Statistical Arbitrage

We present a detailed study of portfolio optimisation based on cointegration, a statistical tool that here exploits a long-run equilibrium relationship between stock prices and an index price. We compare the theoretical and empirical properties of cointegration optimal equity portfolios with those of portfolios optimised on the tracking error variance. From an eleven year out of sample performance analysis we

A methodology to create statistical arbitrage in stock Index S&P500 is presented. A synthetic asset based on the cointegration relationship of the stocks with Index was constructed. In order to capture the dynamic of the market time adaptive algorithms have been developed and discussed. The pair trading strategy was applied in different periods between S&P500 and synthetic asset and the results were evaluated. Different metrics have shown that the Multvariate Kalman Algorithm creates statistical arbitrage in index with much lower Maximum Drawdown and higher profit. The algorithm is neutral as the beta is close to zero and the Sharp Ratio remains high in all cases.

An important revenue stream for electric battery operators is often arbitraging the hourly price spreads in the day-ahead auction. The optimal approach to this is challenging if risk is a consideration as this requires the estimation of density functions. Since the hourly prices are not normal and not independent, creating spread densities from the difference of separately estimated price densities is generally intractable. Thus, forecasts of all intraday hourly spreads were directly specified as an upper triangular matrix containing densities. The model was a flexible four-parameter distribution used to produce dynamic parameter estimates conditional upon exogenous factors, most importantly wind, solar and the day-ahead demand forecasts. These forecasts supported the optimal daily scheduling of a storage facility, operating on single and multiple cycles per day. The optimization is innovative in its use of spread trades rather than hourly prices, which this paper argues, is more at...

We present empirical results on the statistical and economic viability of a market timing trading strategy that is based on rotation between two risky assets. Using data on Exchange Traded Funds (ETFs), and models for both the returns and the volatility of the underlying assets, we compare the performance of the suggested models with the standard benchmarks of a buy-andhold strategy and an equally weighted portfolio. The underlying intuition for the use of such a strategy rests with literature on sign and volatility predictability. The rotation strategy, as we apply it in this paper, is not risk-neutral and assumes the presence of arbitrage opportunities in the markets. Furthermore, the model specification uses the interplay between relative returns and relative volatilities in picking-up the asset with the highest return. Our results show that even a naive model that is based on a moving average of relative returns can outperform both benchmarks and that more elaborate specifications for the rotation model may yield additional performance gains. We also find that, in many cases, the rotation strategy yields statistically significant sign predictions of the relative returns and volatility. While our results are conditional to the data that we have used in our analysis they, nevertheless, support the market timing literature and show that an active trading strategy can be based on the concept of rotation.

In this study, we propose a variation of the statistical arbitrage trading strategy, “TVECM pair trading strategy”, which minimizes risk from its market neutral property and remains its profitability. To study performance of the strategy, we examine the 5-minutes intraday price relationship between pairs of assets in Thailand’s Stock Spot (SET) and Futures (TFEX) Markets and conduct backtesting. Three pairs of series of the same underlying asset (SET50, KTB, TRUE) which trade between 2nd July, 2014 and 29th August, 2014 are studied. Considering the differences of investor behaviors in different market condition, different level of mispricing spread and existence of the transaction cost in practical trading, the price relationship is estimated following the Threshold Vector Error Correction Model (TVECM). The TVECM pair trading strategy applies the estimated parameters to create trading signals. Applying the formulated strategy, the arbitrage opportunities are found. The performance of the TVECM pair trading strategy is found to be superior to the traditional pair trading strategy.

This is the first paper to consider pairs trading as a mechanism by which the Law of One Price is enforced between stocks and ADRs. Using intraday contemporaneous data spanning 2007-2009, pairs trading between UK stocks and ADRs yields 5% annually net of costs, taxes, and systematic risk. Unlike arbitrage in other settings, stock-ADR pairs traders face minimal uncertainty toward price convergence, yielding stable returns. Hence, ADR arbitrage is characterized by low return volatility and a high incidence of small quickly-disappearing mispricings. Our work provides evidence against automatically e cient prices, and supports the view that mispricings incentivize arbitrageurs to enforce market e ciency.

The subject of high-frequency market maker spread optimization is an active area of reasearch. In this paper I apply closed form approximations of bid and ask spreads, as derived by Guéant, Lehalle, and Tapia [3], to trade-by-trade transaction and quote data. The model maximizes expected utility of PnL, using imposed inventory limits to facilitate the transformation of the optimizing Hamilton-Jacobi-Bellman equations into linear differential equations. These are further reduced to closed-form approximations that limit computational need considerably, making them viable solutions in a high-frequency environment. These are applied statically to trade-by-trade data, and discussed with regard to assumptions and limitations. Naïve approximations of dynamic variables are explored superficially, and the resulting changes in end-of-day PnL discussed.

This research is designed to help quantify one of the "slippages" which are often recognized in quant strategies. The idea is that whenever the actual executed prices are away (both time and size) from the model prices, the realized returns will suffer. The slippage for a particular statistical arbitrage strategy is quantified. It is shown that portion of the loss is due to using different prices for estimating the parameters of the strategy. The main source of the loss is the use of intraday in place of market on close prices. Five years of intraday transaction data from NYSE TAQ database are used. Analysis shows that on average the daily loss due to intraday prices accounts for 0.03% of the initial capital. For the period 2003 -2006 the accumulated loss is approximately 30%. The described approach can be of use to new quantitative analysts who create and backtest trading strategies. It could also be used during the due diligence process of a fund that is interested in investing in a statistical arbitrage strategy. The recommendation from this research is to require a backtest done by using intraday and market on close prices in order to identify the size of such loss.

A number of recent emerging applications call for studying data streams, potentially infinite flows of information updated in real-time. When multiple co-evolving data streams are observed, an important task is to determine how these streams depend on each other, accounting for dynamic dependence patterns without imposing any restrictive probabilistic law governing this dependence. In this paper we argue that flexible least squares (FLS), a penalized version of ordinary least squares that accommodates for time-varying regression coefficients, can be deployed successfully in this context. Our motivating application is statistical arbitrage, an investment strategy that exploits patterns detected in financial data streams. We demonstrate that FLS is algebraically equivalent to the well-known Kalman filter equations, and take advantage of this equivalence to gain a better understanding of FLS and suggest a more efficient algorithm. Promising experimental results obtained from a FLS-based algorithmic trading system for the S&P 500 Futures Index are reported.

This paper investigates pairs trading strategy by using the cointegration method among the 10 most popular agricultural future markets. It is found that only in 2 pairs shows trading signal. The pairs trading strategy is performed in two stages that are the formation period and the trading period with daily futures data from 2004 to 2015. After the formation period was constructed, it is assumed that the cointegration error continues to hold the trading period same as it does for the formation period. The pairs trading strategy is created by the long position cotton and the short position coffee and also long position cotton and short position the livecattle. It is found that the profitability of this strategy worked well in both formation period and trading period.

Compared with previous research, the present work extends existing literature by considering long-run relations among major international stock market indices, under different market conditions, and the implications of these relations on the implementation of statistical arbitrage strategies. The examined data contain two bust phases interrupted by a mild bullish period. Employing cointegration analysis, reported results initially indicate that changes in market performance affect the stability of long-run relations, therefore suggesting that arbitrageurs should perform rebalancing among the examined indices when a change in a market trend is evident. Furthermore, extreme market performance harms the mean-reverting properties of a potential long-run relation while moderate market performance points to cointegration between a pair of indices. However, the absence of a stationary spread does not suggest the potential of abnormal returns realization, in the short-run, through exploitation of deviations from its mean value. The applicability of our results may be of importance to market participants since the cointegration approach has recently received considerable attention by hedge funds adopting statistical arbitrage strategies.

Purpose – This paper aims to enhance a co-skew-based risk measurement methodology initially
introduced in Polimenis (2012), by extending it for the joint estimation of the jump betas for two stocks.
Design/methodology/approach – The authors introduce the possibility of idiosyncratic jumps and analyze the robustness of the estimated sensitivities when two stocks are jointly fit to the same set of latent jump factors. When individual stock skews substantially differ from those of the market, the requirement that the individual skew is exactly matched is placing a strain on the single stock estimation system.
Findings – The authors argue that, once the authors relax this restrictive requirement in an enhanced joint framework, the system calibrates to a more robust solution in terms of uncovering the true magnitude of the latent parameters of the model, at the same time revealing information about the level of idiosyncratic skews in individual stock return distributions.
Research limitations/implications – Allowing for idiosyncratic skews relaxes the demands placed on the estimation system and hence improves its explanatory power by focusing on matching systematic skew that is more informational. Furthermore, allowing for stock-specific jumps that are not related to the market is a realistic assumption. There is now evidence that idiosyncratic risks are priced as well, and this has been a major drawback and criticism in using CAPM to assess risk premia. Practical implications – Since jumps in stock prices incorporate the most valuable information, then quantifying a stock’s exposure to jump events can have important practical implications for financial risk management, portfolio construction and option pricing.
Originality/value – This approach boosts the “signal-to-noise” ratio by utilizing co-skew moments, so that the diffusive component is filtered out through higher-order cumulants. Without making any distributional assumptions, the authors are able not only to capture the asymmetric sensitivity of a stock to latent upward and downward systematic jump risks, but also to uncover the magnitude of idiosyncratic stock skewness. Since cumulants in a Levy process evolve linearly in time, this approach is horizon independent and hence can be deployed at all frequencies.

We improve upon the power of the statistical arbitrage test in Hogan, Jarrow, Teo, and Warachka (2004). Our methodology also allows for the evaluation of return anomalies under weaker assumptions. We then compare strategies based on their convergence rates to arbitrage and identify strategies whose probability of a loss declines to zero most rapidly. These strategies are preferred by investors with finite horizons or limited capital. After controlling for market frictions and examining convergence rates to arbitrage, we find that momentum and value strategies offer the most desirable trading opportunities.

Abstract: Quantitative trading in oil based markets are investigated over 2003-2010, with focus on WTI, Brent, heating oil and gas oil. A total of 861 spreads are considered. A novel optimal statistical arbitrage trading model is applied, with generalised stepwise ...

This paper introduces the concept of statistical arbitrage, a long horizon trading opportunity that generates a riskless profit and is designed to exploit persistent anomalies. Statistical arbitrage circumvents the joint hypothesis dilemma of traditional market efficiency tests because its definition is independent of any equilibrium model and its existence is incompatible with market efficiency. We provide a methodology to test for statistical arbitrage and then empirically investigate whether momentum and value trading strategies constitute statistical arbitrage opportunities. Despite adjusting for transaction costs, the influence of small stocks, margin requirements, liquidity buffers for the marking-to-market of

The objective of this study is to develop a financially profitable Pairs trading model for trading in Dhaka Stock Exchange. Pairs Trade is a statistical arbitrage investment strategy. The study used daily stock prices of a sample of 20 stocks listed in Dhaka Stock Exchange. The research first identified a pair of stocks whose prices have a long-run equilibrium using Johansen?s test for cointegration. The cointegrated stock pair is then modeled using a Vector Error Correction Model. The residual obtained from the estimated model serves as the guide to implementing Pairs Trading Strategy. The research finally identified three pairs of stocks which have general long-run equilibriums. Based on the residual series of these pairs, we implemented pairs trading strategy for a period of one to two months using real time data but doing hypothetical trading. It generated significant returns for all trades carried out using both in-sample and out-of-sample data. Given that Bangladesh stock market is frequently subjected to unprecedented volatility, a market-neutral investment strategy like Pairs Trading can be a valuable option to retail and institutional investors. We recommend undertaking policy initiatives required to allow investors to utilize this strategy in Bangladesh.

The objective of this work is to present an ‘arbitrage statistics’ strategy that trades Call options in Brazilian derivatives market. The developed algorithm performs an valuation of the nominal values of a random variable (Z), based on Radon-Nikodým derivative, together with a pre-selection of trades forming a subset of the database base selected from a parametric analysis over the model. To build the algorithm, a database of PETR4 Call options traded from January 2th, 2015 to December 11 th, 2019 was used, as well as all closing prices of the PETR4 share for the same period. From the data consolidated we realize a fitting process on the distribution of returns of PETR4 for a mixture of gaussian densities distribution (here called Mistura de Normais distribution), considering the Kolmogorov-Smirnov test, obtaining this way an empirical observed probability, in other words, the probability measure of the “real world” (P). In parallel, from the pricing formula of a Call option we develop algebraically a way to estimate the probability of occurrence that an option be superior to its strike, in other words, the probability measure in the risk-neutral world ( Q ). Based on these values, the aleatory variable Z (ratio between the probability measures Q  and P) is calculated and the strategy is applied by dividing in two parts: first, the parametric assessment of the each factor analysis and the execution of a sensitivity analysis over the results. Second, applying the “refined” strategy (adjusted based on the previous assessment) considering the combination between each different factor from the previous phase, obtaining the final results. The quality assessment of the strategy is based on the distribution of returns and the calculation of the median and average of the returns from the simulations. Another objective of this study is to suggest to financial market an arbitrage statistics strategy for derivatives market that is independent of the choice of the option pricing model (“model free”) and that is able to explore possible discrepancies and singularities of the Brazilian stock and options market.

Compared with previous research, the present work extends existing literature by considering long-run relations among major international stock market indices, under different market conditions, and the implications of these relations on the implementation of statistical arbitrage strategies. The examined data contain two bust phases interrupted by a mild bullish period. Employing cointegration analysis, reported results initially indicate that changes in market performance affect the stability of long-run relations, therefore suggesting that arbitrageurs should perform rebalancing among the examined indices when a change in a market trend is evident. Furthermore, extreme market performance harms the mean-reverting properties of a potential long-run relation while moderate market performance points to cointegration between a pair of indices. However, the absence of a stationary spread does not suggest the potential of abnormal returns realization, in the short-run, through exploitation of deviations from its mean value. The applicability of our results may be of importance to market participants since the cointegration approach has recently received considerable attention by hedge funds adopting statistical arbitrage strategies.