The global economy is a complex system where financial markets are the nervous system that disseminates signals. From our every day experience with complex systems – our human body is such a system – we are aware that minor deficiencies can have a disproportionate impact. Financial market conventions may appear as petty details of execution and therefore irrelevant, but in actual fact the subtleties of execution have a big macroeconomic impact.

Electronic trading

Today, there is a stark contrast between how traders initiate and conclude trades and how these transactions are settled where financial assets are actually exchanged between buyer and seller. 80% or more of the transaction volume is concluded electronically over a computer: traders sit in front of computer screens observing price graphs with real time bid and ask prices. Literally, with a mouse click they buy and sell millions of assets, such as buying EUROS and selling USD. Within seconds and minutes they can make any number of trades.

2 day settlement of trades

Settlement of a trade is the exchange and delivery of the underlying assets. The completion of a transaction occurs two business days after its conclusion; if for example a foreign exchange deal is concluded on Friday, it is settled the following Tuesday. The time of delivery varies for different assets; for currencies it is generally 2 days, for equities typically 3 days, and only for a few assets is it a day. Delivery takes so long because the banks use old mainframe computers that process transactions in batches. During the course of the day the computer queue the transactions and then process them at night. Transactions are processed in batches, which run in 24 hour cycles and so the banking infrastructure can only make interest payments for positions that are open over night. For currency markets, the positions have to be open at 5 PM Eastern Standard Time. If positions are closed out before 5 PM EST, they do not pay interest, whether they have been open for a few seconds or 23 hours. The batch based banking infrastructure means that intra-day traders, who open and close position during the course of a day and do not have open at 5 PM EST do not receive or pay interest.

90% is intra-day trading

The daily transaction volume in today’s financial markets is gigantic, for the foreign exchange market alone the transaction volume is close to 4 trillion USD or equivalent to 30% of the US GDP. Trading happens at a high pace with traders opening and closing positions in rapid succession. It is estimated that 90 to 95 percent of the positions are held for less then 24 hours, typically for only minutes or a few hours. So it is only 5 to 10 percent of the total volume of positions opened and closed that pay interest. The standard textbooks discussing interest rates assume that interest is paid on all transactions, but this is not the case, quite to the contrary, 90+ transaction volume pays no interest.

Payment of interest is a compensation for the risk of holding the underlying asset, which needs to be paid pro rata temporis, as is the case for the billing of electricity usage or the time spent on a telephone conversation. Today, interest rate payments are discrete, no interest payments are made for positions held intra-day, i.e. not beyond 5 PM EST. Interest is only paid, if positions are held beyond 5 PM and then accrues in daily increments.

Phenomenon of carry trade

For the Japanese Yen, which pays a paltry 0.05 percent interest, the bias introduced by the batch based settlement system is marginal, whereas for the South African Rand, which today pays 7 percent interest, the bias is big: the intra-day trader pays no interest, whereas the inter-day trader keeping the position open over night that is longer than 5 PM EST receives interest. This has the effect that traders going short South African Rand intra-day, do not have to pay interest and there is thus a hidden subsidy to sell the South African Rand. Because of this subsidy there are at the margin more traders shorting the South African Rand than would otherwise be the case. The central bank of South Africa has to compensate for the downward pressure exerted by the intra-day traders shorting the currency by setting daily interest rates higher than would be the case otherwise. This gives rise to the so-called ‘carry trade’, where intra-day traders earn a higher return than warranted by the long-term risk. Long-term investors regularly take advantage of this outcome and buy currencies paying a high rate of interest with the effect that high interest rate currencies have a tendency to appreciate, which is, however, interrupted by occasional rapid sell offs, when the market has gotten ahead of itself and there is a cascade of margin calls.

For a long time Economists have observed that high interest rate currencies have a tendency to appreciate. They have been at a loss to explain this behavior, because according to standard theory, high interest rate currencies should depreciate. In our analysis the explanation is the bifurcation between intra-day trading, where no interest is paid, and inter-day trading with interest rate payments.

Yield curve starts at 1 day

Today, the shortest interest rate payment is for positions held over night, i.e., one day. Accordingly, the yield curve starts at one day and extends up to ten for most fixed income markets and occasionally up to 30 years, as in the U.S. The one-day interest rate is a benchmark in the financial system, which is used to price a whole range of other interest rate products. Changes in the one-day interest rate permeate the fixed income market and affect the real economy, where increases in the one-day rate of interest, stifle the real economy.

In extreme situations, when confidence in global currency markets wanes, central bankers have to hike the one-day interest rate as a measure of last resort to protect the currency. As the one-day interest rate is a reference for the real economy, any increase in interest rate disrupts the real economy and is a huge cost. In Turkey, in 2000 and 2001, for example, the central bank had to increase interest rates to 8′000 percent at the height of its crisis, driving many banks and corporations into bankruptcy with over 1 Mio people losing their jobs.

If the yield curve starts with the one-second interest rate, the central bank can, in an emergency, increase the second interest rate as a signal to the currency markets to bring the flow of buyers and sellers back into balance. The second interest rate is a factor of 86′400 (number of seconds per day) away from the daily interest rates, thus there is a lot of time for the second interest rate to drop back to its normal level, so central bank intervention will not impact the real economy that relies on the daily interest rate as a benchmark.

Secret central bank interventions

During the past 12 months the central banks appear to have been intervening in the currency markets to stabilize exchange rates. The apparent calm in the currency markets is thus deceiving. Global investors are increasingly nervous about the finances of governments. It is only a matter of time before there will be a run on a currency. When this happens secret interventions will not be enough to stem the tide. The central bank under assault will be forced as a measure of last resort to increase the one-day interest rate, which in turn is a harsh break on the real economy. This is the last thing that the government and central bank want in such a situation but is unavoidable under these circumstances. To make things worse, the central bank action has the perverse effect within the currency market, of providing an added incentive for the intra-day traders to short the currency: this is like flying a plane with inverted steering, where pulling up the plane actually has the reverse effect. So initially, the action of increasing the rate of interest will actually make things worse and the currency will drop even faster. So the central bank will be forced to raise interest rates even more than initially anticipated. The way out is to introduce second-by-second interest rate payments, where all traders, both intra-day and inter-day traders, have to pay interest.

Digital Age

The global economy is based on instant communication, be it over the Internet or telephone. The financial system, which transacts trillions of USD on a daily basis, is electronic in terms of trade initiation but settlement is batch based and takes two business days. This is an anachronism and has the effect that 90 percent of all the trading is subject to the wrong incentives, because there are no interest rate payments. This destabilizes the currency markets and is the reason for the existence of the carry trade. Even more dangerous, the central bankers do not possess the appropriate tools to stabilize currency markets in case of emergency.

Technology of second by second interest rate payments

The technology for second by second interest rate payments has existed for several years and has withstood the test of practice and is ready for large-scale implementation. Introducing it is not expensive. As first step, we need public awareness for the issue. Second, central bankers and governments have to twist the arms of the big investment banks that dominate the currency and fixed interest rate markets and force them to introduce instant delivery with second by second interest rate payments. The big investment banks will need some convincing to give up the hidden profit margins due to the non-transparency of the old system. These vested interests cannot stand in the way of the overall social benefits of instant delivery with second by second interest payments. The benefits include more stable financial markets, disappearance of misalignment due to carry trade, lower interest rate volatility with improved economic growth and last but not least a reduction of systemic risk due to instantaneous settlement.

I clearly remember when we discovered the first scaling law in the late 80s (for a full account see our book). At the time, the research tools were primitive and graphical visualization could not be taken for granted. When Ueli Müller, a researcher in our team, made the first print out of the original scaling law, I thought that this was a test of the graphics program to draw a straight line, so good was the fit. The first scaling law states that there is a fixed relationship between the average price move and the time interval over which the price move is measured. The most striking feature of this scaling law is that ‘intraday’ proportionality is the same as that of longer-term data of days, weeks, months and even years. This self-similarity indicates that short- and long-term price moves are more closely related than we are inclined to believe.

A few years later, we discovered another scaling law of the number of directional price changes per time period. This scaling law, which belongs to the same class of scaling laws that we have just discovered, did not receive sufficient attention at the time and was accidentally not included in the book ‘Introduction to High Frequency Finance’, published in 2001. In 2005, we started to systematically search for additional scaling laws. We did not only look for scaling laws in relation to physical time but for relative and specific events, e.g., turning points.

We define an event as having occurred, when the price has moved down by more than 0.5% from its last high or the reverse; the next event has happened when the price has moved up by more than 0.5% from its last low. We then investigate the behavior of the price curve in the intervals between these events. We observe the following: whenever the price changes its direction with a 0.5% threshold, the average overshoot before it reaches its next low or high respectively is an average 0.5%. This relationship holds for ultra-small thresholds of 0.01% to 5 percent or even more, in other words the average overshoot is equal to the threshold. If a price has started a new trend with a threshold of 0.5% then the first 0.5% overshoot represents the expected average overshoot. Only when the market has exaggerated the move and has gone beyond this point to say 1%, 2%, 3% or more of overshoot, is it considered a tail event with an increased likelihood for a rebound.

Another important new scaling law deals with the length of the coastline of the sum of the entire price move; both up and down. If we consider price moves of 0.05% and discard any smaller price moves, then the average sum of total price move during the course of a year is an astounding 2500 percent for exchange rates, such as EUR_USD. If we only consider price moves of 0.1%, then the total coastline reduces to 1250%. For thresholds of 0.2%, the total coastline length is 670%, for 0.4% it is 340%, 0.8% thresholds 175% and for 1.6% only 90%.

How can we leverage these scaling laws for model building?

Scaling laws are efficient at condensing a lot of data, they are computed as follows: for every x quantity, we observe quantity y and then average y. The scaling law tells us, how average y changes with x. The intellectual beauty of scaling laws is that by considering all possible thresholds of x, we automatically include data of all y. The scaling law consists of an interception to the y-axis and the slope; so only two numbers ‘intercept’ and ‘slope’ summarize the whole time series with all its data, very elegant. Scaling laws only provide information about averages and do not make a statement about the distribution.

A remarkable feature of the scaling laws is that only little data is required to arrive at accurate estimates of the scaling parameters. I currently teach at the Essex University, where one of my students had accidentally only received a short data sample of one month but his estimates of the scaling parameters were astonishingly accurate. This is no small feat in economics where everything seems to be afloat.

In economics and finance it is standard practice to come up with the following type of model: variable x is a function of variable y, w and v. Where variable y, w, and v, may originate either from completely different time series (some of them collected with daily, weekly or monthly data) or from the same data series but sampled at different frequencies. Typically, there is the unspoken understanding that the sampling frequency of the data is only a minor issue; a consequence of the availability of the data, in actual fact its impact is more profound. The sampling frequency modulates the observations, just remember the length of the coastline. If an indicator based on monthly data is compared with another indicator that is updated with every 0.05% price move, then the first indicator relates to a coastline of a length of 20% to 30%, whereas the second relates to a coastline of 2500%. It goes without saying that the statistical properties of these indicators are different and the results may not mesh easily. To use an analogy, to disregard a scaling law is like planning a road trip with different road maps that have different yardsticks, but assuming that they are all the same.

Scaling laws have an important role as a yardstick for measurements and more importantly carry a significant message for the design of economic and financial models. Traditionally, economic models have assumed that markets have an equilibrium price level, where prices match fundamentals and forces of demand and supply are in balance. Increasingly, economists are becoming aware that there is no such thing as a fundamental price and that there is a need to find a substitute for the role of fundamental price, which is a kind of anchor, where market prices are expected to gravitate towards. I conjecture that scaling laws are a substitute and are an indicator for the dynamic equilibrium where financial markets and the economy at large gravitate, not in terms of absolute price levels but rates of change.

Why is there no fundamental price, this concept seems so intuitive? Just consider the question, of what is the fundamental price of gold? Is it the current market price quoted on the over the counter market or on the CME, the Chicago Board of Trade? To be pedantic, is it the bid or ask price that is quoted at this very second on the market, or is it the price that I read in my newspaper that publishes daily closing prices, which may be two or more percent away from the current price? Or is the fundamental price, the end of month price or for that matter the end of quarter or end of year price? Is the price the same for small or big quantities of gold? Anyway market prices are subject to the randomness of market oscillations and investor exuberance and a more objective measure for fundamental prices may be actual production costs. Where do we measure production costs in South Africa or in Australia and which gold mine should be used as the benchmark, or more involved questions, what interest rate assumptions should be made to compute the production costs, or how do we input costs for energy or over how many years are the production facilities amortized? However attractive the concept of fundamental prices seems at first glance it hinges on too many assumptions and is thus not a robust reference point.

Scaling laws are an indicator of the dynamic equilibrium. In context of the overshoot scaling law: if the market price starts a new trend, of say a 1% downward move computed from its previous peak, there is an average overshoot of another 1%, which is the dynamic equilibrium. If the price overshoots by 2% or more, the market is clearly off equilibrium. The scaling law is a metric to determine, how far the market has diverged from its equilibrium. With the scale of market quake (SMQ) service, we do exactly this: we measure the extent in which the market price has diverged from its dynamic equilibrium.

The research of scaling laws in financial markets has just started. Even though, we have discovered 12 new scaling laws, there are many other scaling laws still to be discovered. The more scaling laws are known, the easier it is to understand, where the financial markets and economy general has its dynamic equilibrium. Other important questions have not been answered: how do the scaling laws originate and why are they so pervasive and hold for so many orders of magnitude? Is it because financial markets are a half open system, where there are a large number of participants, where nobody is the ‘master’ and everyone competes with the other participants that have different time horizons and position sizes?

Because scaling laws hold true for so many orders of magnitude, we can really leverage the usage of high frequency data: we can calibrate the models with tick by tick data and then apply the resultant model to lower frequency data, where data is sparse. This gives financial and economic model builders a substitute for the lack of long-term data. Scaling law research in economics is in its infancy and a lot of exciting research remains to be done.

Richard Olsen is founder and chief executive of Olsen Ltd and the Chairman of OANDA, a leading foreign exchange broker and market maker.

Olsen Ltd is a research and development company and investment manager based in Zurich, Switzerland. Olsen has yielded practical applications and managed accounts and third-party products, investing in currencies as a separate asset class or as an overlay to an existing currency exposure.

Author: Richard B. Olsen, Founder and CEO of Olsen Ltd

In economics the traditional methodology of research is to first formulate a general hypothesis and then to prove the conjecture. The debate of the efficient-market hypothesis is an example of this approach: researchers put forward the hypothesis stating that a market is efficient only if all known information is reflected in the market prices. The hypothesis was introduced because researchers believed that markets could only fulfill their role of ensuring an optimal allocation of resources, if all information was reflected in the market prices. The hypothesis of market efficiency spurred a large debate, which was not as rewarding as expected because the evidence was indecisive.

The debate of efficient-market hypothesis was motivated by a desire to prove that financial markets are indeed efficient in allocating resources. So in this sense, prior political beliefs impacted the research agenda. High frequency finance takes a different tack. There is no prior hypothesis: the collected data has to speak for itself. The researcher is open to surprise and has no hidden agenda.

Our recent discovery of 17 new scaling laws illustrates the methodology, we would have never predicted the existence of so many scaling laws and were completely surprised by the results. As soon as we had made the discovery, it opened the door to improve our technology of how we compute volatility and design trading models. We succeeded in our research, because we were open to surprise and had spent a lot of time studying the detailed properties of the empirical data. Economic phenomena are highly complex and subtle. If we start off with constraining objectives, we may miss the point and go off on a tangent.

The approach of high frequency finance has an apparent disadvantage: the reality of economics is far more complex than we would ever expect and the dream of a rapid answer to an economic problem is an illusion; we have to acknowledge that a lot of work is required before we can hope to solve a particular issue. What do you prefer, a solution that seems to solve all the issues, but is crap, or spend more time to discover a durable answer?

High frequency finance goes beyond econophysics, a relatively new interdisciplinary research field that applies theories and methods used in physics and other natural sciences and relies heavily on validating its results with empirical data. High frequency finance is agnostic: the discipline starts with data collection and then iteratively generalizes the observed phenomena to discover appropriate explanations. We seek inspiration in other sciences, not just natural science, but are always looking for bespoke solutions that go to the heart of the problem and rely on a minimum of prior assumptions.

The current crisis is a wake up call to break the shackles of economics. High frequency finance shows the way forward: What is now needed is to make the financial resources available for the many researchers worldwide that are eager to dive into the masses of economic and financial data and unlock their secrets.

Author: Richard B. Olsen, Founder and CEO of Olsen Ltd

High frequency finance focuses on the messiness of the tick by tick data produced by financial markets. The discipline is not hamstrung by theories that have been formulated in the abstract, as is the case for classical economics. The approach is to first study the detailed statistical properties of the data and in an iterative process build models that explain the observations. The discipline follows the approach that natural scientists take for granted: to first observe the phenomena of nature and then, inspired by these observations, to build appropriate theories that explain the recorded facts.

Today, in the age of electronic trading there are masses of data. Liquid financial markets spew out market prices every second and faster. So for one instrument alone it is possible to collect from 50′000 to 100′000 and more price ticks every day. These masses of data points are meaningful, because market makers set prices by monitoring price updates from competing market makers on a tick by tick basis and benchmark their prices relative to the overall market. They set prices in a way to balance demand and supply. Even the slightest deviations may mean huge losses. On an ongoing basis market makers fine tune their pricing to ensure that the prices published are at exactly the right levels.

In high frequency finance investigating these masses of prices, we have discovered 17 new scaling laws that hold over several orders of magnitude, see scientific article with the title ‘An extensive set of scaling laws and the FX coastline’ by J. B. Glattfelder et al.. Scaling laws are observed, when two properties maintain the same proportions over a range of values. In our case, the scaling laws persist from ultra-small values of 0.01 percent price changes to magnitudes of 5 percent price changes and more. An example of such a scaling law is the size of average price overshoot that occurs, whenever a new price trend has started. Say you observe that a market price has moved down by 1 percent from its recent peak, how much further will the price move down? Will the price revert after an additional average price move of 0.1 percent, 0.5, 1 or more percent? as it turns out, the average overshoot is 1 percent: this property scales and holds true for thresholds of 0.01 percent up to 5 percent and possibly higher. So, if the price has moved down from its recent high by 2 percent, then on average there will follow another 2 percent move.

The remarkable feature of this and the other scaling laws described in the above paper is that they apply to both intra-day market moves and longer-term price movements spanning days, weeks and months. There is no difference in behavior for intra-day and longer-term data. This result is remarkable: it indicates that we can use the abundance of intra-day data to develop robust models and then inspired by fractal theory use these models appropriately scaled to explain long-term data.

The world is evolving at a rapid pace: just think of the changes that have occurred over the past ten years. Today, we take the Internet,  mobile phones, etc. for granted – only 10 years ago, these technologies were in their infancy. Economists cannot hope to develop robust economic models that are fed with long-term data alone. They would need access to a 100′000 year history of our modern economy to build models with long-term data alone, but this does not exist. By building fractal models that are primed using the abundance of intra-day data and then scale them to be applicable for long-term phenomena, we overcome the fact that we do not have sufficient long-term data. For traditional economists this is a big challenge and will require an extra effort. They will first have to focus on developing models for liquid markets and then expand their scope. At Olsen, we have started this process and have succeeded in building models that are the same for short-term and long-term time horizons, the only difference is their respective time scale.

The discipline of high frequency finance is still in its infancy. If we compare its prowess with the success story of computer sciences, then in terms Moore’s law, which was published 1965, high frequency finance as the technology stands today is comparable to 1968 computer technology, so a long way to go. How will a break through in economics help us? Today, we do not access to efficient predictive services for our economy. We can use the technology to build a global information system for the economy and its financial market. Olsen’s Scale of Market Quake service, which is the equivalent of a Richter scale for the foreign exchange markets, is a step in this direction.

Author: Richard B. Olsen, Founder and CEO of Olsen Ltd

Richard Olsen challenges three received notions that mire the global economy in counter-productive habits that destroy value: that market prices in gross time tell us everything we need to know; that such information as we have is a trustworthy indicator of things to come; and that the chain of events in price evolution is orderly and self-correcting.

Olsen Ltd. has discovered and validated 17 new power laws that prove this firm’s long-held belief: much of the market’s volatility is invisible to casual, low-resolution analysis. While much work remains to be done, Olsen is taking steps to encourage the accumulation and analysis of very-high-resolution data to fuel sophisticated models that leverage the insights and power of the new scaling laws. With two strategic objectives: to increase return as a product of the predictive capacity of better trading models, and to counter the effect of inevitably irrational behavior by providing liquidity in the face of skewed pricing patterns…

Clicking here will retrieve an Acrobat version of the illustration.

We have discovered 17 new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns out to be surprisingly long. The new laws substantially extend the catalogue of stylised facts and sharply constrain the space of possible theoretical explanations of the market mechanisms…

Clicking here will retrieve an Acrobat version of the illustration.