pieces of text will become cultural monuments, with many transit routes in and out, and with a wealth of personal commentary.  Indices, after all, capture a lot of intelligence and work in abstracting a book - why not put it to use.  Also, it side-steps the famous Borges taxonomy probem, and always remains fully open.   The internet in general, and sites like Wikipedia do some of this for you, but it isn't the same idea.  With my idea we're exploiting a probably well-crafted index designed around the time the book was written, probably with the involvement and approval of the author, which captures some of the structure and flow of the book.  

Soon we'll have an additional option to read through a book, moving at speed.  The idea remains indifferent to one's position on copyright, and of course there'll be nay-sayers who'll decry the already too-disposable approach to reading we have moved to.    I disagree and see it as an enhanced mode of reading, which treat concepts not individual books as the core nuggets you're seeking.  Indices of the world, unite, you have nothing to lose except your identity.

Anatomy of a convert - Fake Bonds

Why are yield translators relevant to the current thread on understanding convertible bonds?  The reason is that if you want to have a model which gives you an estimate of the price of a convert, you need to have a yield curve in place so that you can find out the value today of a bunch of future payments over the coming years of the life of the convertible you're looking at.  Many of the points of a yield curve are invented or interpolated by a so-called bootstrapping algorithm.  But they're bootstrapped around a few real market facts, real market rates, currently trading that very moment in the market.  From this smattering of real-world points, a whole curve gets magic'ed into existence.  And as I previously mentioned, those real world points, those real world markets - cash markets, government bill and bond markets, swap markets, Eurodollar futures markets (all of which I'll come back to), each has their own history, their own typical loan durations, typical rate quoting conventions.  And where you have a panoply of disparate rate conventions that you'd like to pull together into a single coherent picture of yields, then that's exactly where your yield translators come in.

To flesh this out a bit, I'd like to create a couple of artificial contracts, with many real world details trashed for the purposes of clarity.  Then what I'd like to do is show you how a yield curve works on getting a present value for those made-up contracts of mine.  I'll just initially pluck a yield curve or two out of thin air.  After you see how it is used, then we'll turn our attention to creating a real, honest to goodness, no scrimping yield curve, with a view to having it help us price a convert.  We can use the family of fake bonds to see what a difference the various shapes of yield curve make on valuation, perhaps see when it pays to have accurate yield curves, and when it doesn't really pay to have accuracy.

First up, I'd like in my family of fake bonds a contract which just has a single redemption payment in a year's time.  Then one with a single payment in two, and so on for a ten year horizon.  So we have our first ten family members.  But converts often pay a coupon, so I'd like my eleventh to have twice yearly payments of 4% annualised, running for five years, and ending with a full redemption payment.  Number twelve is the same coupon-bond like payment history, but with 8% annualised.  And finally, I'd like a 6% bi-annual coupon, running for a ten year period, with a redemption at the end.  In all cases, I'd like the face value of these bonds to be £1,000,000.  By the way, this is unrealistic, since usually the face value is £100 or £1,000.  But if we wanted £1,000,000 worth of exposure then we'd just buy 1,000 or them, or 100 of them, respectively.  Why not just make it simple, and let us assume we're buying one of them, and the face value is £1,000,000.

The first ten I'll call fake zero coupon bonds (I'll explain the terminology later, for now it is just a name).  11 I'll call my fully sweetened convert.  12 I'll call my lightly sweetened convert.  13 I'll call my straight bond.

 Now, each of the 13 contracts embody 13 loan you've made (or acquired) to some institution or body who you regard as unimpeachably trust-worthy.  Who do you have in mind?  A family member?  A big bank?  A company with lots of cash?  A company with a long history?  A local state? A government?  A government from a particular time in history?  Perhaps a shell company whose only purpose in life is to fund your coupon payments and your final redemption out of a pot of cash it already have stored safely?  Think about it, and whatever works for you, that's how credit-worthy our fake family of issuers are.  These future cash payments, in other words, are just about as certain is it is possible to be with respect to future cash flows.  This is a pragmatic point I'm making here about certainty.  We're not talking philosophical certainty but a much more contingent and localised certainty.

The final piece of damage I'll inflict upon reality is to assume the world really does operate 24 hours per day, 365 days per year - namely everybody works weekends, and there are no public holidays.

Anatomy of a convert - Pioneers

J.J. Hill.  His company issued the first convertible.










Meyer Weinstein.   He was one of the first to hedge convertibles with other securities.  Using heuristic techniques.

E.O. Thorp.  He showed a mathematical approach to valuing a convertible as a bond converting into a warrant.

Fischer Black.  He got a CAPM-friendly solution to the pricing of a call warrant and in return got a call on the Nobel prize for economic science, but it expired just out of the money.






Since then, absolutely nothing of real importance except for a melding of credit and volatility factors into pricing models.

A lot of basics of fixed income modelling already was in place as early as 1913.  See the below book.