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The profitability of a trading system based on the momentum-like effects of price jumps was tested on the time series of 7 assets (EUR/USD, GBP/USD, USD/CHF and USD/JPY exchange rates and Light Crude Oil, E-Mini S&P 500 and VIX Futures), in each case for 7 different frequencies (ranging from 1-Minute to 1-Day), over a period of more than 20 years (for all assets except for the VIX) ending in the second half of 2015. The proposed trading system entered long and short trades in the direction of price jumps, for the closing price of the period in which the jump occurred. The position was held for a fixed number of periods that was optimized on the in-sample period. Jumps were identified with the non-parametric L-Estimator whose inputs (period used for local volatility calculation and confidence level used for jump detection) were also optimized on the in-sample period. The proposed system achieved promising results for the 4 currency markets, especially at the 15-minute and 30-minute frequencies at which 3 out of the 4 tested currencies turned profitable (with highest profits achieved by USD/CHF, followed by EUR/USD and GBP/USD), with the profits totaling up to 30-50% p.a. in the case of a high-leverage scenario, or 15-25% in the case of a low-leverage scenario. Additionally, the 5-minute frequency turned profitable for USD/CHF and the 4-hour frequency for GBP/USD, while the 1-minute frequency was unprofitable in all cases due to the commissions and the 1-day frequency contained too few jumps to make any conclusions. As for the futures markets, the system achieved profits only on the Light Crude Oil market, on the frequencies of 1-hour, 4-hour and 1-day, with the profits totaling up to 20% p.a. in the case of high leverage or 10% p.a. in the case of low leverage. For USD/JPY, E-Mini S&P 500 Futures and VIX Futures the system achieved mostly a loss. We attribute this (in the latter two cases) to the effect of a rising market risk premium in the case of negative jumps, going against the jump-momentum effect used by the system.
Three different classes of data mining methods (k-Nearest Neighbour, Ridge Regression and Multilayer Perceptron Feed-Forward Neural Networks) are applied for the purpose of quantitative trading on 10 simulated time series, as well as real world time series of 10 currency exchange rates ranging from 1.11.1999 to 12.6.2015. Each method is tested in multiple variants. The k-NN algorithm is applied alternatively with the Euclidian, Manhattan, Mahalanobis and Maximum distance function. The Ridge Regression is applied as Linear and Quadratic, and the Feed-Forward Neural Network is applied with either 1, 2 or 3 hidden layers. In addition to that Principal Component Analysis (PCA) is eventually applied for the dimensionality reduction of the predictor set and the meta-parameters of the methods are optimized on the validation sample. In the simulation study a Stochastic-Volatility Jump-Diffusion model, extended alternatively with 10 different non-linear conditional mean patterns, is used, to simulate the asset price behaviour to which the tested methods are applied. The results show that no single method was able to profit on all of the non-linear patterns in the simulated time series, but instead different methods worked well for different patterns. Alternatively, past price movements and past returns were used as predictors. In the case when the past price movements were used, quadratic ridge regression achieved the most robust results, followed by some of the k-NN methods. In the case when past returns were used, k-NN based methods were the most consistently profitable, followed by the linear ridge regression and quadratic ridge regression. Neural networks, while being able to profit on some of the time series, did not achieve profit on most of the others. No evidence was further found of the PCA method to improve the results of the tested methods in a systematic way. In the second part of the study, the models were applied to empirical foreign exchange rate time series. Overall the profitability of the methods was rather low, with most of them ending with a loss on most of the currencies. The most profitable currency was EURUSD, followed by EURJPY, GBPJPY and EURGBP. The most successful methods were the linear ridge regression and the Manhattan distance based k-NN method which both ended with profits for most of the time series (unlike the other methods). Finally, a forward selection procedure using the linear ridge regression was applied to extend the original predictor set with some technical indicators. The selection procedure achieved limited success in improving the out-sample results for the linear ridge regression model but not the other models.
Quantitative investment strategies are often selected from a broad class of candidate models estimated and tested on historical data. Standard statistical technique to prevent model overfitting such as out-sample back-testing turns out to be unreliable in the situation when selection is based on results of too many models tested on the holdout sample. There is an ongoing discussion how to estimate the probability of back-test overfitting and adjust the expected performance indicators like Sharpe ratio in order to reflect properly the effect of multiple testing. We propose a consistent Bayesian approach that consistently yields the desired robust estimates based on an MCMC simulation. The approach is tested on a class of technical trading strategies where a seemingly profitable strategy can be selected in the naïve approach.