The profitability of pairs trading strategies: distance,cointegration and copula methods

We perform an extensive and robust study of the performance of three different pairs trading strategies—the distance, cointegration and copula methods—on the entire US equity market from 1962 to 2014 with time-varying trading costs. For the cointegration and copula methods, we design a computationally efficient two-step pairs trading strategy. In terms of economic outcomes, the distance, cointegration and copula methods show a mean monthly excess return of 91, 85 and 43 bps (38, 33 and 5 bps) before transaction costs (after transaction costs), respectively. In terms of continued profitability, from 2009, the frequency of trading opportunities via the distance and cointegration methods is reduced considerably, whereas this frequency remains stable for the copula method. Further, the copula method shows better performance for its unconverged trades compared to those of the other methods. While the liquidity factor is negatively correlated to all strategies’ returns, we find no evidence of their correlation to market excess returns. All strategies show positive and significant alphas after accounting for various risk-factors. We also find that in addition to all strategies performing better during periods of significant volatility, the cointegration method is the superior strategy during turbulent market conditions.     

A semiparametric graphical modelling approach for large-scale equity selection

We propose a new stock selection strategy that exploits rebalancing returns and improves portfolio performance. To effectively harvest rebalancing gains, we apply ideas from elliptical-copula graphical modelling and stability inference to select stocks that are as independent as possible. The proposed elliptical-copula graphical model has a latent Gaussian representation; its structure can be effectively inferred using the regularized rank-based estimators. The resulting algorithm is computationally efficient and scales to large data-sets. To show the efficacy of the proposed method, we apply it to conduct equity selection based on a 16-year health care stock data-set and a large 34-year stock data-set. Empirical tests show that the proposed method is superior to alternative strategies including a principal component analysis-based approach and the classical Markowitz strategy based on the traditional buy-and-hold assumption.     

A good pair: alternative pairs-trading strategies

This paper studies alternative techniques for identifying stock pairs in a pairs-trading strategy over 1980–2014. We consider two main techniques: the distance approach and the cointegration approach. We also consider a range of parameterizations of the trading system design. Parameterization of the trading system matters for the profitability of pairs trading. We find that the cointegration approach, despite using an optimal in-sample parameterization, yields significant returns only in the 1980s. The distance approach performs better, producing significantly positive risk-adjusted returns in all sub-periods. However, when transaction costs are properly taken into account, the returns largely disappear in recent years.     

On the relationship between classical chain ladder and granular reserving

We connect classical chain ladder to granular reserving. This is done by defining explicitly how the classical run-off triangles are generated from individual iid observations in continuous time. One important result is that the development factors have a one to one correspondence to a histogram estimator of a hazard running in reversed development time. A second result is that chain ladder has a systematic bias if the row effect has not the same distribution when conditioned on any of the aggregated periods. This means that the chain ladder assumptions on one level of aggregation, say yearly, are different from the chain ladder assumptions when aggregated in quarters and the optimal level of aggregation is a classical bias variance trade-off depending on the data-set. We introduce smooth development factors arising from non-parametric hazard kernel smoother improving the estimation significantly.     

Do the stock and CDS markets price credit risk equally in the long-run?

In this paper, we examine the existence and stability of the long-run equilibrium relation between the price of credit risk in the stock and CDS markets for a sample of non-financial iTraxx Europe companies during the 2004–2017 period. We show that standard cointegration tests with no breaks frequently fail to detect cointegration. Once we formally account for the breaks in the cointegrating vector, we are able to detect cointegration over the entire sample period for the vast majority of the companies considered. An application of these results to CDS-equity trading shows that the profitability of traditional trading strategies crucially depends on the presence of cointegration and on the stability of the cointegrating vector. Finally, we find that CDS illiquidity factors decrease the likelihood of the stock and CDS market cointegration.     

Commodity Spread Option with Cointegration

We derive the valuation formula of a European call option on the spread of two cointegrated commodity futures prices, based on the Gibson–Schwartz with cointegration (GSC) model. We also analyze the American commodity spread option including the early exercise premium representation and an analytical approximation valuation formulae with cointegration. In the numerical analysis, we compare the spread option values calculated by the GSC model and the Gibson–Schwartz (GS) model that ignores cointegration. Consistent with the intuition that the cointegration prevents the prices from diverging, the GSC model prices the commodity spread option lower than the GS model which have longer maturity of more than 6 years. In other words, the GS model may overprice the commodity spread options for those with longer maturity without taking account of cointegration. Thus, incorporating cointegration is important for valuation and hedging of long-term commodity spread options such as large scale oil refining plant developments.     

Micro-level stochastic loss reserving for general insurance

The vast literature on stochastic loss reserving concentrates on data aggregated in run-off triangles. However, a triangle is a summary of an underlying data-set with the development of individual claims. We refer to this data-set as ‘micro-level’ data. Using the framework of Position Dependent Marked Poisson Processes) and statistical tools for recurrent events, a data-set is analyzed with liability claims from a European insurance company. We use detailed information of the time of occurrence of the claim, the delay between occurrence and reporting to the insurance company, the occurrences of payments and their sizes, and the final settlement. Our specifications are (semi)parametric and our approach is likelihood based. We calibrate our model to historical data and use it to project the future development of open claims. An out-of-sample prediction exercise shows that we obtain detailed and valuable reserve calculations. For the case study developed in this paper, the micro-level model outperforms the results obtained with traditional loss reserving methods for aggregate data.     

Intraday indirect arbitrage between European index ETFs

We investigate intraday arbitrage between close substitute Exchange-traded Funds (ETFs) on two major European indices: FTSE100 and DAX30. Using intraday data, we establish arbitrage links between our ETFs through cointegration and error correction models. We then apply an arbitrage identification procedure on approximately 18 million intraday matched quotes, resulting in 1.95% and 0.2% of observations on the ETF pairs for FTSE100 and DAX30 as arbitrage opportunities. They occur on specific days in our sample, disappear relatively quickly, and result in economically insignificant profits from arbitrage trades within the mispricing window, indicating overall price efficiency.     

The modified dividend–price ratio

We show that log-dividends (d) and log-prices (p) are cointegrated, but, instead of de facto assuming the stationarity of the classical log dividend–price ratio, we allow the data to reveal the cointegration vector between d and p. We define the modified dividend–price ratio (mdp), as the long run trend deviation between d and p. Using S&P 500 data for the period 1926 to 2012, we show that mdp provides substantially improved forecasting results over the classical dp ratio. Out of sample, while the dp ratio cannot outperform the “simplistic forecast” benchmark for any useful horizon, an investor who employs the mdp ratio will do significantly better in forecasting 3-, 5- and 7-year returns with an R_OS² of 7%, 26% and 31% respectively. In some sense mdp can be considered as a de-noising of the classical ratio as it addresses the major weakness in dp, its presumed inability in revealing business cycle variation in expected returns. Unlike dp, mdp exhibits positive correlation with the risk free return component, and can discern if a low dividend state coincides with a low yield state.     

Financial integration in the pacific basin region: RIP by PANIC attack?

We exploit advances in panel data econometrics to test whether real interest parity holds in the Pacific Basin region. We test for a unit root in the difference between either the US, Japanese or Euro area real interest rate and the real interest rates from a panel of eleven Pacific Basin economies. Unlike extant studies that test for RIP using panel data, we use Bai and Ng’s (2004) PANIC test which allows for a very general model of cross-section dependence, including the possibility of cross-unit cointegration. Ignoring the possibility of cross-unit cointegration can lead to severe size distortions and to an over-rejection of the null hypothesis of a unit root. We overturn earlier findings based on first-generation panel tests, and demonstrate that cross-unit cointegration leads to incorrect conclusions. We find that RIP holds in the Pacific region. Real interest rates converge to the US rate. We find no support for the hypothesis that Pacific Basin real interest rates converge to either the Japanese or Euro area rates.     

Pairs trading with a mean-reverting jump–diffusion model on high-frequency data

This paper develops a pairs trading framework based on a mean-reverting jump–diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a three-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads’ mean-reversion speed and jump behaviour. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61% p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk–return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.     

Cointegration analysis of the intensity of the ERM currencies under the European Monetary System

This paper examines the (long-run) intra-zonal elasticities between the spot exchange rates of the deutschemark and other major ERM currencies (French franc, Belgian franc, Dutch guilder, Danish krone, Italian lira and British pound) under the EMS. The findings show that under the fixed-but-adjustable rate system, the hypothesis of no cointegration can be rejected for all chosen ERM currency pairs and unit restriction on zonal elasticities can be accepted for almost all cointegrated currency pairs. On the other hand, under the fixed-rate system, Danish krone, Italian lira and British pound fail the cointegration test and the zonal elasticities for all cointegrated currency pairs are rejected to be unity. The study signifies less intense linkages of the ERM currencies without parity realignments. Finally, the deutschmark took the role of error-correcting process for one cointegrated currency pair under the fixed-but-adjustable-rate system, and it performed the same role for two pairs under the fixed-rate system. Hence, deutschmark should not be assumed a priori statistically exogenous under the EMS     

On the Long Run Effects of Public Capital and Disaggregated Public Capital on Aggregate Output

We study the cointegration properties of data on aggregate output, five proxies for labor, two proxies for private capital, public capital, and disaggregated public capital for the United States for 1948–1993. We find evidence of multiple cointegrating vectors; we typically find three or four cointegrating vectors depending on which combination of proxies is evaluated. When public capital is disaggregated by type there is less evidence for cointegration. Finally, innovations in public capital have long lasting effects on output, labor, and private capital, and innovations to output, labor, and private capital also have long lasting effects on public capital.     

A folding methodology for multivariate extremes: estimation of the spectral probability measure and actuarial applications

In this paper, the folding methodology developed in the context of univariate Extreme Value Theory (EVT) by You et al. is extended to a multivariate framework. Under the usual EVT assumption of regularly varying tails, our multivariate folding allows for the estimation of the spectral probability measure. A new weakly consistent estimator based on the classical empirical estimator is proposed. Its behaviour is illustrated through simulations and an actuarial application relative to reinsurance pricing in the case of an insurance data-set.     

Cointegration: how short is the long run?

When testing for cointegration and faced with short sample periods, it is common for researchers to turn to more frequently sampled observations, that is, to move from annual to quarterly or monthly data, in order to increase the number of observations. We argue that such a gain in the degrees of freedom is more apparent than real. Essentially, cointegration is a long-run concept and hence requires long spans of data to give tests for cointegration much power rather than merely large numbers of observations. Using Monte Carlo simulations, we demonstrate this for four popular tests for cointegration.     

Divisia Monetary Aggregates,the Great Ratios,and Classical Money Demand Functions

King et al. ( 1991 ) evaluate the empirical relevance of a class of real business cycle models with permanent productivity shocks by analyzing the stochastic trend properties of postwar U.S. macroeconomic data. They find a common stochastic trend in a three‐variable system that includes output, consumption, and investment, but the explanatory power of the common trend drops significantly when they add money balances and the nominal interest rate. In this paper, we revisit the cointegration tests in the spirit of King et al., using improved monetary aggregates whose construction has been stimulated by the Barnett critique. We show that previous rejections of the balanced growth hypothesis and classical money demand functions can be attributed to mismeasurement of the monetary aggregates.     

Resurrecting the size effect: Evidence from a panel nonlinear cointegration model for the G7 stock markets

Firm size is known to be an important factor affecting stock returns. This study proposes a panel threshold cointegration model to investigate the impact of the size effect on stock returns for the panel of G7 countries: Canada, France, Germany, Italy, Japan, the U.K., and the U.S. over the period 1991:1–2012:12. The empirical analysis is based upon the nonlinear cointegration framework using the asymmetric ARDL cointegration methodology (Shin et al., 2011). This methodological approach permits a much richer degree of flexibility in the dynamic adjustment process toward equilibrium, than in the classical linear model. Our findings indicate the presence of asymmetric adjustment around a unique long-run equilibrium. In particular, the empirical analysis provides evidence of asymmetric effects between stock returns and the size effect, while controlling for the book-to-market ratio and the price-to-earnings ratio.     

On Cointegration and Exchange Rate Dynamics

Baillie and Bollerslev (1989) have recently argued that nominal dollar spot exchange rates are cointegrated. Here we examine an immediate implication of their finding, namely, that cointegration implies an error-correction representation yielding forecasts superior to those from a martingale benchmark, in light of a large earlier literature highlighting the predictive superiority of the martingale. In an out-of-sample forecasting exercise, we find the martingale model to be superior. We then perform a battery of improved cointegration tests and find that the evidence for cointegration is much less strong than previously thought, a result consistent with the outcome of the forecasting exercise.     

Interest parity,cointegration, and the term structure: Testing in an integrated framework

In this paper, we develop a methodology for testing jointly the validity of the expectations hypothesis of the term structure (EHTS) and the uncovered interest rate parity (UIRP) within the framework provided by cointegration theory. For this purpose, we use data on interest rates from the U.S. dollar-Libor, GBP-Libor, and Euro-Libor markets with maturities ranging from 7 days to 12 months. The main findings of our analysis are as follows: (i) we fail to find the correct rank of the cointegration space suggested by our methodology; (ii) with the application of tests for parameter stability in cointegrated models, we show that our cointegration results are sample independent and that the estimated coefficients do not suffer from instabilities in recursive estimations; (iii) from the moving average representation of the model, we estimate the common stochastic trends whose components establish, in the USD/Euro case, the interdependence of interest rates in the formation of the driving forces of the system; (iv) we manage to identify with the two theories a sub-space of the estimated cointegration space.     

Did Gladstone make a difference? Rhetoric and reality in mid-Victorian finance

'Gladstonian finance' is generally taken to mean balancing the budget, limiting the level of public expenditure, and making progress in paying off the national debt. Gladstone also distinguished himself from contemporary Conservatives (and most classical economists) by having no especial dislike for direct taxes. After putting Gladstone's public utterances in the context of his rivals, classical political economy, and contemporary views of the role of the state, we use cointegration analysis to see if Gladstone, as Chancellor or Prime Minister, made a statistically detectable difference to trends in public spending, taxation, the balance of the budget or the size of the national debt. He did not.