Fischer Black, and Myron Scholes are perhaps the two most important economists of the Twentieth Century.  Between them they devised the Black-Scholes formula in 1973, and their colleague Robert Merton took forward their research and made it a practical tool for pricing and trading options.  Merton and Scholes were both awarded the Nobel Prize for Economics in 1997.

Options are the right to buy or sell an asset at a pre-determined price at a pre-determined point in the future.  For example, someone may wish to buy the right to buy Vodafone shares in December 2014 at a price of 250 pence (they are 210 pence now), and for this they will be expected to pay a small price for this right.  It is a very similar concept to someone going to the bookies and making a similar transaction.

Black-Scholes takes into account the following inputs: the asset’s underlying value (i.e. share price), at what level the investor wants to buy/sell the asset, the number of days until the settlement of the investment, the cost of money (interest rates), and the volatility of the asset.  The latter is measured by the expected daily movements of the asset.  The formula is expressed thus:

formula

Every single financial institution in the world uses this formula, one way or another, to price, trade, and monitor derivatives.  The formula tells us what the probabilities are of assets reaching certain price levels given current observations.  It can be tweaked, of course, but this basic formula is one of the cornerstones of all international investment banking.  It is used every second of every minute of the working day.  It is one of the main tools used by pension funds and insurance companies to manage and optimise their portfolios.

The problem is though, it does not really work.

Embedded within the formula is an assumption of liquidity, but this is an assumption that no-one can ever make.  As any one of the inputs change, the overall risk profile (usually expressed in Greeks) changes too.  For example, as our Vodafone share prices increases, then the likelihood of it reaching 250p also increases, and this means that the risk exposure of both counterparties also change.  This is fine and understood.  The market is expected to be liquid enough for both banks to realign their risks accordingly.  The problem comes if there is no liquidity.

As markets have grown, so too have they become interconnected.  Effects in the Turkish, Ukrainian, Nigerian, and Indonesian markets are having a profound effect on our markets right now.  As money flows out of these markets it will look for a new home in, say, European bonds.  The problem is that instruments that are using the Black-Scholes formula cannot cope with great shocks.  Typically markets enter into a void of liquidity following a shock.  The formula kicks out a new risk number as our market has fallen 10% overnight leaving one of our counterparties with an enormous exposure that he cannot get out of as the liquidity is unavailable.

The problem exacerbates as he, in his rush to sell, sells the market lower triggering further stop-losses, and setting the market into a spiral.  This shock in the market then spreads as the capital flows out creating shocks in neighbouring markets, which then suffer a liquidity gap.  And so on.  As local markets close, there is usually a gap until the next one, which, in turn, assumes a gap in prices.  Sophisticated algorithmic funds, which shoot millions of orders in the markets every second on the basis of historic price observations (correlations between unconnected instruments), will then switch off and remove their price support (around 80% of all trade in developed markets comes from these funds).

In other words, the model breaks.  The risks taken on board by both of our counterparties at the point of trade no longer resemble the risks with the market lower and liquidity non-existent.  The Barings collapse is a very good example of this.

Investment banking is all about buying and selling risk.  Once we have bought risk, we will most often look to lay off some of the exposure.  Increasingly often we begin to use proxies to lay off risks.  The interconnection of the markets mean that we can find lookalike products that we can use as proxies to warehouse part of our risk exposure – we may wish to lay off our exposure to Vodafone, for example, by taking an opposing position in BT.  Not perfect, often untidy but more often than not will do the trick for a limited time.  Positions on the FTSE can, in part, be laid off with opposing positions on the Dax, Gilts with Bunds and so on.  The trick is to generate a sufficient pool of liquidity.

Here London has a clear advantage.  It is the world’s largest financial centre, and sits between the Asian and American timelines, so some risks can be offset, but not all.  We open just as Asia is closing, and close before the States.  We are only connected to the major exchanges, and then some like Canada and Australia, barely.  And we are closed at weekends.

An opportunity exists to develop a tax regime, and an infrastructure for the UK to become a 24 hour exchange.  The interconnection between markets, and the ‘gap risk’ issue posed by Black-Scholes offers up a golden chance for the UK to become the world market’s clearing centre.  This is, of course, something that could only be done outside of the EU.

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