Erik Hjalmarsson

Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market

We study the impact of algorithmic trading in the foreign exchange market using a long time series of high-frequency data that specifically identifies computer-generated trading activity. Using both a reduced-form and a structural estimation, we find clear evidence that algorithmic trading causes an improvement in two measures of price efficiency in this market: the frequency of triangular arbitrage opportunities and the autocorrelation of high-frequency returns. Relating our results to the recent theoretical literature on the subject, we show that the reduction in arbitrage opportunities is associated primarily with computers taking liquidity, while the reduction in the autocorrelation of returns owes more to the algorithmic provision of liquidity. We also find evidence that algorithmic traders do not trade with each other as much as a random matching model would predict, which we view as consistent with their trading strategies being highly correlated. However, the analysis shows that this high degree of correlation does not appear to cause a degradation in market quality.

Rise of the Machines: Algorithmic Trading in the Foreign Exchange Market: Rise of the Machines

We study the impact of algorithmic trading (AT) in the foreign exchange market using a long time series of high-frequency data that identify computer-generated trading activity. We find that AT causes an improvement in two measures of price efficiency: the frequency of triangular arbitrage opportunities and the autocorrelation of high-frequency returns. We show that the reduction in arbitrage opportunities is associated primarily with computers taking liquidity. This result is consistent with the view that AT improves informational efficiency by speeding up price discovery, but that it may also impose higher adverse selection costs on slower traders. In contrast, the reduction in the autocorrelation of returns owes more to the algorithmic provision of liquidity. We also find evidence consistent with the strategies of algorithmic traders being highly correlated. This correlation, however, does not appear to cause a degradation in market quality, at least not on average.

Testing for Cointegration Using the Johansen Methodology When Variables are Near-Integrated

We investigate the properties of Johansens (1988, 1991) maximum eigenvalue and trace tests for cointegration under the empirically relevant situation of near-integrated variables. Using Monte Carlo techniques, we show that in a system with near-integrated variables, the probability of reaching an erroneous conclusion regarding the cointegrating rank of the system is generally substantially higher than the nominal size. The risk of concluding that completely unrelated series are cointegrated is therefore non-negligible. The spurious rejection rate can be reduced by performing additional tests of restrictions on the cointegrating vector(s), although it is still substantially larger than the nominal size.

Jackknifing stock return predictions

We show that the general bias reducing technique of jackknifing can be successfully applied to stock return predictability regressions. Compared to standard OLS estimation, the jackknifing procedure delivers virtually unbiased estimates with mean squared errors that generally dominate those of the OLS estimates. The jackknifing method is very general, as well as simple to implement, and can be applied to models with multiple predictors and overlapping observations. Unlike most previous work on inference in predictive regressions, no specific assumptions regarding the data generating process for the predictors are required. A set of Monte Carlo experiments show that the method works well in finite samples and the empirical section finds that out-of-sample forecasts based on the jackknifed estimates tend to outperform those based on the plain OLS estimates. The improved forecast ability also translates into economically relevant welfare gains for an investor who uses the predictive regression, with jackknifed estimates, to time the market.

New Methods for Inference in Long-Horizon Regressions

I develop new results for long-horizon predictive regressions with overlapping observations. I show that rather than using autocorrelation robust standard errors, the standard t -statistic can simply be divided by the square root of the forecasting horizon to correct for the effects of the overlap in the data. Further, when the regressors are persistent and endogenous, the long-run ordinary least squares (OLS) estimator suffers from the same problems as the short-run OLS estimator, and it is shown how similar corrections and test procedures as those proposed for the short-run case can also be implemented in the long run. An empirical application to stock return predictability shows that, contrary to many popular beliefs, evidence of predictability does not typically become stronger at longer forecasting horizons.

Frequency of Observation and the Estimation of Integrated Volatility in Deep and Liquid Financial Markets

Using two newly available ultrahigh-frequency datasets, we investigate empirically how frequently one can sample certain foreign exchange and U.S. Treasury security returns without contaminating estimates of their integrated volatility with market microstructure noise. Using volatility signature plots and a recently-proposed formal decision rule to select the sampling frequency, we find that one can sample FX returns as frequently as once every 15 to 20 seconds without contaminating volatility estimates; bond returns may be sampled as frequently as once every 2 to 3 minutes on days without U.S. macroeconomic announcements, and as frequently as once every 40 seconds on announcement days. With a simple realized kernel estimator, the sampling frequencies can be increased to once every 2 to 5 seconds for FX returns and to about once every 30 to 40 seconds for bond returns. These sampling frequencies, especially in the case of FX returns, are much higher than those often recommended in the empirical literature on realized volatility in equity markets. We suggest that the generally superior depth and liquidity of trading in FX and government bond markets contributes importantly to this difference.

The Stambaugh Bias in Panel Predictive Regressions

This paper analyzes predictive regressions in a panel data setting. The standard fixed effects estimator suffers from a small sample bias, which is the analogue of the Stambaugh bias in time-series predictive regressions. Monte Carlo evidence shows that the bias and resulting size distortions can be severe. A new bias-corrected estimator is proposed, which is shown to work well in finite samples and to lead to approximately normally distributed t-statistics. Overall, the results show that the econometric issues associated with predictive regressions when using time-series data to a large extent also carry over to the panel case. The results are illustrated with an application to predictability in international stock indices.

Efficiency in housing markets: Which home buyers know how to discount?

We test for efficiency in the market for Swedish co-ops by examining the negative relationship between the sales price and the present value of future rents. If the co-op housing market is efficient, the present value of co-op rental payments due to underlying debt obligations of the cooperative should be fully reflected in the sales price. However, we find that, on average, a one hundred kronor increase in the present value of future rents only leads to a 45 to 65 kronor reduction in the sales price; co-ops with higher rents are thus relatively overpriced compared to those with lower rents. Our analysis indicates that pricing tends to be more efficient in areas with higher educated and wealthier buyers. By relying on cross-sectional relationships in the data, our results are less sensitive to transaction costs and other frictions than time-series tests of housing market efficiency.

Should We Expect Significant Out-of-Sample Results when Predicting Stock Returns?

Using Monte Carlo simulations, I show that typical out-of-sample forecast exercises for stock returns are unlikely to produce any evidence of predictability, even when there is in fact predictability and the correct model is estimated.

Characteristic-Based Mean-Variance Portfolio Choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.