## Sunday, 20 March 2016

### Liquidity and central bank policy

These things a twenty first century central banker knows:

The corporate world is gotten more complex since the advent of financial engineering.  The continuous expectation of investors to maximise risk adjusted returns leads to increased chances that the firm might succumb  to the temptation of gearing, with the result that the firm goes out of business.  Not all firms are exposed evenly to this risk - it clusters, and those industries most at risk are those with funding and asset mismatches.  This is almost the definition of the base business model of retail banking sector.  So banks have to set up shop at the foot of the volcano.  That's their job.  And those banks all have to do this, to a greater or lesser extent.

If a central banker want to avoid systemic risks, he tries to put in place measures which address this risk.  Perhaps a demand for higher capital buffers (some of which capital operates a s a liquidity buffer).  But banks respond to these capital requirements by grossing down their balance sheets rather than taking the direct hit to their share price as a result of the likely reduction in equity returns which happens when the regulator asks banks to sit on more capital.

In the limit, the banks become not only heavily regulated by government, but the key mechanism for allocating credit (capital) to those parts of the economy that need it becomes a quasi-government function.  Bank returns become largely policy driven and the financial services industry starts to resemble a government department with ludicrously paid employees.  It is not that regulator imposition has unforeseen effects on liquidity of firms and systemic liquidity per so, it is that these banks need to place their business at the foot of the volcano in the first place.  You can't legislate geography away, so to speak.

When firms go bust, they often go through an illiquidity phase on their way to extinction.  This must continue to happen for Schumpeterian reasons, so policy setters need to distinguish when to act and when not to act.  This determines their actions vis-a-vis their role as final liquidity providers - i.e. lenders of last resort.  But if you do this too generously you end up with an economy of zombie corporations - Japan has faced this situation for decades.  And if you don't do it too actively, you enable avoidable contractions and recessions.  The ease with which various central banks pull this trigger largely drives the modern discussion of progressivism versus the Austrian or neo-classical approach in politics.

Finally, even if central bankers and policy makers decided that they'd run the risk of forcing banks to hold dramatically more capital, as a kind of ground zero solution to the negative consequences of the inherently systemic nature of banking, the industry would migrate increasingly to the shadow banking sector.  This is already happening to some degree - witness the birth of so-called peer to peer lending.

### Liquidity in context IV - the life of a de facto corporate liquidity manager

This posting is about dumbing down liquidity management in language which  most people can easily understand and relate to.  Liquidity management is mostly about the maintenance of good operational cash flow balances to cover the expected and predictably unexpected vicissitudes and seasonalities of corporate life.  There was a time not that long ago (up until the 1960s) when operational cash flow management was a private little secret of the treasury department.  They skimmed some free cash flow from operations and kept a store of it to meet more or less expected corporate cash call events.  When looked at this way, you suddenly realise that financial demands can in theory be a lot more predictable than operational events.  It is more certain knowing when you need to repay your bonds than it does when you'll need to pay for repairs to an uninsured industrial accident.

These events in question (cash calls) each and every one of them can have an uncertainty added to the cash-amount and time schedule you'd normally think of as the definitive parameters.  If you could model all cash call events somehow, then the aggregate cash schedule and its concomitant variance would feed into a pretty decent corporate liquidity management model.  At its most fundamental, these cash calls are modelled as call options on zero coupon bonds.  Each event will have its own notional value, volatility expectation, strike price.  When you aggregate this portfolio of real options up you've got your funding liquidity mostly modelled.  One must be realistic about just what fraction of the operating corporate environment is amenable to modelling, and also with respect to just how fast the situation could change.  The more chaotic the likelihood of change is, then the more difficult it is to extract value from a liquidity management regime.  Or to put this more dramatically, there's a level of chaos in the liquidity environment above which it doesn't make much sense to model liquidity.  What you modelled today becomes largely detached from which realistically could happen tomorrow.  In general, if the future state of some system is so unpredictable based on today's models, then those models aren't much use.

Why did liquidity management stop being a private skimming operation of the treasury department in the 1960s?  Partly because of the advances in financial engineering from the 1960s onward (Treynor) which paved the way for more sophisticated financial engineering at corporate finance departments.  Similarly, macro-economic  climate became incredibly volatile following Nixon's decision to end Breton Woods agreement, leading to currency volatility and destabilising inflation.  Corporate treasurers responded by bringing some basic financial engineering to the largely in-house management of corporate cash calls.  Finally, financial engineering was also focusing the minds of corporate executives at technology companies starting in late 1950s silicon valley, via the issuing of executive stock options, which accounting bodies valued as stock price minus strike - effectively ignoring the intrinsic value element (we had to wait for the Black-Scholes equation for that).  This caused them to tilt in favour of investment returns over (liquidity) risk.  In essence, to really manage a firm's liquidity so that there is always a sufficient cash buffer in the end detracts from short term investment gains.  Corporate executives, especially in 'innovative' technology companies were now personally incentiveised to maximise precisely these short term investment returns, in ways which used less capital.

What new tricks did they come up with?

How about taking those ideas in fixed income financial engineering and look to calculate the duration of cash flows with a view to matching those cash flowsOr perhaps finding some third party to write some liquidity options for you so you can have them as a form of cheap liquidity insurance.Or renegotiate the clauses around commitment in the contracts you have with banks over your loans.Or get loans from the capital markets, dis-intermediating your firm's normal pool of lending banks.Perhaps stealing that idea of Markowitz and paying close attention to the free lunch you can achieve through diversification - in this case, the diversification of your funding sources.Lastly, don't just have a pool of liquidity buffer cash sitting at a bank earning perhaps a negative real rate in times of high and volatile inflation, which not buy assets with this pool of cash, gaining a higher return which maintaining the average liquidity profile of the pool.

## Friday, 4 March 2016

### Liquidity in context III

Yesterday I talked about bottom up asset liquidity.  Today I shall continue reviewing the various forms of words which appear in discussions of liquidity.

Liquidity mismatch.
Think of a firm's need for cash as a demand curve.  And its ability to get its hands on cash as a supply curve.  A liquidity mismatch occurs when this set of curves are out of sync.

I shall give two made up examples - an industrial goods manufacturer and a multi-strategy hedge fund.  First the industrial goods company.

The company already has a number of loans, bonds, convertibles outstanding with a number of market participants.  It also has operating cash and holds a number of near-cash securities.  On top of all of this, it has a set of assets and new projects and ongoing projects.  These ongoing projects deliver cash flows into the organisation.  The expected magnitude and timing of these cash-flows is an ongoing estimation problem for the CFO.  It is also a function of the economy generally, of sales, of a broad range of conditions, in other words.

Meanwhile its financial liabilities (those loans and bonds) have a mostly very clear timeline of coupon payments and repayment dates.  It is, of course, part of the CFO's job to manage all of this, but they are operating in an uncertain world.  Projects may bleed, they may fail catastrophically.  Macro-economic disaster might befall the economy.  What resources does the firm have to draw on to meet those more-or-less well known short term cash demands?

Side note.  The need for cash doesn't in general need to be short term, but that is clearly the most pressing end of the timeline.  The immediate future is the period which most rapidly becomes 'now' and 'now' is when a creditor may declare its dissatisfaction with the borrowing firm.

The firm has cash and cash equivalents.  Some of this is considered operating cash - money in the till, to use a shop-keeping analogy.  This cash in a sense needs to be there for the smooth operation of the day to day business of the firm.  But in an emergency this might be considered a pot to be raided.  If the company is prudent, it will also have cash and near cash reserves (certificates of deposit, short term sovereign securities).  A very conservative company might chose to have enough cash in these reserves to pay the next n months, but of course, the n months will pass, and that pot needs to be replenished.  The pot itself is depleted only in exceptional circumstances.  The downside of having too big a pot of cash and cash equivalents is that it is capital sitting earning not much more than a risk free return.  And firms have as a goal the desire to produce a return on equity in excess of the risk free rate.  Otherwise why would an investor invest in a firm in the first place?

So, assuming a new demand for cash materialised, where else might the firm look?  Perhaps new loans or new bonds.  Perhaps a rights issue (a request from current and potential equity investors to give the company cash in return for ultimate fractional ownership in the company).  Perhaps cost savings.  Perhaps the shuttering of certain projects, with concomitant staff reductions.  Perhaps the sale of certain assets in the market - plant, financial securities.  Perhaps the monetisation of some fraction of its asset base.  But as you can imagine, all these options take time, and perhaps some mark down on sale prices - after all, the market might perceive the firm as executing a fire sale, so might be tempted to offer fire-sale prices.

This misalignment of (potentially immediate, potentially short term) demands for cash with (somewhat longer term) supply is what is known as a liquidity mismatch.

If you think about it, to say that a firm is experiencing a liquidity problem in the first place is to identify a more or less dramatic liquidity mismatch.  So in a sense most liquidity problems are liquidity mismatch problems, and the word liquidity can often be considered as a synonym for a liquidity mismatch problem.

In case 2, the multi-strategy hedge fund, there is a little stub of a management company managing a potentially much larger pool of investments on behalf of investors.  The management firm itself, often a partnership, received equity investment by founding partners, who are said to have committed their cash for the long(-ish)term.  It will have well understood staffing costs and fixed costs.  In some ways, the investment management firm is a bit like 'head office' for a large goods manufacturer, but without the regional factories, offices, large staff, input supply chains, etc.  So the cash flows of the management firm are somewhat clearer.  Also those management firms might have loans but they won't typically be as well developed as with non-financial firms.  For multi-strategy hedge funds, the 'work' happens in the collection of financial assets and liabilities within its fund(s).  These investors in the fund can be flighty, and prime brokers can also adjust the generosity of their leverage terms.  Both of these create the possibility of a liquidity demand.  The fund manager only has the set of assets and liabilities in the fund to supply this needed cash.  So for them asset liquidity modelling and funding liquidity are important, as are a full incorporation of the set of firm constraints on liquidity scenarios.  And where it is unrealistic to fully model the constraints, to approximate them very conservatively.

Despite the seeming differences, both firms managing the possibility of liquidity mismatch are doing the same thing, namely being continually responsive to the balance between demands for cash with sources of cash.

In the next posting I look at the variance (and vol. of vol.) on the demand side of the 'liquidity mismatch' risk which firms of all kinds face.

## Thursday, 3 March 2016

### Liquidity in context - II

Last time I was thinking about funding liquidity and had in my head the multi-strategy hedge fund.  The two primary demands for cash come from prime brokers, who might offer less favourable leverage terms to the hedge fund, which would manifest itself as a demand for more cash to be deposited with them for a given set of holdings on the hedge fund's book at that PB.  The fund would then stump up more cash or gross down their set of holdings.  The second demand is if a significant number and weight of investors in the fund decided, subject to their gates, to redeem their investment.  Th.is is either going to be funded out of the hedge fund's cash (or cash equivalents) bucket or it will make them sell some of their assets and liabilities.  Which brings me on to ...

Asset Liquidity. (Or more strictly speaking, bottom up asset liquidity).
A firm owns a number of units of some security.  The 'asset liquidity' question arises about that holding.  The form of the question is always one of T|CF, C|TF or F|C,T and the source of the answer comes from (1) two facts about the firm and (2) a set of facts about the market for that security.

The primary firm fact is the position size.  The secondary fact is which collection of constraints are apposite for the liquidation of that asset.  The constraints impose costs (financial, time, fraction) on the unwind.

The market facts are more numerous.  Measuring a market's liquidity is a large subject and the set of data to come to an opinion about its current liquidity is probably asset type and market-specific.  But in general they are statistical reads on the market.

The final piece of the puzzle is how to codify the various statistical reads on the market to produce a liquidity response curve for that market at that time.  Actually, it is not a 2D curve but a 3D surface, with the primary independent variable being F*E, the fraction of the fund's holding of this security being targeted in the liquidity scenario at hand, multiplied by the exposure, E this firm  has to the asset (in simple cases, its quantity).  The surface exists for every exposure point.  In the most general case, the set of curves would extend into negative exposure values for F*E, allowing for asymmetric markets.  The slightly  simpler case is to assume the market is symmetrical and the sign of the exposure is not important.

Whilst in theory all those response curves exist, for any given day, you may only be interested in a single one of them, namely the curve associated with the F*E value in play on that day in your firm.

Usually, either the cost threshold is a parameter of the liquidity run, or the time threshold is given.  In this case, the surface becomes a curve.  E.g. Time(F*E|F=100%, C<1%)  - a safe and compete wind down curve / asset liquidity estimate.  Cost(F*E|F=50%,T=3d) - a drop dead target of 3d to reduce the holding size by half.  Both of these are asset liquidity estimates.

Think of the cost and time curves both in terms of the absolute cost (EUR) or time (days) for a position of size F*E to be unwound, in which case this is an upward sloping convex curve of some sort or another; or think of the cost as a cost per unit, in which case its convexity is fully explained by the expect saturation cost associated with bringing a larger and larger fraction to market.  Very liquid markets have a flat per-unit response curve both for time and cost.

I will call these per-unit response curves lower case $t_m(F_s \times E_f|F_s,C_s,n_s)$ where $m$ stands for a market object, $s$ being a liquidity scenario parameter and $f$ being a fact of the firm and $n_f$ being the collection of firm unwind constraints.  Likewise the second of the possible asset liquidity measures is $c_m(F_s \times E_f|F_s,T_s,n_s)$.

## Wednesday, 2 March 2016

### Liquidity in context - I

In this posting I'd like to talk about a couple of liquidity related phrases and their meaning.

First of all the word 'liquidity' itself.  Someone at some point in history decided that describing the degree to which an entity is able to meet its obligations through access to cash when required required a metaphor of a liquid.  If flows everywhere, which I think must be the point originally.  It is from this starting point that you get a liquidation activity, which is when non-liquid assets get disposed of (sold) for cash.  The word liquidation now also carries a strong separate sense, meaning to have its structure (solidity) destroyed (melted).  I think this is secondary.  From bankruptcy terminology, the word has entered common parlance to mean to end or terminate something or someone.

Liquidity risk.
This term, in contradistinction to market risk, credit risk, macro-economic risk (pan-market risk), etc., is an umbrella term describing the measurement and management of the risk that an entity (typically a firm) cannot meet one or more obligations (financial obligations).  As such it is a species of financial risk,  as opposed to non-financial risk.  Cash is a financial asset after all, so no surprise there.

Funding liquidity.
Organisations fund their operations through equity investment in the firm, financial markets debt, bank loans, and various forms of credit or leverage agreement.  Each potential provider of this funding is making an ongoing endless decision about the firm with respect to how worried they are about getting their investment back.  It is this ongoing endless decision which is one of the causes of funding liquidity risk.  Take, for example, a modern hedge fund.  It may have received cash from equity investors in the firm.  This cash received is used to fund projects within the firm.  The resulting equity represents a liability to the hedge fund.  It owes the equity investors.  How much they owe is a function of how the world values that equity component.  Is it work only as much as the original capital investment (i.e. the book cost, in accounting terms) or has the firm managed to grow its enterprise value and hence does the world now value the equity stake higher?  How ongoing is the re-appraisal of the value of the firm's equity?  This can vary a lot.  Publicly listed companies have active secondary markets and hence the current value of the equity is continuously evaluated.  Private firms (as a majority of hedge funds are) get their equity marked much less frequently.  Also, in one sense the final owner of the equity is irrelevant for these purposes.  Whereas equity owners may (and do) decide whether to sell their stake on the secondary market or privately all the time, the principal agents of the firm still regard this liability as ever-present.  In the general case, normal transactions in the secondary market may provide liquidity to the owners of the equity but the company itself has long since used the original capital for various purposes.  In abstract, the  equity owner owns this asset forever (even though their identity changes from secondary market trade to secondary market trade).

Next come bank loans.  Again, cash came in to the fund and a series of obligations got created.  These obligations are utterly different to the firm's obligation to the equity owner.  The loan obligation includes a lot more certainty and specificity - interest payments need to be made on certain dates, the loan has a maturity which is well understood.    Firms use loans on an ongoing basis, so there's always a chance that the loan providers worsen the terms of the loan or fail to consider rolling the loan.  This is a potential cause of funding liquidity risk.  Similarly for all forms of capital market bond - the lender is a collection of market participants, but otherwise the structure and risks are the same.  Next a hedge fund might get leverage from prime brokers.  This amounts to a greater or lesser spending capacity for the hedge fund, at a fee for the prime broker.  Finally the hedge fund itself has a number of investors in the fund vehicle itself.  These investors can be much more flighty and might decide on an ongoing basis to either keep their money in that fund, or redeem their investment, subject to an often complex set of company-imposed withdrawn constraints often called 'gates'.

Funding liquidity risk can be instigated by the firm's loan creditors, the fixed income market in its aggregate willingness to lend the firm new money on an ongoing basis, its investors and even by secondary effects of its equity holders, insofar as selling pressure on the firm's equity may feed back negatively into direct funding sources.  Funding liquidity risk is ultimately caused by one of two drivers - first, the set of funders collectively decide that the firm is less worthy of funding and second the set of funders either individually or collectively themselves become stressed and are caused to reduce the level of their funding to that (and potentially other) firms.

So much for the causes, the mechanism is also two parted.  Firms have ongoing funding requirements.  The degree to which this is lumpy or smooth is a whole world in itself.  But if a firm experiences a funding liquidity episode, then the funders singly or collectively might change or exercise clauses in the current set of in play funding transactions to make the level of funding reduce, or secondly they might worsen terms of new funding transactions with the firm and in the limit completely refuse to offer any additional new funding.  Loans, bonds and converts offer a degree of stability in their prospectuses which allows for funding stability.  Prime brokers can much more rapidly change the terms of their implicit funding pretty much overnight, and hence are a potential cause of much more immediate and unpredictable funding liquidity risk for a hedge fund.  Hedge fund don't often have loans or bonds though, so their primary funding liquidity risk vectors are investor and prime broker flightiness.  So when it comes to estimating the nature of the funding obligation (how much needs to be liquidated and by when or at what cost) then modelling investor gates and the volatility of PB leverage will need to be examined to establish the magnitudes of liquidity risks in various scenarios.

## Tuesday, 1 March 2016

### Behavioural Economics diagram

I wanted to try to fit into one image the various levels of my understanding of the word of behavioural economics and here it is.  The idea is it is a bastardisation of the normal distribution, which is associated in my head with the rationalist, probabilist, utility maximising approach to so called economic thinking.

1.  The distribution x-axis scale is ratio based and not linear or difference bases.  From psychophysics, we learn that humans are better at giving relative price valuations than absolute ones

2. The meaning of gain versus loss feels totally different for us.  The same economic loss or benefit expressed as a loss or a gain is valued differently by us - we have to lose.

3.  The mean of this comedic curve waggles around a lot, with a listening ear, being swayed by priming effects, driving anchoring effect.

4.  Certainty effect - as you move from 99% to 100% there's a discontinuity in human thinking.  A certainty premium.

5. Then at the ends, before the certainty effect discontinuity, there are 2 threads each at either extreme point.  This represents our perceived attitude to risk based on the two dimensions of - loss or gain; and likely, unlikely.  On the loss side, we like to 'go for broke' facing a likely loss whereas become risk adverse facing an unlikely loss.  Whereas on the gain side, we are risk adverse facing a likely gain (a bird in the hand is worth two in the bush) and facing an unlikely gain, we become 'no guts no glory' risk welcoming.

### Liquidity constraints

An interesting angle on summarising liquidity is to think of constraints.  Constraints in the most general sense.  A constraint can be a financial obligation (for example, an expectation by creditors that a company meet its short term liabilities) or a policy constraint (the SEC mandates that mutual funds need to state regularly the fraction of their assets they could liquidate in a three day time frame, an exchange has rules for liquidity providers in a market, the European regulator demands that a hedge fund prove that it can meet reasonable worst case expectations for investor redemptions given the set of investor gates and share classes in place).

Whilst this is no doubt a massively complex domain, in essence what is happening is that certain constraints are being introduced on one or more target hypothetical unwindings.  These are really liquidity scenarios.  The constraints represent more or less realistic representations of the business context within that liquidity scenario operates.

Or put another way, the liquidity scenario itself is defined by not only a goal but also a collection of constraints.  This represents the goal of a liquidity algorithm.

There are three levels of interest when it comes to liquidity algorithms.  The first is a firm perspective.  The firm can be a financial or a non-financial firm.  Non-financial firms may be required (by auditors operating in a specific corporate legal environment) to demonstrate they can meet their short term creditor obligations.  To become confident that this can happen, the capital structure and operating cash flows of the company need to be estimated.  This is often what a credit analyst does.  If the firm is a financial institution or fund, then it can be said to have additional opportunities to meet it same set of funding obligations through liquidating some of its positions.  This analysis would pull in market measures of liquidity for the pool of assets and liabilities of the fund.

For specific markets, there are ways to measure how liquid in general that market is.  This is useful for market participants as a fact in its own right, but it is also useful feed-in data for financial firms with a large number of marketable securities.

And at the macro-economic level, regulators and ultimately governments are interested in systemic perspectives on liquidity, but as a potential early warning indicator, and, through policy response, in mitigating systemic weakness in the prevailing environment.  Regulators reach into markets and into firms and impose a policy environment for them, which is another way of saying that, even from the point of view of the firm, in the general case the firm may need to be cognisant of its own balance sheet, the state of the relevant markets and finally the overarching policy or regulatory environment.

These three perspectives always interact.

If this is the overall shape of the liquidity landscape, how best can a general data point be represented?  I think, for the firm on any given date, a useful 3 dimensional point emerges, <T,C,F>, representing time, cost and fraction.  Imagine that any two of these three dimensions can be fixed or controlled, then a bottom up liquidity analysis algorithm would provide for the third.

For example, a fully general purpose liquidity system can be supplied with a cost and a fraction (assuming effectively no liquidity slippage on selling an asset - cost = 0 - and assuming a requirement of having to sell all of one's holding of that asset - Fraction = 1) then a time (number of days to liquidate) can be the result of the bottom up algorithm.  This I refer to as T|CF

A second example, say you want to know what the cost would be in selling 100%of your holding in 3 days (C|FT).

Third, F|CT tells you how much of your holding you can sell at a given cost in a given number of days.

So there are at least 3 classes of problem to solve in a (corporate) liquidity system - T|CF, C|FT and F|CT, subject to a range of bespoke constraints originating in policy and non-policy constraints.

It should be obvious that you need a lot of data to do this properly.  Balance sheet data, equity owner or investor data,  market data, constraints data.  From this data you solve one of more of the primary classes of liquidity problem - T|CF, C|FT and/or F|CT.  Of these, T|CF is of primary importance and the one which naturally comes to mind first.  But each data point <T,C,F> can in theory inform all three classes of problem.  Part of what the liquidity algorithm does is constrained aggregation, interpolation, extrapolation and (re-)presentation for end consumers.

A last point, when expressed as a point <T,C,F> represents actual values, but when represented in | notation, the given elements represent  thresholds - i.e. T|CF means "how many days would it take for me to get rid of (at least) F% of my holding of an asset at (no more than) C% cost.