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Table 7 Performance of the trading strategies on the test sample, based on model assembling

From: Forecasting and trading cryptocurrencies with machine learning under changing market conditions

  B&H Ensemble 4 Ensemble 5 Ensemble 6
Bitcoin
Nº of days in the market (relative frequency in %) 325 (100%) 142 (43.69) 73 (22.46) 17 (5.231)
Win rate (%) 51.69 52.82 54.79 52.94
Average profit per day in the market (%)  − 0.2210  − 0.1892 0.0705 0.5356
SD of profit per day in the market (%) 3.271 3.600 3.814 4.351
Annual return (%)  − 54.86  − 25.74 5.868 10.61
Annual return with trading costs of 0.5% (%)  − 52.791  − 23.66 1.247
Annualized sharpe ratio (%)  − 129,1  − 66.44 16.83 54.95
Bootstrap p-value against B&H 0.0551 0.0269 0.0426
Daily CVaR at 1% (%) 11.60 9.443 8.070 3.882
Maximum drawdown (%) 67.17 48.06 30.94 11.15
Ethereum
Nº of days in the market (relative frequency in %) 325 (100%) 113 (34.77) 56 (17.23) 30 (9.231)
Win rate (%) 46.15 53.98 60.71 63.33
Average profit per day in the market (%)  − 0.4048 0.0515 0.5951 0.8862
SD of profit per day in the market (%) 5.142 5.329 5.906 5.428
Annual return (%)  − 76.72 6.653 44.65 34.25
Annual return with trading costs of 0.5% (%)  − 28.35 9.622 14.35
Annualized sharpe ratio (%)  − 150.4 10.91 80.17 95.05
Bootstrap p-value against B&H 0.0140 0.0130 0.0278
CVaR at 1% (%) 17.81 13.40 12.63 7.661
Maximum drawdown (%) 89.67 45.86 28.92 14.40
Litecoin
Nº of days in the market (relative frequency in %) 325 (100%) 103 (31.69) 53 (16.31) 12 (3.692)
Win rate (%) 46.46 51.46 50.94 50.00
Average profit per day in the market (%)  − 0.3025 0.1673 0.5094 0.0729
SD of profit per day in the market (%) 4.872 4.688 4.311 4.636
Annual return (%)  − 66.35 21.03 34.86 0.9746
Annual return with trading costs of 0.5% (%)  − 17.66 5.730  − 4.984
Annualized sharpe ratio (%)  − 118,7 38.48 91.35 6.025
Bootstrap p-value against B&H 0.0442 0.0546 0.1157
CVaR at 1% (%) 14.45 10.70 6.921 4.699
Maximum drawdown (%) 86.80 43.07 23.46 13.75
  1. This table displays several statistics on the performance of the trading strategies in the test sample based on model assembling. The models considered are Linear, Random Forest (RF) and Support Vector Machine (SVM) and their binary versions, in a total of six models. Only long positions are considered, hence Ensemble 4, Ensemble 5 and Ensemble 6, refer to trading strategies designed upon the activation and maintenance of a long position when at least 4, 5 and 6 models agree on a positive trading sign for the next day, respectively. For clarity purposes, the table also presents, in the second column, the relevant statistics for the Buy-and-Hold (B&H) strategy. The trading signal for each model is obtained from the 1-step forecast using a rolling window with a constant length of 648 days. The win rate is equal to the ratio between the number of days when the ensemble model gives the right positive sign for the next day and the total of days in the market (previous line). The next two lines refer to the mean and standard deviation of the returns when the positions are active. The annual return is the compound return per year given by the accumulated discrete daily returns considering all days in the test sample, including zero-return days when the strategies prescribe not entering into the market. The next line refers to the compound return per year considering a proportional round-trip transaction cost of 0.5%. The Annualized Sharpe Ratio is the ratio between the daily mean return and the standard-deviation of daily returns considering all days in the test sample, multiplied by \(\sqrt {365}\). The bootstrap p-values are the probabilities of the daily mean return of the proposed model, considering all days in the sample, being higher than the daily mean return of the Buy-and-Hold strategy that consists of being long all the time given the null that these mean returns are equal. These p-values are obtained using 100,000 bootstrap samples created with the circular block procedure of Politis and Romano (1994), with an optimal block size chosen according to Politis and White (2004) and Politis and White (2009). The CVaR at 1% measures the average loss conditional upon the fact that the VaR at the 1% level has been exceeded. Finally, the Maximum Drawdown is computed as the maximum observed loss from a peak to a trough of the accumulated value of the trading strategy, before a new peak is attained, relative to the value of that peak. All values are in percentage, except the nº of days in the market and the p-values.