Advanced Statistics: Swing Trading
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.045 | ||||
| Sharpe ratio (Glass type estimate) | -0.673 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.667 | ||||
| df | 83.000 | ||||
| t | -1.782 | ||||
| p | 0.961 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.419 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.076 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.415 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.080 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.343 | ||||
| Upside Potential Ratio | 0.894 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.051 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.045 | ||||
| Covariance | -0.000 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.287 | ||||
| p(b) | 0.613 | ||||
| t(a) | -1.650 | ||||
| p(a) | 0.949 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | 5.726 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -0.716 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.709 | ||||
| df | 83.000 | ||||
| t | -1.893 | ||||
| p | 0.969 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.462 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.035 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.458 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.040 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.364 | ||||
| Upside Potential Ratio | 0.847 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.051 | ||||
| Upside SD | 0.038 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 82.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | -0.000 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.269 | ||||
| p(b) | 0.606 | ||||
| t(a) | -1.789 | ||||
| p(a) | 0.961 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | 6.519 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.097 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.155 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -16.911 | ||||
| VaR(95%) (moments method) | -0.037 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.026 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.045 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.045 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.281 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.281 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.445 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | -0.259 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.259 | ||||
| df | 1833.000 | ||||
| t | -0.686 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.000 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.482 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.482 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.367 | ||||
| Upside Potential Ratio | 1.748 | ||||
| Upside part of mean | 0.125 | ||||
| Downside part of mean | -0.152 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 57.000 | ||||
| N negative terms | 1777.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1834.000 | ||||
| Mean of predictor | 0.326 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.518 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | 0.003 | ||||
| r | 0.060 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 1832.000 | ||||
| t(b) | 2.571 | ||||
| p(b) | 0.470 | ||||
| t(a) | -0.786 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | -2.238 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.102 | ||||
| Sharpe ratio (Glass type estimate) | -0.309 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.309 | ||||
| df | 1833.000 | ||||
| t | -0.817 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.049 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.432 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.049 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.432 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.421 | ||||
| Upside Potential Ratio | 1.643 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.075 | ||||
| N nonnegative terms | 57.000 | ||||
| N negative terms | 1777.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1834.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.517 | ||||
| SD of criterion | 0.102 | ||||
| Covariance | 0.003 | ||||
| r | 0.061 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 1832.000 | ||||
| t(b) | 2.611 | ||||
| p(b) | 0.470 | ||||
| t(a) | -0.878 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.109 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | -2.621 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1834.000 | ||||
| Minimum | 0.885 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.120 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 82.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 96.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.121 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.307 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.088 | ||||
| Maximum | 0.176 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.135 | ||||
| Inter Quartile Range | 0.080 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.072 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.094 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.971 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.974 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.479 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.478 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8745566570839932.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 90705219290455139137892898570240.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||