arXiv subjects

Fabrizio Lillo

Publications and source records attributed to Fabrizio Lillo.

At least 127 records · Page 7Linked to original sources

arXiv2010

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary when short selling is not allowed and T>N, the considered methods are unable to outperform the sample covariance in terms of realized risk but can give much more diversified portfolios than the one obtained with the sample covariance. When T<N the use of the sample covariance matrix and of the pseudoinverse gives portfolios with very poor performance.

q-fin.PM↗

arXiv2010

Statistical identification with hidden Markov models of large order splitting strategies in an equity market

Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory variation of market members of the Spanish Stock Exchange. Our methodology probabilistically detects trading sequences, which are characterized by a net majority of buy or sell transactions. We interpret these patches of sequential buying or selling transactions as proxies of the traded hidden orders. We find that the time, volume and number of transactions size distributions of these patches are fat tailed. Long patches are characterized by a high fraction of market orders and a low participation rate, while short patches have a large fraction of limit orders and a high participation rate. We observe the existence of a buy-sell asymmetry in the number, average length, average fraction of market orders and average participation rate of the detected patches. The detected asymmetry is clearly depending on the local market trend. We also compare the hidden Markov models patches with those obtained with the segmentation method used in Vaglica {\it et al.} (2008) and we conclude that the former ones can be interpreted as a partition of the latter ones.

q-fin.TR↗

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↗

arXiv2008

Diffusive behavior and the modeling of characteristic times in limit order executions

We present an empirical study of the first passage time (FPT) of order book prices needed to observe a prescribed price change Delta, the time to fill (TTF) for executed limit orders and the time to cancel (TTC) for canceled ones in a double auction market. We find that the distribution of all three quantities decays asymptotically as a power law, but that of FPT has significantly fatter tails than that of TTF. Thus a simple first passage time model cannot account for the observed TTF of limit orders. We propose that the origin of this difference is the presence of cancellations. We outline a simple model, which assumes that prices are characterized by the empirically observed distribution of the first passage time and orders are canceled randomly with lifetimes that are asymptotically power law distributed with an exponent lambda_LT. In spite of the simplifying assumptions of the model, the inclusion of cancellations is enough to account for the above observations and enables one to estimate characteristics of the cancellation strategies from empirical data.

physics.soc-ph↗

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↗

arXiv2008

The non-random walk of stock prices: The long-term correlation between signs and sizes

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.

q-fin.ST↗

arXiv2008

Statistical properties of thermodynamically predicted RNA secondary structures in viral genomes

By performing a comprehensive study on 1832 segments of 1212 complete genomes of viruses, we show that in viral genomes the hairpin structures of thermodynamically predicted RNA secondary structures are more abundant than expected under a simple random null hypothesis. The detected hairpin structures of RNA secondary structures are present both in coding and in noncoding regions for the four groups of viruses categorized as dsDNA, dsRNA, ssDNA and ssRNA. For all groups hairpin structures of RNA secondary structures are detected more frequently than expected for a random null hypothesis in noncoding rather than in coding regions. However, potential RNA secondary structures are also present in coding regions of dsDNA group. In fact we detect evolutionary conserved RNA secondary structures in conserved coding and noncoding regions of a large set of complete genomes of dsDNA herpesviruses.

q-bio.QM↗

arXiv2007

Specialization of strategies and herding behavior of trading firms in a financial market

The understanding of complex social or economic systems is an important scientific challenge. Here we present a comprehensive study of the Spanish Stock Exchange showing that most financial firms trading in that market are characterized by a resulting strategy and can be classified in groups of firms with different specialization. Few large firms overally act as trending firms whereas many heterogeneous firm act as reversing firms. The herding properties of these two groups are markedly different and consistently observed over a four-year period of trading.

q-fin.ST↗

arXiv2007

Kullback-Leibler distance as a measure of the information filtered from multivariate data

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to statistical uncertainty. We explain the effectiveness of our method by comparing four filtering procedures, two of them being based on spectral analysis and the other two on hierarchical clustering. We compare these techniques as applied both to simulations of factor models and empirical data. We investigate the ability of these filtering procedures in recovering the correlation matrix of models from simulations. We discuss such an ability in terms of both the heterogeneity of model parameters and the length of data series. We also show that the two spectral techniques are typically more informative about the sample correlation matrix than techniques based on hierarchical clustering, whereas the latter are more stable with respect to statistical uncertainty.

physics.data-an↗

arXiv2007

The limit order book on different time scales

Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.

q-fin.TR↗

arXiv2007

Inverted and mirror repeats in model nucleotide sequences

We analytically and numerically study the probabilistic properties of inverted and mirror repeats in model sequences of nucleic acids. We consider both perfect and non-perfect repeats, i.e. repeats with mismatches and gaps. The considered sequence models are independent identically distributed (i.i.d.) sequences, Markov processes and long range sequences. We show that the number of repeats in correlated sequences is significantly larger than in i.i.d. sequences and that this discrepancy increases exponentially with the repeat length for long range sequences.

q-bio.GN↗

arXiv2007

Scaling laws of strategic behaviour and size heterogeneity in agent dynamics

The dynamics of many socioeconomic systems is determined by the decision making process of agents. The decision process depends on agent's characteristics, such as preferences, risk aversion, behavioral biases, etc.. In addition, in some systems the size of agents can be highly heterogeneous leading to very different impacts of agents on the system dynamics. The large size of some agents poses challenging problems to agents who want to control their impact, either by forcing the system in a given direction or by hiding their intentionality. Here we consider the financial market as a model system, and we study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations of allometric nature between the variables characterizing the trading activity of different institutions. We observe power law distributions in the investment time horizon, in the number of transactions needed to execute a large order and in the traded value exchanged by large institutions and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.

q-fin.ST↗

arXiv2006

Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framework of the model, the most likely proximate cause of this power law is a power law heterogeneity of traders' investment time horizons .

physics.soc-ph↗

arXiv2006

Market reaction to temporary liquidity crises and the permanent market impact

We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden, large variation of the spread, corresponding to a temporary crisis of liquidity in a double auction financial market. We find that the spread decays very slowly to its normal value as a consequence of the strategic limit order placement of liquidity providers. We consider several quantities, such as order placement rates and distribution, that affect the decay of the spread. We measure the permanent impact both of a generic event altering the spread and of a single transaction and we find an approximately linear relation between immediate and permanent impact in both cases.

physics.soc-ph↗

arXiv2006

Market efficiency and the long-memory of supply and demand: Is price impact variable and permanent or fixed and temporary?

In this comment we discuss the problem of reconciling the linear efficiency of price returns with the long-memory of supply and demand. We present new evidence that shows that efficiency is maintained by a liquidity imbalance that co-moves with the imbalance of buyer vs. seller initiated transactions. For example, during a period where there is an excess of buyer initiated transactions, there is also more liquidity for buy orders than sell orders, so that buy orders generate smaller and less frequent price responses than sell orders. At the moment a buy order is placed the transaction sign imbalance tends to dominate, generating a price impact. However, the liquidity imbalance rapidly increases with time, so that after a small number of time steps it cancels all the inefficiency caused by the transaction sign imbalance, bounding the price impact. While the view presented by Bouchaud et al. of a fixed and temporary bare price impact is self-consistent and formally correct, we argue that viewing this in terms of a variable but permanent price impact provides a simpler and more natural view. This is in the spirit of the original conjecture of Lillo and Farmer, but generalized to allow for finite time lags in the build up of the liquidity imbalance after a transaction. We discuss the possible strategic motivations that give rise to the liquidity imbalance and offer an alternative hypothesis. We also present some results that call into question the statistical significance of large swings in expected price impact at long times.

physics.soc-ph↗

arXiv2005

There's more to volatility than volume

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyze recent results of Ane and Geman (2000) and Gabaix et al. (2003), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.

physics.soc-ph↗

arXiv2005

Scaling and data collapse for the mean exit time of asset prices

We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a quadratic scaling law and it has associated a pre-factor which is specific to the analyzed stock. We perform a series of statistical tests to determine which kind of correlation are responsible for this specificity. The main contribution is associated with the autocorrelation property of stock returns. We introduce and solve analytically both a two-state and a three-state Markov chain models. The analytical results obtained with the two-state Markov chain model allows us to obtain a data collapse of the 20 measured MET profiles in a single master curve.

physics.soc-ph↗

arXiv2005

Cluster analysis for portfolio optimization

We consider the problem of the statistical uncertainty of the correlation matrix in the optimization of a financial portfolio. We show that the use of clustering algorithms can improve the reliability of the portfolio in terms of the ratio between predicted and realized risk. Bootstrap analysis indicates that this improvement is obtained in a wide range of the parameters N (number of assets) and T (investment horizon). The predicted and realized risk level and the relative portfolio composition of the selected portfolio for a given value of the portfolio return are also investigated for each considered filtering method.

physics.soc-ph↗