Heterogeneous real-time trading strategies in the foreign exchange market

The foreign exchange (FX) market is worldwide, but the dealers differ in their geographical locations (time zones), working hours, time horizons, home currencies, access to information,transaction costs, and other institutional constraints. The variety of time horizones is large: from intra-day dealers, who close their positions every evening, to long-term investors and central banks. Depending on the constraints, the different market participats need different strategies to reach their goal, which is usually maximizing the profit, or rather a utility function including risk. Different intra-day trading strategies can be studied only if high-density data are available. Oslen & Associates (O & A) has collected and analysed large amounts of FX quotes by market makers around the clock (up to 5000 non-equally spaced prices per day for the German mark against US$). Based on these data, a set of real-time intra-day trading models has been developed. These models give explicit trading recommendations under realistic constraints. They are allowed to trade only during the opening hours of a market, depending on the time zone and local holidays. The models have been running real-time for more than three years, thus leading to an ex ante test. The test results, obtained with a risk-sensitive performance measure, are presented. All these trading models are profitable, but they differ in their risk behaviour and dealing frequency. If a certain profitable intra-day algorithm is tested with different working hours, its success can considerably change. A systematic study shows that the best choice of working hours is usually when the most important markets for the particular FX rate are active. All the results demonstrate that the assumption of a homogeneous 24-hour FX market with identical dealers, following an identical ‘rational expectation’, is far from reality. To explain the market dynamics, a heterogeneous model of the market with different types of dealers is more appropriate.     

Moments of multivariate regime switching with application to risk-return trade-off

We use a Fourier transform to derive multivariate conditional and unconditional moments of multi-horizon returns under a regime-switching model. These moments are applied to examine the relevance of risk horizon and regimes for buy-and-hold investors. We analyze the impact of time-varying expected returns and risk (variance and covariance) on portfolio allocations' “term structure”—portfolio allocations as a function of the investment horizon. Using monthly observations on S&P composite index and 10-year Government Bond, we find that the term structure of the optimal allocations depends on market conditions measured by the probability of being in bull state. At short horizons and when this probability is low, buy-and-hold investors decrease their holdings of risky assets. We also find that the conditional optimal portfolio performs quite well at short and intermediate horizons and less at long horizons.     

Market heterogeneities and the causal structure of volatility

Abstract

The correlation between historical and realized volatilities is studied empirically for a large range of time intervals. Similarly, the correlation between the volatility changes and the realized volatilities is studied. Both quantities measure the response functions of the market participants. These correlations show explicitly the heterogeneous structure of the market according to the characteristic time horizons of the different agents. It reveals a volatility cascade from long to short time horizons, with a structure different from the one observed in turbulence. A comparison is made with several theoretical processes used in finance, allowing a better understanding of the role and interactions of the market participants (intra-day trader, portfolio manager, central banks, pension funds, …). Moreover, we have developed a new ARCH-type process that incorporates the different groups of agents, with their characteristic memories. This process reproduces well the empirical response function, and allows us to quantify the importance of each group.     

SYMMETRIC VERSUS ASYMMETRIC CONDITIONAL COVARIANCE FORECASTS: DOES IT PAY TO SWITCH?

Volatilities and correlations for equity markets rise more after negative returns shocks than after positive shocks. Allowing for these asymmetries in covariance forecasts decreases mean‐variance portfolio risk and improves investor welfare. We compute optimal weights for international equity portfolios using predictions from asymmetric covariance forecasting models and a spectrum of expected returns. Investors who are moderately risk averse, have longer rebalancing horizons, and hold U.S. equities benefit most and may be willing to pay around 100 basis points annually to switch from symmetric to asymmetric forecasts. Accounting for asymmetry in both variances and correlations significantly lowers realized portfolio risk.     

Stochastic regularization for the mean-variance allocation scheme

Despite being based on sound principles, the original Markovitz portfolio allocation theory cannot produce sound allocations, and restrictions or modifications need to be imposed from outside the theory in order to obtain meaningful portfolios. This is unsatisfactory, and the reasons for this failure are discussed, in particular, the unavoidable small eigenvalues of the covariance. Within the original principles of risk minimization and return maximization, several modifications of the original theory are introduced. First, the strategic and tactical time horizons are separated. A base long-term allocation is chosen at the strategic time horizon, while the portfolio is optimized at the tactical time horizon using information from the price histories. Second, the tactical portfolio is financed by the strategic one, and a funding operator is introduced. The corresponding optimal allocation (without constraints) has one free parameter fixing the leverage. Third, the transaction costs are taken into account. This includes the current re-allocation cost, but crucially the expected costs of the next reallocation. This last term depends on the sensitivity of the allocation with respect to the covariance, and the expectation introduces another dependency on the (inverse) covariance. The new term regularizes the original minimization problem by modifying the lower part of the spectrum of the covariance, leading to meaningful portfolios. Without constraints, the final Lagrangian can be minimized analytically, with a solution that has a structure similar to the original Markovitz solution, but with the inverse covariance regularized by the expected transaction costs.     

Momentum and Autocorrelation in Stock Returns

This article studies momentum in stock returns, focusing onthe role of industry, size, and book-to-market (B/M) factors.Size and B/M portfolios exhibit momentum as strong as that inindividual stocks and industries. The size and B/M portfoliosare well diversified, so momentum cannot be attributed to firm-or industry-specific returns. Further, industry, size, and B/Mportfolios are negatively autocorrelated and cross-seriallycorrelated over intermediate horizons. The evidence suggeststhat stocks covary "too strongly" with each other. I argue thatexcess covariance, not underreaction, explains momentum in theportfolios.     

Forecasting oil price realized volatility using information channels from other asset classes

Motivated from Ross (1989) who maintains that asset volatilities are synonymous to the information flow, we claim that cross-market volatility transmission effects are synonymous to cross-market information flows or “information channels” from one market to another. Based on this assertion we assess whether cross-market volatility flows contain important information that can improve the accuracy of oil price realized volatility forecasting. We concentrate on realized volatilities derived from the intra-day prices of the Brent crude oil and four different asset classes (Stocks, Forex, Commodities and Macro), which represent the different “information channels” by which oil price volatility is impacted from. We employ a HAR framework and estimate forecasts for 1-day to 66-days ahead. Our findings provide strong evidence that the use of the different “information channels” enhances the predictive accuracy of oil price realized volatility at all forecasting horizons. Numerous forecasting evaluation tests and alternative model specifications confirm the robustness of our results.     

Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis

In this paper we present a statistical analysis of four foreign exchange spot rates against the U.S. Dollar with several million intra-day prices over 3 years. The analysis also includes gold prices and samples of daily foreign exchange prices over 15 years. The mean absolute changes of logarithmic prices are found to follow a scaling law against the time interval on which they are measured. This empirical law holds although the distributions of the price changes strongly differ for different interval sizes.Systematic variations of the volatility are found even during business hours by an intra-day analysis of price changes. Seasonal heteroskedasticity is observed with a period of one day as well as one week as the result of an analogous intra-week analysis; taking this into account is necessary for any future study of intra-day price change distributions and their generating process. The same type of analysis is also made for the bid-ask spreads.     

Time zone normalization of FX seasonality

Abstract

This paper provides empirical evidence that the particular intra-day seasonality observed in the Foreign Exchange market is indeed due to the different geographical locations of its traders. Analysing more than 2 years of real transactions from a microscopic perspective, we design a procedure that accounts for the time zones from which traders operate. The resulting normalized intra-day seasonality shows a pattern akin to those observed in regulated exchanges where traders are more active at the beginning and at the end of their session.     

Systematic risk and timescales

Abstract

In this paper we propose a new approach to estimating the systematic risk (the beta of an asset) in a capital asset pricing model (CAPM). The proposed method is based on a wavelet multiscaling approach that decomposes a given time series on a scale-by-scale basis. At each scale, the wavelet variance of the market return and the wavelet covariance between the market return and a portfolio are calculated to obtain an estimate of the portfolio's beta. The empirical results show that the relationship between the return of a portfolio and its beta becomes stronger as the wavelet scale increases. Therefore, the predictions of the CAPM model are more relevant in the medium long run as compared to short time horizons.     

Marking the future: a review of time horizons

This paper examines the variety of time horizons used by futures researchers. It summarizes responses from a survey that asked future researches (1) how far ahead they think about the future, (2) why they choose their time intervals, and (3) the importance of being clear about time intervals for the future. Findings reveal that time horizons differ and are generally shaped by the nature of each futures researcher's work. The paper concludes with a brief discussion on the use of time horizons and importance of futures research.     

A portfolio view of consumer credit

To compute risk-adjusted returns and gauge the volatility of their portfolios, lenders need to know the covariances of their loans’ returns with aggregate returns. We use unique credit bureau data to measure individuals’ ‘covariance risk’, i.e., the covariance of their default risk with aggregate consumer default rates, and more generally to analyze the distribution of credit, including the effects of credit scores. We find significant heterogeneity in covariance risk across consumers. Also, the amount of credit they obtain significantly increases with their credit scores, and decreases with their covariance risk (especially revolving credit), though the effect of covariance risk is smaller.     

Insider trading and shareholder investment horizons

This paper examines the effects of shareholder investment horizons on insider trading. We find that insiders are less likely to trade on private information and the profitability of insider trades is lower when shareholder investment horizons are longer. We further examine two channels through which shareholders with longer investment horizons can impede insider trading: direct monitoring and better information environment. Consistent with the direct monitoring channel, we show that insiders in firms with longer shareholder investment horizons are more likely to shift trades from the month right before earnings announcements to the month right after earnings announcements. Moreover, the impact of investment horizons are stronger in firms with higher ex ante litigation risk, with lower corporate governance quality, and that are not targets of hedge fund activists. Consistent with the information environment channel, we show that longer shareholder investment horizons increase the frequencies of information disclosure and insiders in firms with longer shareholder investment horizons are more likely to trade in an isolated manner rather than in sequences.     

Volatility cascades in cryptocurrency trading

This paper studies volatility cascades across multiple trading horizons in cryptocurrency markets. Using one-minute data on Bitcoin, Ethereum and Ripple against the US dollar, we implement the wavelet Hidden Markov Tree model. This model allows us to estimate the transition probability of high or low volatility at one time scale (horizon) propagating to high or low volatility at the next time scale. We find that when moving from long to short horizons, volatility cascades tend to be symmetric: low volatility at long horizons is likely to be followed by low volatility at short horizons, and high volatility is likely to be followed by high volatility. In contrast, when moving from short to long horizons, volatility cascades are strongly asymmetric: high volatility at short horizons is now likely to be followed by low volatility at long horizons. These results are robust across time periods and cryptocurrencies.     

Bid-ask Spreads, Trading Volume and Volatility: Intra-day Evidence from the London Stock Exchange

This paper examines intra-day variations in the bid-ask spread, volatility and volume for stocks traded on the London Stock Exchange. The data set used consists of quote and transactions data for a large sample of 835 stocks traded during the first quarter of 1991. The focus of the study is twofold; first, is to document a number of stylized facts regarding the intra-day behaviour of spread, trading volume, volatility etc. Second, the paper tests some predictions of two theoretical models of intra-day behaviour: the Admati and Pfleiderer and the Brock and Kleidon models. In addition, the paper also studies qualitatively the intra-day behaviour of several variables of interest including volume per transaction, transactions per fifteen-minute interval and spreads/trading volume for stocks of differing liquidity. The results suggest that the bid-ask spread is wide at the open, constant through the day and rises slightly at the close. Trading volume, in contrast is not highest at the open and the close. Volatility, based on the mid-point of the inside spread, shows a U-shaped pattern. Volume per transaction, in contrast, is fairly constant throughout the day. Further, the intra-day trading volume pattern differs for liquid and illiquid stocks. The results provide mixed support for current theoretical models of intra-day behaviour of spread, volume and volatility on the London Stock Exchange     

Opening prices on the New York Stock Exchange

The prices of opening transactions on the New York Stock Exchange are determined quite differently from prices of subsequent transactions. This paper tests the null hypothesis that opening prices are as representative of contemporaneous equilibrium stock values as subsequent intra-day transactions prices. With one possible exception, there is no basis for rejecting this hypothesis, despite the very different trading mechanisms used in opening trades and intra-day trades.     

The statistical properties of the innovations in multivariate ARCH processes in high dimensions

The long memory linear ARCH process is extended to a multivariate universe, where the natural cross-product structure of the covariance is generalized by adding two bi-linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data and the (inverse square root of the) covariance matrix. Simple measures of quality assessing the independence and unit magnitude of the residual distributions are proposed. The salient statistical properties of the computed residuals are studied for three data sets of size 54, 55 and 330. Both new terms introduced in the covariance help to produce uncorrelated residuals, but the mean residual magnitudes are much larger than one. The large magnitudes of the residuals are due to the exponential decay of the covariance eigenvalues, corresponding to directions with very small fluctuations in the historical sample. Because the postulated properties of the innovations cannot be obtained regardless of the parameter values, subsequent inferences reach a fundamental limitation in a large multivariate universe.     

Why do forecasters disagree? Lessons from the term structure of cross-sectional dispersion

Key sources of disagreement among economic forecasters are identified by using data on cross-sectional dispersion in forecasters’ long- and short-run predictions of macroeconomic variables. Dispersion among forecasters is highest at long horizons where private information is of limited value and lower at short forecast horizons. Moreover, differences in views persist through time. Such differences in opinion cannot be explained by differences in information sets; our results indicate they stem from heterogeneity in priors or models. Differences in opinion move countercyclically, with heterogeneity being strongest during recessions where forecasters appear to place greater weight on their prior beliefs.     

深市买卖价差逆向选择成分的估算与分析

本文以深市150家上市公司为样本，估算买卖价差逆向选择成分，研究逆向选择成分与公司特征之间的关系，并探讨其日内变化模式。研究发现信息不对称对深市买卖价差的贡献度为39％。公司规模越大，其股票的逆向选择成分越小；逆向选择成分随着交易量水平的上升而降低；高价股的逆向选择成分比低价股低。总体而言，逆向选择成分在早市呈现“倒U”型，在午市呈现“L”型。逆向选择成分与公司特征之问的关系及逆向选择成分的日内变动模式的实证分析结果，符合信息不对称与公司特征之问的逻辑关系及信息不对称的日内变动模式。     

The impact of portfolio diversification on mean reverting components of stock indices

Positive autocorrelations are introduced into stock index portfolios when they are formed from individual stock indices while negative autocorrelations are induced in returns by increasing the investment horizon. Using monthly data of six international stock indices, this paper examines the diversification effect with different investment horizons on autocorrelations of stock index portfolios. The results show that portfolio diversification does not alter the impact of the investment horizon on autocorrelations. Different investment horizons, however, have great impact on the diversification effect on autocorrelations. With short (long) horizons, the average autocorrelation coefficient increases (decreases) with an increase in the portfolio size, suggesting that mean-reverting component dominates the delayed adjustment effect in long horizons and vice versa in short horizons. Our results are robust across two 10-year sub-periods.The author would like to thank an anonymous referee of this Journal for the comments on an earlier version of this paper and the Research Committee of Hong Kong Baptist University for the financial support in this research.