arXiv subjects

J. Doyne Farmer

Publications and source records attributed to J. Doyne Farmer.

At least 55 records · Page 3Linked to original sources

arXiv2012

Historical Costs of Coal-Fired Electricity and Implications for the Future

We study the costs of coal-fired electricity in the United States between 1882 and 2006 by decomposing it in terms of the price of coal, transportation costs, energy density, thermal efficiency, plant construction cost, interest rate, capacity factor, and operations and maintenance cost. The dominant determinants of costs have been the price of coal and plant construction cost. The price of coal appears to fluctuate more or less randomly while the construction cost follows long-term trends, decreasing from 1902 - 1970, increasing from 1970 - 1990, and leveling off since then. Our analysis emphasizes the importance of using long time series and comparing electricity generation technologies using decomposed total costs, rather than costs of single components like capital. By taking this approach we find that the history of coal-fired electricity costs suggests there is a fluctuating floor to its future costs, which is determined by coal prices. Even if construction costs resumed a decreasing trend, the cost of coal-based electricity would drop for a while but eventually be determined by the price of coal, which fluctuates while showing no long-term trend.

physics.soc-ph↗

arXiv2012

Stability analysis of financial contagion due to overlapping portfolios

Common asset holdings are widely believed to have been the primary vector of contagion in the recent financial crisis. We develop a network approach to the amplification of financial contagion due to the combination of overlapping portfolios and leverage, and we show how it can be understood in terms of a generalized branching process. By studying a stylized model we estimate the circumstances under which systemic instabilities are likely to occur as a function of parameters such as leverage, market crowding, diversification, and market impact. Although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. Under our model there is a critical threshold for leverage; below it financial networks are always stable, and above it the unstable region grows as leverage increases. The financial system exhibits "robust yet fragile" behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. Our model and methods of analysis can be calibrated to real data and provide simple yet powerful tools for macroprudential stress testing.

q-fin.GN↗

arXiv2012

A proposal for impact-adjusted valuation: Critical leverage and execution risk

The practice of valuation by marking-to-market with current trading prices is seriously flawed. Under leverage the problem is particularly dramatic: due to the concave form of market impact, selling always initially causes the expected leverage to increase. There is a critical leverage above which it is impossible to exit a portfolio without leverage going to infinity and bankruptcy becoming likely. Standard risk-management methods give no warning of this problem, which easily occurs for aggressively leveraged positions in illiquid markets. We propose an alternative accounting procedure based on the estimated market impact of liquidation that removes the illusion of profit. This should curb the leverage cycle and contribute to an enhanced stability of financial markets.

q-fin.GN↗

arXiv2012

Statistical Basis for Predicting Technological Progress

Forecasting technological progress is of great interest to engineers, policy makers, and private investors. Several models have been proposed for predicting technological improvement, but how well do these models perform? An early hypothesis made by Theodore Wright in 1936 is that cost decreases as a power law of cumulative production. An alternative hypothesis is Moore's law, which can be generalized to say that technologies improve exponentially with time. Other alternatives were proposed by Goddard, Sinclair et al., and Nordhaus. These hypotheses have not previously been rigorously tested. Using a new database on the cost and production of 62 different technologies, which is the most expansive of its kind, we test the ability of six different postulated laws to predict future costs. Our approach involves hindcasting and developing a statistical model to rank the performance of the postulated laws. Wright's law produces the best forecasts, but Moore's law is not far behind. We discover a previously unobserved regularity that production tends to increase exponentially. A combination of an exponential decrease in cost and an exponential increase in production would make Moore's law and Wright's law indistinguishable, as originally pointed out by Sahal. We show for the first time that these regularities are observed in data to such a degree that the performance of these two laws is nearly tied. Our results show that technological progress is forecastable, with the square root of the logarithmic error growing linearly with the forecasting horizon at a typical rate of 2.5% per year. These results have implications for theories of technological change, and assessments of candidate technologies and policies for climate change mitigation.

physics.soc-ph↗

arXiv2012

How does the market react to your order flow?

We present an empirical study of the intertwined behaviour of members in a financial market. Exploiting a database where the broker that initiates an order book event can be identified, we decompose the correlation and response functions into contributions coming from different market participants and study how their behaviour is interconnected. We find evidence that (1) brokers are very heterogeneous in liquidity provision -- some are consistently liquidity providers while others are consistently liquidity takers. (2) The behaviour of brokers is strongly conditioned on the actions of {\it other} brokers. In contrast brokers are only weakly influenced by the impact of their own previous orders. (3) The total impact of market orders is the result of a subtle compensation between the same broker pushing the price in one direction and the liquidity provision of other brokers pushing it in the opposite direction. These results enforce the picture of market dynamics being the result of the competition between heterogeneous participants interacting to form a complicated market ecology.

q-fin.TR↗

arXiv2011

Complex dynamics in learning complicated games

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is complicated, and if not, what is? We investigate this question here, defining a complicated game as one with many possible moves, and therefore many possible payoffs conditional on those moves. We investigate two-person games in which the players learn based on experience. By generating games at random we show that under some circumstances the strategies of the two players converge to fixed points, but under others they follow limit cycles or chaotic attractors. The dimension of the chaotic attractors can be very high, implying that the dynamics of the strategies are effectively random. In the chaotic regime the payoffs fluctuate intermittently, showing bursts of rapid change punctuated by periods of quiescence, similar to what is observed in fluid turbulence and financial markets. Our results suggest that such intermittency is a highly generic phenomenon, and that there is a large parameter regime for which complicated strategic interactions generate inherently unpredictable behavior that is best described in the language of dynamical systems theory

nlin.CD↗

arXiv2011

Heterogeneity, correlations and financial contagion

We consider a model of contagion in financial networks recently introduced in the literature, and we characterize the effect of a few features empirically observed in real networks on the stability of the system. Notably, we consider the effect of heterogeneous degree distributions, heterogeneous balance sheet size and degree correlations between banks. We study the probability of contagion conditional on the failure of a random bank, the most connected bank and the biggest bank, and we consider the effect of targeted policies aimed at increasing the capital requirements of a few banks with high connectivity or big balance sheets. Networks with heterogeneous degree distributions are shown to be more resilient to contagion triggered by the failure of a random bank, but more fragile with respect to contagion triggered by the failure of highly connected nodes. A power law distribution of balance sheet size is shown to induce an inefficient diversification that makes the system more prone to contagion events. A targeted policy aimed at reinforcing the stability of the biggest banks is shown to improve the stability of the system in the regime of high average degree. Finally, disassortative mixing, such as that observed in real banking networks, is shown to enhance the stability of the system.

q-fin.GN↗

arXiv2011

Segmentation algorithm for non-stationary compound Poisson processes

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated to a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galvan, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.

physics.data-an↗

arXiv2010

Tick size and price diffusion

A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature on the role of tick size on market microstructure. However, tick size can also affect price properties at longer time scales, and relatively less is known about the effect of tick size on the statistical properties of prices. The present paper is divided in two parts. In the first we review the effect of tick size change on the market microstructure and the diffusion properties of prices. The second part presents original results obtained by investigating the tick size changes occurring at the New York Stock Exchange (NYSE). We show that tick size change has three effects on price diffusion. First, as already shown in the literature, tick size affects price return distribution at an aggregate time scale. Second, reducing the tick size typically leads to an increase of volatility clustering. We give a possible mechanistic explanation for this effect, but clearly more investigation is needed to understand the origin of this relation. Third, we explicitly show that the ability of the subordination hypothesis in explaining fat tails of returns and volatility clustering is strongly dependent on tick size. While for large tick sizes the subordination hypothesis has significant explanatory power, for small tick sizes we show that subordination is not the main driver of these two important stylized facts of financial market.

q-fin.ST↗

arXiv2010

An empirical study of the tails of mutual fund size

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.

q-fin.GN↗

arXiv2010

What drives mutual fund asset concentration?

Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which dictates that fund performance is size independent and fund growth is essentially random. The random process is characterized by entry, exit and growth. We present a new time-dependent solution for the standard equations used in the industrial organization literature and show that relaxation to the steady-state solution is extremely slow. Thus, even if these processes were stationary (which they are not), the steady-state solution, which is a very heavy-tailed power law, is not relevant. The distribution is instead well-approximated by a less heavy-tailed log-normal. We perform an empirical analysis of the growth of mutual funds, propose a new, more accurate size-dependent model, and show that it makes a good prediction of the empirically observed size distribution. While mutual funds are in many respects like other firms, market efficiency introduces effects that make their growth process distinctly different. Our work shows that a simple model based on market efficiency provides a good explanation of the concentration of assets, suggesting that other effects, such as transaction costs or the behavioral aspects of investor choice, play a smaller role.

q-fin.ST↗

arXiv2010

The cause of universality in growth fluctuations

Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth fluctuations. The fluctuations display characteristic features, including double exponential scaling in the body of the distribution and power law scaling of the standard deviation as a function of size. To explain this we propose a remarkably simple additive replication model: At each step each individual is replaced by a new number of individuals drawn from the same replication distribution. If the replication distribution is sufficiently heavy tailed then the growth fluctuations are Levy distributed. We analyze the data from bird populations, firms, and mutual funds and show that our predictions match the data well, in several respects: Our theory results in a much better collapse of the individual distributions onto a single curve and also correctly predicts the scaling of the standard deviation with size. To illustrate how this can emerge from a collective microscopic dynamics we propose a model based on stochastic influence dynamics over a scale-free contact network and show that it produces results similar to those observed. We also extend the model to deal with correlations between individual elements. Our main conclusion is that the universality of growth fluctuations is driven by the additivity of growth processes and the action of the generalized central limit theorem.

physics.soc-ph↗

arXiv2010

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.

q-fin.ST↗

arXiv2009

Market impact and trading profile of large trading orders in stock markets

We empirically study the market impact of trading orders. We are specifically interested in large trading orders that are executed incrementally, which we call hidden orders. These are reconstructed based on information about market member codes using data from the Spanish Stock Market and the London Stock Exchange. We find that market impact is strongly concave, approximately increasing as the square root of order size. Furthermore, as a given order is executed, the impact grows in time according to a power-law; after the order is finished, it reverts to a level of about 0.5-0.7 of its value at its peak. We observe that hidden orders are executed at a rate that more or less matches trading in the overall market, except for small deviations at the beginning and end of the order.

q-fin.TR↗

arXiv2009

The Role of Design Complexity in Technology Improvement

We study a simple model for the evolution of the cost (or more generally the performance) of a technology or production process. The technology can be decomposed into $n$ components, each of which interacts with a cluster of $d-1$ other, dependent components. Innovation occurs through a series of trial-and-error events, each of which consists of randomly changing the cost of each component in a cluster, and accepting the changes only if the total cost of the entire cluster is lowered. We show that the relationship between the cost of the whole technology and the number of innovation attempts is asymptotically a power law, matching the functional form often observed for empirical data. The exponent $α$ of the power law depends on the intrinsic difficulty of finding better components, and on what we term the {\it design complexity}: The more complex the design, the slower the rate of improvement. Letting $d$ as defined above be the connectivity, in the special case in which the connectivity is constant, the design complexity is simply the connectivity. When the connectivity varies, bottlenecks can arise in which a few components limit progress. In this case the design complexity is more complicated, depending on the details of the design. The number of bottlenecks also determines whether progress is steady, or whether there are periods of stasis punctuated by occasional large changes. Our model connects the engineering properties of a design to historical studies of technology improvement.

physics.soc-ph↗

arXiv2009

Studies of the limit order book around large price changes

We study the dynamics of the limit order book of liquid stocks after experiencing large intra-day price changes. In the data we find large variations in several microscopical measures, e.g., the volatility the bid-ask spread, the bid-ask imbalance, the number of queuing limit orders, the activity (number and volume) of limit orders placed and canceled, etc. The relaxation of the quantities is generally very slow that can be described by a power law of exponent $\approx0.4$. We introduce a numerical model in order to understand the empirical results better. We find that with a zero intelligence deposition model of the order flow the empirical results can be reproduced qualitatively. This suggests that the slow relaxations might not be results of agents' strategic behaviour. Studying the difference between the exponents found empirically and numerically helps us to better identify the role of strategic behaviour in the phenomena.

q-fin.TR↗

arXiv2009

The Reality Game

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend on the amount wagered on those outcomes. By varying the `reality map', which relates the amount wagered to the probability of the outcome, it is possible to move continuously from a purely objective game in which probabilities have no dependence on wagers to a purely subjective game in which probabilities equal the amount wagered. We study self-reinforcing games, in which betting more on an outcome increases its odds, and self-defeating games, in which the opposite is true. This is investigated in and out of equilibrium, with and without rational players, and both numerically and analytically. We introduce a method of measuring the inefficiency of the game, similar to measuring the magnitude of the arbitrage opportunities in a financial market. We prove that convergence to equilibrium is is a power law with an extremely slow rate of convergence: The more subjective the game, the slower the convergence.

q-fin.GN↗

arXiv2008

How markets slowly digest changes in supply and demand

In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative predictions about the volume and time dependence of market impact, the bid-ask spread, order book dynamics, and volatility. Comparisons to data yield some encouraging successes. This framework suggests a novel interpretation of financial information, in which agents are at best only weakly informed and all have a similar and extremely noisy impact on prices. Most of the processed information appears to come from supply and demand itself, rather than from external news. The ideas reviewed here are relevant to market microstructure regulation, agent-based models, cost-optimal execution strategies, and understanding market ecologies.

q-fin.TR↗